CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Hermann Minkowski - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"938596b1-7595-4af6-87af-9d3e573eedba","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Hermann_Minkowski","wgTitle":"Hermann Minkowski","wgCurRevisionId":1266256879,"wgRevisionId":1266256879,"wgArticleId":193537,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 Russian-language sources (ru)","Webarchive template wayback links","Articles with short description","Short description matches Wikidata","Use dmy dates from April 2017","Biography with signature","Articles with hCards","Pages with German IPA","Commons category link from Wikidata","Hermann Minkowski","1864 births","1909 deaths","Scientists from Kaunas","People from Suwałki Governorate","Lithuanian Jews","Emigrants from the Russian Empire to the German Empire", "German people of Lithuanian-Jewish descent","German people of Polish-Jewish descent","19th-century German mathematicians","20th-century German mathematicians","German geometers","German number theorists","German relativity theorists","University of Königsberg alumni","Academic staff of the University of Königsberg","Academic staff of ETH Zurich","Academic staff of the University of Bonn","Academic staff of the University of Göttingen","Deaths from appendicitis"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Hermann_Minkowski","wgRelevantArticleId":193537,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en", "pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q57246","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready", "skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints", "ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.15"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/1200px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1206"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/800px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="804"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/640px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="643"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Hermann Minkowski - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Hermann_Minkowski"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Hermann_Minkowski&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Hermann_Minkowski"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Hermann_Minkowski rootpage-Hermann_Minkowski skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Hermann+Minkowski" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Hermann+Minkowski" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Hermann+Minkowski" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Hermann+Minkowski" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Personal_life_and_family" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_life_and_family"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Personal life and family</span> </div> </a> <ul id="toc-Personal_life_and_family-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Education_and_career" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Education_and_career"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Education and career</span> </div> </a> <ul id="toc-Education_and_career-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Work_on_relativity" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Work_on_relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Work on relativity</span> </div> </a> <ul id="toc-Work_on_relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Publications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Publications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Publications</span> </div> </a> <button aria-controls="toc-Publications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Publications subsection</span> </button> <ul id="toc-Publications-sublist" class="vector-toc-list"> <li id="toc-Relativity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relativity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Relativity</span> </div> </a> <ul id="toc-Relativity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Diophantine_approximations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Diophantine_approximations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Diophantine approximations</span> </div> </a> <ul id="toc-Diophantine_approximations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematical_(posthumous)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mathematical_(posthumous)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Mathematical (posthumous)</span> </div> </a> <ul id="toc-Mathematical_(posthumous)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_and_references" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_and_references"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes and references</span> </div> </a> <ul id="toc-Notes_and_references-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <button aria-controls="toc-External_links-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle External links subsection</span> </button> <ul id="toc-External_links-sublist" class="vector-toc-list"> <li id="toc-Archival_collections" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Archival_collections"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Archival collections</span> </div> </a> <ul id="toc-Archival_collections-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hermann Minkowski</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 62 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-62" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">62 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Afrikaans" lang="af" hreflang="af" data-title="Hermann Minkowski" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%85%D9%8A%D9%86%D9%83%D9%88%D9%81%D8%B3%D9%83%D9%8A" title="هيرمان مينكوفسكي – Arabic" lang="ar" hreflang="ar" data-title="هيرمان مينكوفسكي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Herman_Minkovski" title="Herman Minkovski – Azerbaijani" lang="az" hreflang="az" data-title="Herman Minkovski" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%85%DB%8C%D9%86%DA%A9%D9%88%D9%81%D8%B3%DA%A9%DB%8C" title="هرمان مینکوفسکی – South Azerbaijani" lang="azb" hreflang="azb" data-title="هرمان مینکوفسکی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A7%87%E0%A6%B0%E0%A6%AE%E0%A6%BE%E0%A6%A8_%E0%A6%AE%E0%A6%BF%E0%A6%82%E0%A6%95%E0%A6%AB%E0%A7%8D%E2%80%8C%E0%A6%B8%E0%A7%8D%E0%A6%95%E0%A6%BF" title="হেরমান মিংকফ্‌স্কি – Bangla" lang="bn" hreflang="bn" data-title="হেরমান মিংকফ্‌স্কি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D1%96%D0%BD%D0%BA%D0%BE%D1%9E%D1%81%D0%BA%D1%96" title="Герман Мінкоўскі – Belarusian" lang="be" hreflang="be" data-title="Герман Мінкоўскі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D0%B8%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8" title="Херман Минковски – Bulgarian" lang="bg" hreflang="bg" data-title="Херман Минковски" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Catalan" lang="ca" hreflang="ca" data-title="Hermann Minkowski" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Czech" lang="cs" hreflang="cs" data-title="Hermann Minkowski" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Danish" lang="da" hreflang="da" data-title="Hermann Minkowski" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – German" lang="de" hreflang="de" data-title="Hermann Minkowski" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Estonian" lang="et" hreflang="et" data-title="Hermann Minkowski" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CE%AD%CF%81%CE%BC%CE%B1%CE%BD_%CE%9C%CE%B9%CE%BD%CE%BA%CF%8C%CE%B2%CF%83%CE%BA%CE%B9" title="Χέρμαν Μινκόβσκι – Greek" lang="el" hreflang="el" data-title="Χέρμαν Μινκόβσκι" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Spanish" lang="es" hreflang="es" data-title="Hermann Minkowski" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Esperanto" lang="eo" hreflang="eo" data-title="Hermann Minkowski" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Basque" lang="eu" hreflang="eu" data-title="Hermann Minkowski" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%B1%D9%85%D8%A7%D9%86_%D9%85%DB%8C%D9%86%DA%A9%D9%88%D9%81%D8%B3%DA%A9%DB%8C" title="هرمان مینکوفسکی – Persian" lang="fa" hreflang="fa" data-title="هرمان مینکوفسکی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – French" lang="fr" hreflang="fr" data-title="Hermann Minkowski" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%97%A4%EB%A5%B4%EB%A7%8C_%EB%AF%BC%EC%BD%94%ED%94%84%EC%8A%A4%ED%82%A4" title="헤르만 민코프스키 – Korean" lang="ko" hreflang="ko" data-title="헤르만 민코프스키" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D6%80%D5%B4%D5%A1%D5%B6_%D5%84%D5%AB%D5%B6%D5%AF%D5%B8%D5%BE%D5%BD%D5%AF%D5%AB" title="Հերման Մինկովսկի – Armenian" lang="hy" hreflang="hy" data-title="Հերման Մինկովսկի" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B9%E0%A4%B0%E0%A4%AE%E0%A4%A8_%E0%A4%AE%E0%A4%BF%E0%A4%A8%E0%A5%8D%E0%A4%95%E0%A5%8B%E0%A4%B5%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A5%80" title="हरमन मिन्कोवस्की – Hindi" lang="hi" hreflang="hi" data-title="हरमन मिन्कोवस्की" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Croatian" lang="hr" hreflang="hr" data-title="Hermann Minkowski" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Indonesian" lang="id" hreflang="id" data-title="Hermann Minkowski" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Italian" lang="it" hreflang="it" data-title="Hermann Minkowski" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A8%D7%9E%D7%9F_%D7%9E%D7%99%D7%A0%D7%A7%D7%95%D7%91%D7%A1%D7%A7%D7%99" title="הרמן מינקובסקי – Hebrew" lang="he" hreflang="he" data-title="הרמן מינקובסקי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B9%E0%B2%B0%E0%B3%8D%E0%B2%AE%E0%B2%BE%E0%B2%A8%E0%B3%8D_%E0%B2%AE%E0%B2%BF%E0%B2%82%E0%B2%95%E0%B3%8B%E0%B2%B5%E0%B3%8D%E2%80%8D%E0%B2%B8%E0%B3%8D%E0%B2%95%E0%B2%BF" title="ಹರ್ಮಾನ್ ಮಿಂಕೋವ್‍ಸ್ಕಿ – Kannada" lang="kn" hreflang="kn" data-title="ಹರ್ಮಾನ್ ಮಿಂಕೋವ್‍ಸ್ಕಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Haitian Creole" lang="ht" hreflang="ht" data-title="Hermann Minkowski" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D0%B8%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9" title="Герман Минковский – Kyrgyz" lang="ky" hreflang="ky" data-title="Герман Минковский" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Arminius_Minkowski" title="Arminius Minkowski – Latin" lang="la" hreflang="la" data-title="Arminius Minkowski" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Hermanis_Minkovskis" title="Hermanis Minkovskis – Latvian" lang="lv" hreflang="lv" data-title="Hermanis Minkovskis" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Lithuanian" lang="lt" hreflang="lt" data-title="Hermann Minkowski" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Hungarian" lang="hu" hreflang="hu" data-title="Hermann Minkowski" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D0%B8%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8" title="Херман Минковски – Macedonian" lang="mk" hreflang="mk" data-title="Херман Минковски" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Malagasy" lang="mg" hreflang="mg" data-title="Hermann Minkowski" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B9%E0%B5%86%E0%B5%BC%E0%B4%AE%E0%B5%BB_%E0%B4%AE%E0%B4%BF%E0%B5%BB%E0%B4%95%E0%B5%97%E0%B4%B8%E0%B5%8D%E0%B4%95%E0%B5%8D%E0%B4%95%E0%B4%BF" title="ഹെർമൻ മിൻകൗസ്ക്കി – Malayalam" lang="ml" hreflang="ml" data-title="ഹെർമൻ മിൻകൗസ്ക്കി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%B0%E1%83%94%E1%83%A0%E1%83%9B%E1%83%90%E1%83%9C_%E1%83%9B%E1%83%98%E1%83%9C%E1%83%99%E1%83%9D%E1%83%95%E1%83%A1%E1%83%99%E1%83%98" title="ჰერმან მინკოვსკი – Mingrelian" lang="xmf" hreflang="xmf" data-title="ჰერმან მინკოვსკი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%87%D9%8A%D8%B1%D9%85%D8%A7%D9%86_%D9%85%D9%8A%D9%86%D9%83%D9%88%D9%81%D8%B3%D9%83%D9%89" title="هيرمان مينكوفسكى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="هيرمان مينكوفسكى" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Dutch" lang="nl" hreflang="nl" data-title="Hermann Minkowski" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%98%E3%83%AB%E3%83%9E%E3%83%B3%E3%83%BB%E3%83%9F%E3%83%B3%E3%82%B3%E3%83%95%E3%82%B9%E3%82%AD%E3%83%BC" title="ヘルマン・ミンコフスキー – Japanese" lang="ja" hreflang="ja" data-title="ヘルマン・ミンコフスキー" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Hermann Minkowski" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Hermann Minkowski" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B9%E0%A8%B0%E0%A8%AE%E0%A8%A8_%E0%A8%AE%E0%A8%BF%E0%A8%A8%E0%A8%95%E0%A9%8B%E0%A8%B5%E0%A8%B8%E0%A8%95%E0%A9%80" title="ਹਰਮਨ ਮਿਨਕੋਵਸਕੀ – Punjabi" lang="pa" hreflang="pa" data-title="ਹਰਮਨ ਮਿਨਕੋਵਸਕੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Piedmontese" lang="pms" hreflang="pms" data-title="Hermann Minkowski" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Polish" lang="pl" hreflang="pl" data-title="Hermann Minkowski" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Portuguese" lang="pt" hreflang="pt" data-title="Hermann Minkowski" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Romanian" lang="ro" hreflang="ro" data-title="Hermann Minkowski" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B8%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8%D0%B9,_%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD" title="Минковский, Герман – Russian" lang="ru" hreflang="ru" data-title="Минковский, Герман" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Scots" lang="sco" hreflang="sco" data-title="Hermann Minkowski" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hermann Minkowski" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Slovak" lang="sk" hreflang="sk" data-title="Hermann Minkowski" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Slovenian" lang="sl" hreflang="sl" data-title="Hermann Minkowski" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D0%B8%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%B8" title="Херман Минковски – Serbian" lang="sr" hreflang="sr" data-title="Херман Минковски" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Hermann Minkowski" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Finnish" lang="fi" hreflang="fi" data-title="Hermann Minkowski" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Swedish" lang="sv" hreflang="sv" data-title="Hermann Minkowski" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B9%E0%AF%86%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%BE%E0%AE%A9%E0%AF%8D_%E0%AE%AE%E0%AE%BF%E0%AE%A9%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%B5%E0%AF%8D%E0%AE%B8%E0%AF%8D%E0%AE%95%E0%AE%BF" title="ஹெர்மான் மின்கோவ்ஸ்கி – Tamil" lang="ta" hreflang="ta" data-title="ஹெர்மான் மின்கோவ்ஸ்கி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%AE%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%B1%E0%B8%99_%E0%B8%A1%E0%B8%B4%E0%B8%87%E0%B8%84%E0%B9%87%E0%B8%AD%E0%B8%9F%E0%B8%AA%E0%B8%81%E0%B8%B5" title="แฮร์มัน มิงค็อฟสกี – Thai" lang="th" hreflang="th" data-title="แฮร์มัน มิงค็อฟสกี" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Turkish" lang="tr" hreflang="tr" data-title="Hermann Minkowski" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D1%80%D0%BC%D0%B0%D0%BD_%D0%9C%D1%96%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D1%8C%D0%BA%D0%B8%D0%B9" title="Герман Мінковський – Ukrainian" lang="uk" hreflang="uk" data-title="Герман Мінковський" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Hermann_Minkowski" title="Hermann Minkowski – Vietnamese" lang="vi" hreflang="vi" data-title="Hermann Minkowski" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E9%97%B5%E5%8F%AF%E5%A4%AB%E6%96%AF%E5%9F%BA" title="赫尔曼·闵可夫斯基 – Wu" lang="wuu" hreflang="wuu" data-title="赫尔曼·闵可夫斯基" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E9%97%B5%E5%8F%AF%E5%A4%AB%E6%96%AF%E5%9F%BA" title="赫尔曼·闵可夫斯基 – Chinese" lang="zh" hreflang="zh" data-title="赫尔曼·闵可夫斯基" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q57246#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Hermann_Minkowski" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Hermann_Minkowski" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Hermann_Minkowski"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Hermann_Minkowski"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Hermann_Minkowski" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Hermann_Minkowski" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&oldid=1266256879" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Hermann_Minkowski&id=1266256879&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHermann_Minkowski"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHermann_Minkowski"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Hermann_Minkowski&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Hermann_Minkowski&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Hermann_Minkowski" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://en.wikiquote.org/wiki/Hermann_Minkowski" hreflang="en"><span>Wikiquote</span></a></li><li class="wb-otherproject-link wb-otherproject-wikisource mw-list-item"><a href="https://en.wikisource.org/wiki/Author:Hermann_Minkowski" hreflang="en"><span>Wikisource</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q57246" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">German mathematician and physicist (1864–1909)</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Hermann Minkowski</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:De_Raum_zeit_Minkowski_Bild_(cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/220px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg" decoding="async" width="220" height="221" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/330px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg/440px-De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg 2x" data-file-width="1578" data-file-height="1586" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1864-06-22</span>)</span>22 June 1864<br /><div style="display:inline" class="birthplace"><a href="/wiki/Aleksotas" class="mw-redirect" title="Aleksotas">Aleksotas</a>, <a href="/wiki/Suwa%C5%82ki_Governorate" title="Suwałki Governorate">Suwałki Governorate</a>, <a href="/wiki/Congress_Poland" title="Congress Poland">Kingdom of Poland</a> (now in <a href="/wiki/Kaunas" title="Kaunas">Kaunas</a>, <a href="/wiki/Lithuania" title="Lithuania">Lithuania</a>)</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">12 January 1909<span style="display:none">(1909-01-12)</span> (aged 44)<br /><div style="display:inline" class="deathplace"><a href="/wiki/G%C3%B6ttingen" title="Göttingen">Göttingen</a>, <a href="/wiki/German_Empire" title="German Empire">German Empire</a></div></td></tr><tr><th scope="row" class="infobox-label">Citizenship</th><td class="infobox-data category">Russian Empire<sup id="cite_ref-Marshall_Cavendish_1-0" class="reference"><a href="#cite_note-Marshall_Cavendish-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or Germany</td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Albertina_University_of_K%C3%B6nigsberg" class="mw-redirect" title="Albertina University of Königsberg">Albertina University of Königsberg</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist" style="margin-left:1em;text-indent:-1em;"> <ul><li><a href="/wiki/Geometry_of_numbers" title="Geometry of numbers">Geometry of numbers</a></li> <li><a href="/wiki/Minkowski_content" title="Minkowski content">Minkowski content</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></li> <li><a href="/wiki/Minkowski%27s_question-mark_function" title="Minkowski's question-mark function">Minkowski's question-mark function</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li> <li>Work on the <a href="/wiki/Diophantine_approximation" title="Diophantine approximation">Diophantine approximations</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Spouse</th><td class="infobox-data">Auguste Adler</td></tr><tr><th scope="row" class="infobox-label">Children</th><td class="infobox-data">2</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>, <a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Philosophy" title="Philosophy">philosophy</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a> and <a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Ferdinand_von_Lindemann" title="Ferdinand von Lindemann">Ferdinand von Lindemann</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a><br /><a href="/wiki/Louis_Kollros" title="Louis Kollros">Louis Kollros</a><br /><a href="/wiki/D%C3%A9nes_K%C5%91nig" title="Dénes Kőnig">Dénes Kőnig</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header">Signature</th></tr><tr><td colspan="2" class="infobox-full-data"><span class="infobox-signature skin-invert" typeof="mw:File"><a href="/wiki/File:Hermann_Minkowski_signature.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Hermann_Minkowski_signature.svg/150px-Hermann_Minkowski_signature.svg.png" decoding="async" width="150" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Hermann_Minkowski_signature.svg/225px-Hermann_Minkowski_signature.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Hermann_Minkowski_signature.svg/300px-Hermann_Minkowski_signature.svg.png 2x" data-file-width="185" data-file-height="47" /></a></span></td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><th class="sidebar-title"><a href="/wiki/Special_relativity" title="Special relativity">Special relativity</a></th></tr><tr><td class="sidebar-image"><span class="notpageimage" typeof="mw:File"><a href="/wiki/File:World_line.svg" class="mw-file-description" title="The world line: a diagrammatic representation of spacetime"><img alt="The world line: a diagrammatic representation of spacetime" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/200px-World_line.svg.png" decoding="async" width="200" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/300px-World_line.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/World_line.svg/400px-World_line.svg.png 2x" data-file-width="481" data-file-height="491" /></a></span></td></tr><tr><td class="sidebar-content" style="padding-bottom:0.6em;"> <ul><li><a href="/wiki/Principle_of_relativity" title="Principle of relativity">Principle of relativity</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Formulations_of_special_relativity" title="Formulations of special relativity">Formulations</a></li></ul></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Foundations</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Postulates_of_special_relativity" title="Postulates of special relativity">Einstein's postulates</a></li> <li><a href="/wiki/Inertial_frame_of_reference" title="Inertial frame of reference">Inertial frame of reference</a></li> <li><a href="/wiki/Speed_of_light" title="Speed of light">Speed of light</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell's equations</a></li> <li><a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz transformation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">Consequences</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Length_contraction" title="Length contraction">Length contraction</a></li> <li><a href="/wiki/Mass_in_special_relativity" title="Mass in special relativity">Relativistic mass</a></li> <li><a href="/wiki/Mass%E2%80%93energy_equivalence" title="Mass–energy equivalence">Mass–energy equivalence</a></li> <li><a href="/wiki/Relativity_of_simultaneity" title="Relativity of simultaneity">Relativity of simultaneity</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li> <li><a href="/wiki/Thomas_precession" title="Thomas precession">Thomas precession</a></li> <li><a href="/wiki/Relativistic_disk" title="Relativistic disk">Relativistic disk</a></li> <li><a href="/wiki/Bell%27s_spaceship_paradox" title="Bell's spaceship paradox">Bell's spaceship paradox</a></li> <li><a href="/wiki/Ehrenfest_paradox" title="Ehrenfest paradox">Ehrenfest paradox</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski spacetime</a></li> <li><a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Spacetime diagram</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li> <li><a href="/wiki/Light_cone" title="Light cone">Light cone</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%"><a href="/wiki/Dynamics_(mechanics)" class="mw-redirect" title="Dynamics (mechanics)">Dynamics</a></span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Invariant_mass" title="Invariant mass">Proper mass</a></li> <li><a href="/wiki/Four-momentum" title="Four-momentum">Four-momentum</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><div class="hlist" style="font-size:110%;"><ul><li><a href="/wiki/History_of_special_relativity" title="History of special relativity">History</a></li><li>Precursors</li></ul></div></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"> <ul><li><a href="/wiki/Galilean_invariance" title="Galilean invariance">Galilean relativity</a></li> <li><a href="/wiki/Galilean_transformation" title="Galilean transformation">Galilean transformation</a></li> <li><a href="/wiki/Aether_theories" title="Aether theories">Aether theories</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;padding-bottom:0;;color: var(--color-base)"><div class="sidebar-list-title-c"><span style="font-size:120%">People</span></div></div><div class="sidebar-list-content mw-collapsible-content" style="padding-top:0;"><div class="hlist"> <ul><li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/Albert_A._Michelson" title="Albert A. Michelson">Michelson</a></li> <li><a href="/wiki/Edward_W._Morley" title="Edward W. Morley">Morley</a></li> <li><a href="/wiki/George_Francis_FitzGerald" title="George Francis FitzGerald">FitzGerald</a></li> <li><a href="/wiki/Gustav_Herglotz" title="Gustav Herglotz">Herglotz</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a class="mw-selflink selflink">Minkowski</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Max_Abraham" title="Max Abraham">Abraham</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">von Laue</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Richard_C._Tolman" title="Richard C. Tolman">Tolman</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-below hlist" style="background-color: transparent; border-color: #A2B8BF"> <ul><li><span class="nowrap"><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/14px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="14" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/21px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/28px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics portal</a></span></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Special_relativity" title="Category:Special relativity">Category</a></span></li></ul></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Special_relativity_sidebar" title="Template:Special relativity sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Special_relativity_sidebar" title="Template talk:Special relativity sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Special_relativity_sidebar" title="Special:EditPage/Template:Special relativity sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Hermann Minkowski</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="'m' in 'my'">m</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span><span title="/ŋ/: 'ng' in 'sing'">ŋ</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="'k' in 'kind'">k</span><span title="/ɔː/: 'au' in 'fraud'">ɔː</span><span title="'f' in 'find'">f</span><span title="'s' in 'sigh'">s</span><span title="'k' in 'kind'">k</span><span title="/i/: 'y' in 'happy'">i</span></span>,<span class="wrap"> </span>-<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'k' in 'kind'">k</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'f' in 'find'">f</span></span>-/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling">ming-<span style="font-size:90%">KAWF</span>-skee, -⁠<span style="font-size:90%">KOF</span>-</i></a>;<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">German:</span> <span class="IPA nowrap" lang="de-Latn-fonipa"><a href="/wiki/Help:IPA/Standard_German" title="Help:IPA/Standard German">[mɪŋˈkɔfski]</a></span>; 22 June 1864 – 12 January 1909) was a <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and professor at the <a href="/wiki/University_of_K%C3%B6nigsberg" title="University of Königsberg">University of Königsberg</a>, the <a href="/wiki/University_of_Z%C3%BCrich" class="mw-redirect" title="University of Zürich">University of Zürich</a>, and the <a href="/wiki/University_of_G%C3%B6ttingen" title="University of Göttingen">University of Göttingen</a>, described variously as <a href="/wiki/Germany" title="Germany">German</a>,<sup id="cite_ref-Encyclopædia_Britannica_3-0" class="reference"><a href="#cite_note-Encyclopædia_Britannica-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_4-0" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_5-0" class="reference"><a href="#cite_note-:2-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Poland" title="Poland">Polish</a>,<sup id="cite_ref-:3_6-0" class="reference"><a href="#cite_note-:3-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_7-0" class="reference"><a href="#cite_note-:4-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_8-0" class="reference"><a href="#cite_note-:5-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Lithuania" title="Lithuania">Lithuanian</a>-German,<sup id="cite_ref-:6_9-0" class="reference"><a href="#cite_note-:6-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> or <a href="/wiki/Russia" title="Russia">Russian</a>.<sup id="cite_ref-Marshall_Cavendish_1-1" class="reference"><a href="#cite_note-Marshall_Cavendish-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> He created and developed the <a href="/wiki/Geometry_of_numbers" title="Geometry of numbers">geometry of numbers</a> and elements of <a href="/wiki/Convex_geometry" title="Convex geometry">convex geometry</a>, and used <a href="/wiki/Geometry" title="Geometry">geometrical</a> methods to solve problems in <a href="/wiki/Number_theory" title="Number theory">number theory</a>, <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>, and the <a href="/wiki/Theory_of_relativity" title="Theory of relativity">theory of relativity</a>. </p><p>Minkowski is perhaps best known for his foundational work describing space and time as a <a href="/wiki/Four-dimensional_space" title="Four-dimensional space">four-dimensional space</a>, now known as "<a href="/wiki/Minkowski_spacetime" class="mw-redirect" title="Minkowski spacetime">Minkowski spacetime</a>", which facilitated geometric interpretations of <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s <a href="/wiki/Special_theory_of_relativity" class="mw-redirect" title="Special theory of relativity">special theory of relativity</a> (1905). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Personal_life_and_family">Personal life and family</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=1" title="Edit section: Personal life and family"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hermann Minkowski was born in the town of <a href="/wiki/Aleksota" class="mw-redirect" title="Aleksota">Aleksota</a>, the <a href="/wiki/Suwa%C5%82ki_Governorate" title="Suwałki Governorate">Suwałki Governorate</a>, the <a href="/wiki/Congress_Poland" title="Congress Poland">Kingdom of Poland</a>, since 1864 part of the <a href="/wiki/Russian_Empire" title="Russian Empire">Russian Empire</a>, to Lewin Boruch Minkowski, a merchant who subsidized the building of the <a href="/wiki/Kaunas_Synagogue" title="Kaunas Synagogue">choral synagogue in Kovno</a>,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and Rachel Taubmann, both of <a href="/wiki/History_of_Jews_in_Poland" class="mw-redirect" title="History of Jews in Poland">Jewish descent</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Hermann was a younger brother of the <a href="/wiki/Medical_research" title="Medical research">medical researcher</a> <a href="/wiki/Oskar_Minkowski" title="Oskar Minkowski">Oskar</a> (born 1858).<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> In different sources Minkowski's nationality is variously given as German,<sup id="cite_ref-Encyclopædia_Britannica_3-1" class="reference"><a href="#cite_note-Encyclopædia_Britannica-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_4-1" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_5-1" class="reference"><a href="#cite_note-:2-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Poland" title="Poland">Polish</a>,<sup id="cite_ref-:3_6-1" class="reference"><a href="#cite_note-:3-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:4_7-1" class="reference"><a href="#cite_note-:4-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:5_8-1" class="reference"><a href="#cite_note-:5-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> or Lithuanian-German,<sup id="cite_ref-:6_9-1" class="reference"><a href="#cite_note-:6-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> or Russian.<sup id="cite_ref-Marshall_Cavendish_1-2" class="reference"><a href="#cite_note-Marshall_Cavendish-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>To escape Jewish <a href="/wiki/Anti-Jewish_pogroms_in_the_Russian_Empire" class="mw-redirect" title="Anti-Jewish pogroms in the Russian Empire">persecution in the Russian Empire</a>, the family moved to Königsberg in 1872,<sup id="cite_ref-:0_15-0" class="reference"><a href="#cite_note-:0-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> where the father became involved in rag export and later in manufacture of mechanical clockwork tin toys (he operated his firm Lewin Minkowski & Son with his eldest son Max).<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Minkowski studied in <a href="/wiki/K%C3%B6nigsberg" title="Königsberg">Königsberg</a> and taught in <a href="/wiki/Bonn" title="Bonn">Bonn</a> (1887–1894), Königsberg (1894–1896) and <a href="/wiki/Z%C3%BCrich" class="mw-redirect" title="Zürich">Zürich</a> (1896–1902), and finally in <a href="/wiki/G%C3%B6ttingen" title="Göttingen">Göttingen</a> from 1902 until his death in 1909. He married Auguste Adler in 1897 with whom he had two daughters; the <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineer</a> and inventor <a href="/wiki/Reinhold_Rudenberg" title="Reinhold Rudenberg">Reinhold Rudenberg</a> was his son-in-law. </p><p>Minkowski died of <a href="/wiki/Appendicitis" title="Appendicitis">appendicitis</a> in Göttingen on 12 January 1909. <a href="/wiki/Max_Born" title="Max Born">Max Born</a> delivered the obituary on behalf of the mathematics students at Göttingen.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>'s obituary of Minkowski illustrates the deep friendship between the two mathematicians: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Since my student years, Minkowski was my best, most dependable friend who supported me with all the depth and loyalty that was so characteristic of him. Science, which we loved above all else, brought us together; it seemed to us a garden full of flowers. In it, we enjoyed looking for hidden pathways and discovered many a new perspective that appealed to our sense of beauty, and when one of us showed it to the other and we marveled over it together, our joy was complete. He was for me a rare gift from heaven and I must be grateful to have possessed that gift for so long. Now death has suddenly torn him from our midst. However, what death cannot take away is his noble image in our hearts and the knowledge that his spirit continues to be active in us.</p><div class="templatequotecite">— <cite>Hilbert, 1909</cite></div></blockquote> <p>The main-belt <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> <a href="/wiki/12493_Minkowski" class="mw-redirect" title="12493 Minkowski">12493 Minkowski</a> and <a href="/wiki/M-matrix" title="M-matrix">M-matrices</a> are named in Minkowski's honor.<sup id="cite_ref-springer_18-0" class="reference"><a href="#cite_note-springer-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Education_and_career">Education and career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=2" title="Edit section: Education and career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hermann_Minkowski.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Hermann_Minkowski.png/170px-Hermann_Minkowski.png" decoding="async" width="170" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/16/Hermann_Minkowski.png/255px-Hermann_Minkowski.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/16/Hermann_Minkowski.png/340px-Hermann_Minkowski.png 2x" data-file-width="580" data-file-height="854" /></a><figcaption>Minkowski in 1883, at the time of being awarded the Mathematics Prize of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a></figcaption></figure> <p>Minkowski was educated in <a href="/wiki/East_Prussia" title="East Prussia">East Prussia</a> at the <i>Albertina</i> University of Königsberg, where he earned his doctorate in 1885 under the direction of <a href="/wiki/Ferdinand_von_Lindemann" title="Ferdinand von Lindemann">Ferdinand von Lindemann</a>. In 1883, while still a student at Königsberg, he was awarded the Mathematics Prize of the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> for his manuscript on the theory of <a href="/wiki/Quadratic_form" title="Quadratic form">quadratic forms</a>. Due to the very young age of 18, which was unheard of in the mathematics community, and his obscurity as a mathematician at the time, his sharing the award with eminent English mathematician <a href="/wiki/Henry_John_Stephen_Smith" title="Henry John Stephen Smith">Henry Smith</a> (who was certainly a great deal more famous than Hermann and to whom the prize was awarded posthumously) caused severe unrest among English mathematicians. The prize committee, despite the numerous complaints, never changed their decision. He also became a friend of another renowned mathematician, David Hilbert. His brother, <a href="/wiki/Oskar_Minkowski" title="Oskar Minkowski">Oskar Minkowski</a> (1858–1931), was a well-known physician and researcher.<sup id="cite_ref-:0_15-1" class="reference"><a href="#cite_note-:0-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Minkowski taught at the universities of Bonn, Königsberg, Zürich, and Göttingen. At the <a href="/wiki/Federal_Polytechnic_Institute" class="mw-redirect" title="Federal Polytechnic Institute"><i>Eidgenössische Polytechnikum</i></a>, today the <a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a>, he was one of Einstein's teachers. </p><p>Minkowski explored the arithmetic of <a href="/wiki/Quadratic_form" title="Quadratic form">quadratic forms</a>, especially concerning <i>n</i> variables, and his research into that topic led him to consider certain geometric properties in a space of <i>n</i> <a href="/wiki/Dimension" title="Dimension">dimensions</a>. In 1896, he presented his <i><a href="/wiki/Geometry_of_numbers" title="Geometry of numbers">geometry of numbers</a></i>, a geometrical method that solved problems in <a href="/wiki/Number_theory" title="Number theory">number theory</a>. He is also the creator of the <a href="/wiki/Minkowski_Sausage" class="mw-redirect" title="Minkowski Sausage">Minkowski Sausage</a><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Minkowski_cover" class="mw-redirect" title="Minkowski cover">Minkowski cover</a><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> of a curve. </p><p>In 1902, he joined the Mathematics Department of Göttingen and became a close colleague of David Hilbert, whom he first met at university in Königsberg. <a href="/wiki/Constantin_Carath%C3%A9odory" title="Constantin Carathéodory">Constantin Carathéodory</a> was one of his students there. </p> <div class="mw-heading mw-heading2"><h2 id="Work_on_relativity">Work on relativity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=3" title="Edit section: Work on relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a> and <a href="/wiki/Minkowski_diagram" class="mw-redirect" title="Minkowski diagram">Minkowski diagram</a></div> <p>By 1908 Minkowski realized that the special theory of relativity, introduced by his former student <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> in 1905 and based on the previous work of <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a> and <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a>, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which <a href="/wiki/Time" title="Time">time</a> and <a href="/wiki/Space" title="Space">space</a> are not separated entities but intermingled in a four-dimensional <a href="/wiki/Space%E2%80%93time" class="mw-redirect" title="Space–time">space–time</a>, and in which the <a href="/wiki/Lorentz_transformation" title="Lorentz transformation">Lorentz geometry</a> of special relativity can be effectively represented using the invariant interval <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101d249c29d5d550f759172c0b4dd9dbc1279af1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.219ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}-c^{2}t^{2}}"></span> (see <a href="/wiki/History_of_special_relativity" title="History of special relativity">History of special relativity</a>). </p><p>The mathematical basis of Minkowski space can also be found in the <a href="/wiki/Hyperboloid_model" title="Hyperboloid model">hyperboloid model</a> of <a href="/wiki/Hyperbolic_space" title="Hyperbolic space">hyperbolic space</a> already known in the 19th century, because isometries (or motions) in hyperbolic space can be related to <a href="/wiki/Lorentz_transformations" class="mw-redirect" title="Lorentz transformations">Lorentz transformations</a>, which included contributions of <a href="/wiki/Wilhelm_Killing" title="Wilhelm Killing">Wilhelm Killing</a> (1880, 1885), <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a> (1881), <a href="/wiki/Homersham_Cox_(mathematician)" title="Homersham Cox (mathematician)">Homersham Cox</a> (1881), <a href="/wiki/Alexander_Macfarlane" title="Alexander Macfarlane">Alexander Macfarlane</a> (1894) and others (see <a href="/wiki/History_of_Lorentz_transformations" title="History of Lorentz transformations">History of Lorentz transformations</a>). </p><p> The beginning part of his address called "Space and Time" delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908) is now famous:<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=4" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Relativity">Relativity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=5" title="Edit section: Relativity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMinkowski,_Hermann1915" class="citation journal cs1">Minkowski, Hermann (1915) [1907]. <a rel="nofollow" class="external text" href="https://zenodo.org/record/1447307">"Das Relativitätsprinzip"</a>. <i>Annalen der Physik</i>. <b>352</b> (15): <span class="nowrap">927–</span>938. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1915AnP...352..927M">1915AnP...352..927M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.19153521505">10.1002/andp.19153521505</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik&rft.atitle=Das+Relativit%C3%A4tsprinzip&rft.volume=352&rft.issue=15&rft.pages=%3Cspan+class%3D%22nowrap%22%3E927-%3C%2Fspan%3E938&rft.date=1915&rft_id=info%3Adoi%2F10.1002%2Fandp.19153521505&rft_id=info%3Abibcode%2F1915AnP...352..927M&rft.au=Minkowski%2C+Hermann&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1447307&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski,_Hermann1908" class="citation journal cs1">Minkowski, Hermann (1908). <span class="cs1-ws-icon" title="s:de:Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern"><a class="external text" href="https://en.wikisource.org/wiki/de:Die_Grundgleichungen_f%C3%BCr_die_elektromagnetischen_Vorg%C3%A4nge_in_bewegten_K%C3%B6rpern">"Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern" </a></span>. <i>Nachrichten der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse</i>: <span class="nowrap">53–</span>111.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nachrichten+der+Gesellschaft+der+Wissenschaften+zu+G%C3%B6ttingen%2C+Mathematisch-Physikalische+Klasse&rft.atitle=Die+Grundgleichungen+f%C3%BCr+die+elektromagnetischen+Vorg%C3%A4nge+in+bewegten+K%C3%B6rpern&rft.pages=%3Cspan+class%3D%22nowrap%22%3E53-%3C%2Fspan%3E111&rft.date=1908&rft.au=Minkowski%2C+Hermann&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span> <ul><li>English translation: "<a href="https://en.wikisource.org/wiki/Translation:The_Fundamental_Equations_for_Electromagnetic_Processes_in_Moving_Bodies" class="extiw" title="s:Translation:The Fundamental Equations for Electromagnetic Processes in Moving Bodies">The Fundamental Equations for Electromagnetic Processes in Moving Bodies</a>". In: The Principle of Relativity (1920), Calcutta: University Press, 1–69.</li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski,_Hermann1909" class="citation journal cs1">Minkowski, Hermann (1909). <span class="cs1-ws-icon" title="s:de:Raum und Zeit (Minkowski)"><a class="external text" href="https://en.wikisource.org/wiki/de:Raum_und_Zeit_(Minkowski)">"Raum und Zeit" </a></span>. <i>Jahresbericht der Deutschen Mathematiker-Vereinigung</i>. <b>18</b>: <span class="nowrap">75–</span>88. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1909JDMaV..18...75M">1909JDMaV..18...75M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Jahresbericht+der+Deutschen+Mathematiker-Vereinigung&rft.atitle=Raum+und+Zeit&rft.volume=18&rft.pages=%3Cspan+class%3D%22nowrap%22%3E75-%3C%2Fspan%3E88&rft.date=1909&rft_id=info%3Abibcode%2F1909JDMaV..18...75M&rft.au=Minkowski%2C+Hermann&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span> <ul><li>Various English translations on Wikisource: "<a href="https://en.wikisource.org/wiki/Space_and_Time" class="extiw" title="s:Space and Time">Space and Time</a>".</li></ul></li> <li>Blumenthal O. (ed): <i>Das Relativitätsprinzip</i>, Leipzig 1913, 1923 (Teubner), Engl tr (W. Perrett & G. B. Jeffrey) <i>The Principle of Relativity</i> London 1923 (Methuen); reprinted New York 1952 (Dover) entitled <a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">H. A. Lorentz</a>, Albert Einstein, Hermann Minkowski, and <a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Hermann Weyl</a>, <i>The Principle of Relativity: A Collection of Original Memoirs</i>.</li> <li>Space and Time – Minkowski's Papers on Relativity, Minkowski Institute Press, 2012 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9879871-3-6" title="Special:BookSources/978-0-9879871-3-6">978-0-9879871-3-6</a> (free ebook).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Diophantine_approximations">Diophantine approximations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=6" title="Edit section: Diophantine approximations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski,_Hermann1907" class="citation book cs1"><a class="mw-selflink selflink">Minkowski, Hermann</a> (1907). <a rel="nofollow" class="external text" href="http://catalog.hathitrust.org/Record/000424095"><i>Diophantische Approximationen: Eine Einführung in die Zahlentheorie</i></a>. Leipzig-Berlin: R. G. Teubner<span class="reference-accessdate">. Retrieved <span class="nowrap">28 February</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Diophantische+Approximationen%3A+Eine+Einf%C3%BChrung+in+die+Zahlentheorie&rft.place=Leipzig-Berlin&rft.pub=R.+G.+Teubner&rft.date=1907&rft.au=Minkowski%2C+Hermann&rft_id=http%3A%2F%2Fcatalog.hathitrust.org%2FRecord%2F000424095&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Mathematical_(posthumous)"><span id="Mathematical_.28posthumous.29"></span>Mathematical (posthumous)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=7" title="Edit section: Mathematical (posthumous)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski1910" class="citation book cs1"><a class="mw-selflink selflink">Minkowski, Hermann</a> (1910). <a rel="nofollow" class="external text" href="https://archive.org/details/geometriederzahl00minkrich"><i>Geometrie der Zahlen</i></a>. Leipzig-Berlin: B. G. Teubner Verlag. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0249269">0249269</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 February</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometrie+der+Zahlen&rft.place=Leipzig-Berlin&rft.pub=B.+G.+Teubner+Verlag&rft.date=1910&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0249269%23id-name%3DMR&rft.aulast=Minkowski&rft.aufirst=Hermann&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeometriederzahl00minkrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMinkowski,_Hermann1911" class="citation book cs1"><a class="mw-selflink selflink">Minkowski, Hermann</a> (1911). <a rel="nofollow" class="external text" href="http://catalog.hathitrust.org/Record/000169187"><i>Gesammelte Abhandlungen 2 vols</i></a>. Leipzig-Berlin: R. G. Teubner<span class="reference-accessdate">. Retrieved <span class="nowrap">28 February</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gesammelte+Abhandlungen+2+vols&rft.place=Leipzig-Berlin&rft.pub=R.+G.+Teubner&rft.date=1911&rft.au=Minkowski%2C+Hermann&rft_id=http%3A%2F%2Fcatalog.hathitrust.org%2FRecord%2F000169187&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Reprinted in one volume New York, Chelsea 1967.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 16em;"> <ul><li><a href="/wiki/List_of_things_named_after_Hermann_Minkowski" title="List of things named after Hermann Minkowski">List of things named after Hermann Minkowski</a></li> <li><a href="/wiki/Abraham%E2%80%93Minkowski_controversy" title="Abraham–Minkowski controversy">Abraham–Minkowski controversy</a></li> <li><a href="/wiki/Brunn%E2%80%93Minkowski_theorem" title="Brunn–Minkowski theorem">Brunn–Minkowski theorem</a></li> <li><a href="/wiki/Hasse%E2%80%93Minkowski_theorem" title="Hasse–Minkowski theorem">Hasse–Minkowski theorem</a></li> <li><a href="/wiki/Hermite%E2%80%93Minkowski_theorem" title="Hermite–Minkowski theorem">Hermite–Minkowski theorem</a></li> <li><a href="/wiki/Minkowski_addition" title="Minkowski addition">Minkowski addition</a></li> <li><a href="/wiki/Minkowski_(crater)" title="Minkowski (crater)">Minkowski (crater)</a></li> <li><a href="/wiki/Minkowski_distance" title="Minkowski distance">Minkowski distance</a></li> <li><a href="/wiki/Minkowski_functional" title="Minkowski functional">Minkowski functional</a></li> <li><a href="/wiki/Minkowski_inequality" title="Minkowski inequality">Minkowski inequality</a></li> <li><a href="/wiki/Minkowski_model" class="mw-redirect" title="Minkowski model">Minkowski model</a></li> <li><a href="/wiki/Minkowski_plane" title="Minkowski plane">Minkowski plane</a></li> <li><a href="/wiki/Minkowski_problem" title="Minkowski problem">Minkowski problem</a></li> <li><a href="/wiki/Minkowski_problem_for_polytopes" title="Minkowski problem for polytopes">Minkowski problem for polytopes</a></li> <li><a href="/wiki/Minkowski%27s_second_theorem" title="Minkowski's second theorem">Minkowski's second theorem</a></li> <li><a href="/wiki/Minkowski_space" title="Minkowski space">Minkowski space</a></li> <li><a href="/wiki/Minkowski%27s_bound" title="Minkowski's bound">Minkowski's bound</a></li> <li><a href="/wiki/Minkowski%27s_theorem" title="Minkowski's theorem">Minkowski's theorem</a> in geometry of numbers</li> <li><a href="/wiki/Minkowski%E2%80%93Hlawka_theorem" title="Minkowski–Hlawka theorem">Minkowski–Hlawka theorem</a></li> <li><a href="/wiki/Minkowski%E2%80%93Steiner_formula" title="Minkowski–Steiner formula">Minkowski–Steiner formula</a></li> <li><a href="/wiki/Smith%E2%80%93Minkowski%E2%80%93Siegel_mass_formula" title="Smith–Minkowski–Siegel mass formula">Smith–Minkowski–Siegel mass formula</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Separating_axis_theorem" class="mw-redirect" title="Separating axis theorem">Separating axis theorem</a></li> <li><a href="/wiki/Taxicab_geometry" title="Taxicab geometry">Taxicab geometry</a></li> <li><a href="/wiki/World_line" title="World line">World line</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes_and_references">Notes and references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=9" title="Edit section: Notes and references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Marshall_Cavendish-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Marshall_Cavendish_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Marshall_Cavendish_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Marshall_Cavendish_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/encyclopediaofea02mars"><i>Encyclopedia of Earth and Physical Sciences</i></a></span>. New York: Marshall Cavendish. 1998. p. 1203. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780761405511" title="Special:BookSources/9780761405511"><bdi>9780761405511</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopedia+of+Earth+and+Physical+Sciences&rft.place=New+York&rft.pages=1203&rft.pub=Marshall+Cavendish&rft.date=1998&rft.isbn=9780761405511&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fencyclopediaofea02mars&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.dictionary.com/browse/minkowski">"Minkowski"</a>. <i><a href="/wiki/Random_House_Webster%27s_Unabridged_Dictionary" title="Random House Webster's Unabridged Dictionary">Random House Webster's Unabridged Dictionary</a></i>.</span> </li> <li id="cite_note-Encyclopædia_Britannica-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Encyclopædia_Britannica_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Encyclopædia_Britannica_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Hermann-Minkowski">"Hermann Minkowski German mathematician"</a>. <a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a><span class="reference-accessdate">. Retrieved <span class="nowrap">6 January</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Hermann+Minkowski+German+mathematician&rft.pub=Encyclop%C3%A6dia+Britannica&rft_id=https%3A%2F%2Fwww.britannica.com%2Fbiography%2FHermann-Minkowski&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:1-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGregersen2010" class="citation book cs1">Gregersen, Erik, ed. (2010). <i>The Britannica Guide to Relativity and Quantum Mechanics</i> (1st ed.). New York: Britannica Educational Pub. Association with Rosen Educational Services. p. 201. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-61530-383-0" title="Special:BookSources/978-1-61530-383-0"><bdi>978-1-61530-383-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Britannica+Guide+to+Relativity+and+Quantum+Mechanics&rft.place=New+York&rft.pages=201&rft.edition=1st&rft.pub=Britannica+Educational+Pub.+Association+with+Rosen+Educational+Services&rft.date=2010&rft.isbn=978-1-61530-383-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:2-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBracher2007" class="citation book cs1">Bracher, Katherine; et al., eds. (2007). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/biographicalency00hock_878"><i>Biographical Encyclopedia of Astronomers</i></a></span> (Online ed.). New York: Springer. p. <a rel="nofollow" class="external text" href="https://archive.org/details/biographicalency00hock_878/page/n820">787</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-30400-7" title="Special:BookSources/978-0-387-30400-7"><bdi>978-0-387-30400-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Biographical+Encyclopedia+of+Astronomers&rft.place=New+York&rft.pages=787&rft.edition=Online&rft.pub=Springer&rft.date=2007&rft.isbn=978-0-387-30400-7&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbiographicalency00hock_878&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:3-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHayles1984" class="citation book cs1">Hayles, N. Katherine (1984). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/cosmicwebscienti00hayl_0"><i>The Cosmic Web: Scientific Field Models and Literary Strategies in the Twentieth Century</i></a></span>. Cornell University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/cosmicwebscienti00hayl_0/page/46">46</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8014-1742-9" title="Special:BookSources/978-0-8014-1742-9"><bdi>978-0-8014-1742-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cosmic+Web%3A+Scientific+Field+Models+and+Literary+Strategies+in+the+Twentieth+Century&rft.pages=46&rft.pub=Cornell+University+Press&rft.date=1984&rft.isbn=978-0-8014-1742-9&rft.aulast=Hayles&rft.aufirst=N.+Katherine&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcosmicwebscienti00hayl_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:4-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFalconer2013" class="citation book cs1">Falconer, K. J. (2013). <i>Fractals: A Very Short Introduction</i>. Oxford University Press. p. 119. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-967598-2" title="Special:BookSources/978-0-19-967598-2"><bdi>978-0-19-967598-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractals%3A+A+Very+Short+Introduction&rft.pages=119&rft.pub=Oxford+University+Press&rft.date=2013&rft.isbn=978-0-19-967598-2&rft.aulast=Falconer&rft.aufirst=K.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:5-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-:5_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:5_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBardon2013" class="citation book cs1">Bardon, Adrian (2013). <i>A Brief History of the Philosophy of Time</i>. Oxford University Press. p. 68. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-930108-9" title="Special:BookSources/978-0-19-930108-9"><bdi>978-0-19-930108-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Brief+History+of+the+Philosophy+of+Time&rft.pages=68&rft.pub=Oxford+University+Press&rft.date=2013&rft.isbn=978-0-19-930108-9&rft.aulast=Bardon&rft.aufirst=Adrian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-:6-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:6_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:6_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSafraYeshua2003" class="citation book cs1">Safra, Jacob E.; Yeshua, Ilan (2003). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/newencyclopaedia26chic"><i>Encyclopædia Britannica</i></a></span> (New ed.). Chicago, Ill.: Encyclopædia Britannica. p. <a rel="nofollow" class="external text" href="https://archive.org/details/newencyclopaedia26chic/page/665">665</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85229-961-6" title="Special:BookSources/978-0-85229-961-6"><bdi>978-0-85229-961-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.place=Chicago%2C+Ill.&rft.pages=665&rft.edition=New&rft.pub=Encyclop%C3%A6dia+Britannica&rft.date=2003&rft.isbn=978-0-85229-961-6&rft.aulast=Safra&rft.aufirst=Jacob+E.&rft.au=Yeshua%2C+Ilan&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnewencyclopaedia26chic&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFА._И._Хаеш1873" class="citation web cs1 cs1-prop-foreign-lang-source">А. И. Хаеш (1873). <a rel="nofollow" class="external text" href="http://www.berkovich-zametki.com/Nomer16/Chaesh1.htm">"Коробочное делопроизводство как источник сведений о жизни еврейских обществ и их персональном составе"</a> (in Russian). <q>...купец <b>Левин Минковский</b> подарил молитвенному обществу при Ковенском казённом еврейском училище начатую им... постройкой молитвенную школу вместе с плацем, с тем, чтобы общество это озаботилась окончанием таковой постройки. Общество, располагая средствами добровольных пожертвований, возвело уже это здание под крышу, но затем средства сии истощились...</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%D0%9A%D0%BE%D1%80%D0%BE%D0%B1%D0%BE%D1%87%D0%BD%D0%BE%D0%B5+%D0%B4%D0%B5%D0%BB%D0%BE%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%BE%D0%B4%D1%81%D1%82%D0%B2%D0%BE+%D0%BA%D0%B0%D0%BA+%D0%B8%D1%81%D1%82%D0%BE%D1%87%D0%BD%D0%B8%D0%BA+%D1%81%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B9+%D0%BE+%D0%B6%D0%B8%D0%B7%D0%BD%D0%B8+%D0%B5%D0%B2%D1%80%D0%B5%D0%B9%D1%81%D0%BA%D0%B8%D1%85+%D0%BE%D0%B1%D1%89%D0%B5%D1%81%D1%82%D0%B2+%D0%B8+%D0%B8%D1%85+%D0%BF%D0%B5%D1%80%D1%81%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%BC+%D1%81%D0%BE%D1%81%D1%82%D0%B0%D0%B2%D0%B5&rft.date=1873&rft.au=%D0%90.+%D0%98.+%D0%A5%D0%B0%D0%B5%D1%88&rft_id=http%3A%2F%2Fwww.berkovich-zametki.com%2FNomer16%2FChaesh1.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://datos.kvb.lt/en/index.php?option=com_laikotarpiai&task=view&id=19&Itemid=65">"Kaunas: dates and facts. Electronic directory"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Kaunas%3A+dates+and+facts.+Electronic+directory&rft_id=http%3A%2F%2Fdatos.kvb.lt%2Fen%2Findex.php%3Foption%3Dcom_laikotarpiai%26task%3Dview%26id%3D19%26Itemid%3D65&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150108144042/http://www.litvaksig.org/litvaksig-online-journal/box-tax-paperwork-records">"Box-Tax Paperwork Records"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.litvaksig.org/litvaksig-online-journal/box-tax-paperwork-records">the original</a> on 8 January 2015. <q>Kovno. In 1873 the merchant (<a href="https://en.wiktionary.org/wiki/kupez" class="extiw" title="wikt:kupez">kupez</a>), Levin Minkovsky, gave (as a gift) to the prayer association of the Kovno state Jewish school a lot with an ongoing construction of a prayer school that (the construction) he had started so that the association would take care of completing the construction. The association, having some funds from voluntary contributions, had built the structure up to the roof, but then, ran out of money</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Box-Tax+Paperwork+Records&rft_id=http%3A%2F%2Fwww.litvaksig.org%2Flitvaksig-online-journal%2Fbox-tax-paperwork-records&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Minkowski.html">"Minkowski biography"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Minkowski+biography&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FBiographies%2FMinkowski.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.diabetologia-journal.org/webpages/covers/2005/august.html">Oskar Minkowski (1858–1931)</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131229142542/http://www.diabetologia-journal.org/webpages/covers/2005/august.html">Archived</a> 29 December 2013 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. The Jewish genealogy site JewishGen.org (<i>Lithuania</i> database, registration required) contains the birth record in the Kovno rabbinical books of Hermann's younger brother Tuvia in 1868 to Boruch Yakovlevich Minkovsky and his wife Rakhil Isaakovna Taubman.</span> </li> <li id="cite_note-:0-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.hormones.gr/165/article/article.html">"Historical note: Oskar Minkowski (1858–1931). An outstanding master of diabetes research"</a>. 2006.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Historical+note%3A+Oskar+Minkowski+%281858%E2%80%931931%29.+An+outstanding+master+of+diabetes+research&rft.date=2006&rft_id=http%3A%2F%2Fwww.hormones.gr%2F165%2Farticle%2Farticle.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=lVjOAAAAMAAJ&pg=RA1-PA183&lpg=RA1-PA183&dq">Report of the Federal Security Agency (p. 183)</a>; <a rel="nofollow" class="external text" href="http://www.antique-toys.dk/default.asp?id=9&lang=uk&pg=4">Tyra lithographed tin toy dog</a>; <a rel="nofollow" class="external text" href="http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/minkowski-rudolph.pdf">Rudolph Leo Bernhard Minkowski: A Biographical Memoir</a>.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenspan2005" class="citation book cs1">Greenspan, Nancy Thorndike (2005). <i><a href="/wiki/The_End_of_the_Certain_World" title="The End of the Certain World">The End of the Certain World. The Life and Science of Max Born: The Nobel Physicist Who Ignited the Quantum Revolution</a></i>. Basic Books. pp. <span class="nowrap">42–</span>43. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780738206936" title="Special:BookSources/9780738206936"><bdi>9780738206936</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+End+of+the+Certain+World.+The+Life+and+Science+of+Max+Born%3A+The+Nobel+Physicist+Who+Ignited+the+Quantum+Revolution&rft.pages=%3Cspan+class%3D%22nowrap%22%3E42-%3C%2Fspan%3E43&rft.pub=Basic+Books&rft.date=2005&rft.isbn=9780738206936&rft.aulast=Greenspan&rft.aufirst=Nancy+Thorndike&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-springer-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-springer_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmadel2007" class="citation book cs1">Schmadel, Lutz D. (2007). "(12493) Minkowski". <i>Dictionary of Minor Planet Names – (12493) Minkowski</i>. Springer Berlin Heidelberg. p. 783. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-29925-7_8614">10.1007/978-3-540-29925-7_8614</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-00238-3" title="Special:BookSources/978-3-540-00238-3"><bdi>978-3-540-00238-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%2812493%29+Minkowski&rft.btitle=Dictionary+of+Minor+Planet+Names+%E2%80%93+%2812493%29+Minkowski&rft.pages=783&rft.pub=Springer+Berlin+Heidelberg&rft.date=2007&rft_id=info%3Adoi%2F10.1007%2F978-3-540-29925-7_8614&rft.isbn=978-3-540-00238-3&rft.aulast=Schmadel&rft.aufirst=Lutz+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Minkowski_Sausage"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/MinkowskiSausage.html">"Minkowski Sausage"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Minkowski+Sausage&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FMinkowskiSausage.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><span class="citation mathworld" id="Reference-Mathworld-Minkowski_Cover"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/MinkowskiCover.html">"Minkowski Cover"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Minkowski+Cover&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FMinkowskiCover.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDickson,_L._E.1909" class="citation journal cs1"><a href="/wiki/Leonard_Eugene_Dickson" title="Leonard Eugene Dickson">Dickson, L. E.</a> (1909). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/1909-15-05/S0002-9904-1909-01753-7/S0002-9904-1909-01753-7.pdf">"Review: <i>Diophantische Approximationen. Eine Einführung in die Zahlentheorie</i> von Hermann Minkowski"</a> <span class="cs1-format">(PDF)</span>. <i>Bull. Amer. Math. Soc</i>. <b>15</b> (5): <span class="nowrap">251–</span>252. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1909-01753-7">10.1090/s0002-9904-1909-01753-7</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+Diophantische+Approximationen.+Eine+Einf%C3%BChrung+in+die+Zahlentheorie+von+Hermann+Minkowski&rft.volume=15&rft.issue=5&rft.pages=%3Cspan+class%3D%22nowrap%22%3E251-%3C%2Fspan%3E252&rft.date=1909&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1909-01753-7&rft.au=Dickson%2C+L.+E.&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1909-15-05%2FS0002-9904-1909-01753-7%2FS0002-9904-1909-01753-7.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDickson,_L._E.1914" class="citation journal cs1">Dickson, L. E. (1914). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1914-02597-2">"Review: <i>Geometrie der Zahlen</i> von Hermann Minkowski"</a>. <i>Bull. Amer. Math. Soc</i>. <b>21</b> (3): <span class="nowrap">131–</span>132. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1914-02597-2">10.1090/s0002-9904-1914-02597-2</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+Geometrie+der+Zahlen+von+Hermann+Minkowski&rft.volume=21&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E131-%3C%2Fspan%3E132&rft.date=1914&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1914-02597-2&rft.au=Dickson%2C+L.+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1914-02597-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson,_E._B.1915" class="citation journal cs1"><a href="/wiki/Edwin_Bidwell_Wilson" title="Edwin Bidwell Wilson">Wilson, E. B.</a> (1915). <a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1915-02658-3">"Review: <i>Gesammelte Abhandlungen von Hermann Minkowski</i>"</a>. <i>Bull. Amer. Math. Soc</i>. <b>21</b> (8): <span class="nowrap">409–</span>412. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0002-9904-1915-02658-3">10.1090/s0002-9904-1915-02658-3</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.&rft.atitle=Review%3A+Gesammelte+Abhandlungen+von+Hermann+Minkowski&rft.volume=21&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E409-%3C%2Fspan%3E412&rft.date=1915&rft_id=info%3Adoi%2F10.1090%2Fs0002-9904-1915-02658-3&rft.au=Wilson%2C+E.+B.&rft_id=https%3A%2F%2Fdoi.org%2F10.1090%252Fs0002-9904-1915-02658-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHermann+Minkowski" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has original text related to this article: <div style="margin-left: 10px;"><b><a href="https://en.wikisource.org/wiki/Author:Hermann_Minkowski" class="extiw" title="wikisource:Author:Hermann Minkowski">Author:Hermann Minkowski</a></b></div></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/38px-Wikisource-logo.svg.png" decoding="async" width="38" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/57px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/76px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span></div> <div class="side-box-text plainlist">German <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has original text related to this article: <div lang="de" style="margin-left: 10px;"><b><a href="https://en.wikisource.org/wiki/de:Hermann_Minkowski" class="extiw" title="s:de:Hermann Minkowski">Hermann Minkowski</a></b> </div></div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Hermann_Minkowski" class="extiw" title="q:Special:Search/Hermann Minkowski">Hermann Minkowski</a></b></i>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Hermann_Minkowski" class="extiw" title="commons:Category:Hermann Minkowski">Hermann Minkowski</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=29675">Hermann Minkowski</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Archival_collections">Archival collections</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hermann_Minkowski&action=edit&section=11" title="Edit section: Archival collections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://libserv.aip.org/ipac20/ipac.jsp?session=168116Y30L533.282104&profile=rev-icos&source=~!horizon&view=subscriptionsummary&uri=full=3100006~!3971~!2&ri=9&aspect=power&menu=search&ipp=20&spp=20&staffonly=&term=MINKOWSKI&index=.AW&uindex=&aspect=power&menu=search&ri=9&limitbox_1=LO01+=+icos">Hermann Minkowski notebooks, 1882-1906, Niels Bohr Library & Archives</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q57246#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata2908" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q57246#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata2908" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q57246#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000121328417">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/51771612">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/184377/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJx8D8tjCm8jV4xFPfvCQq">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118734091">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n86856296">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12386524f">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12386524f">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35994972">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=mzk2007382040&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/97193">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p070795657">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/75kmpkwr558z5b4">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810603441405606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007297837505171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058519877906706">Catalonia</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA02311340?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=29675">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=24800826000">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:minkowski.hermann">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/125225">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1177439">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/118734091.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118734091">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/032933657">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://hls-dhs-dss.ch/fr/articles/043125">Historical Dictionary of Switzerland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w67w6fff">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Hermann_Minkowski&oldid=1266256879">https://en.wikipedia.org/w/index.php?title=Hermann_Minkowski&oldid=1266256879</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Hermann_Minkowski" title="Category:Hermann Minkowski">Hermann Minkowski</a></li><li><a href="/wiki/Category:1864_births" title="Category:1864 births">1864 births</a></li><li><a href="/wiki/Category:1909_deaths" title="Category:1909 deaths">1909 deaths</a></li><li><a href="/wiki/Category:Scientists_from_Kaunas" title="Category:Scientists from Kaunas">Scientists from Kaunas</a></li><li><a href="/wiki/Category:People_from_Suwa%C5%82ki_Governorate" title="Category:People from Suwałki Governorate">People from Suwałki Governorate</a></li><li><a href="/wiki/Category:Lithuanian_Jews" title="Category:Lithuanian Jews">Lithuanian Jews</a></li><li><a href="/wiki/Category:Emigrants_from_the_Russian_Empire_to_the_German_Empire" title="Category:Emigrants from the Russian Empire to the German Empire">Emigrants from the Russian Empire to the German Empire</a></li><li><a href="/wiki/Category:German_people_of_Lithuanian-Jewish_descent" title="Category:German people of Lithuanian-Jewish descent">German people of Lithuanian-Jewish descent</a></li><li><a href="/wiki/Category:German_people_of_Polish-Jewish_descent" title="Category:German people of Polish-Jewish descent">German people of Polish-Jewish descent</a></li><li><a href="/wiki/Category:19th-century_German_mathematicians" title="Category:19th-century German mathematicians">19th-century German mathematicians</a></li><li><a href="/wiki/Category:20th-century_German_mathematicians" title="Category:20th-century German mathematicians">20th-century German mathematicians</a></li><li><a href="/wiki/Category:German_geometers" title="Category:German geometers">German geometers</a></li><li><a href="/wiki/Category:German_number_theorists" title="Category:German number theorists">German number theorists</a></li><li><a href="/wiki/Category:German_relativity_theorists" title="Category:German relativity theorists">German relativity theorists</a></li><li><a href="/wiki/Category:University_of_K%C3%B6nigsberg_alumni" title="Category:University of Königsberg alumni">University of Königsberg alumni</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_K%C3%B6nigsberg" title="Category:Academic staff of the University of Königsberg">Academic staff of the University of Königsberg</a></li><li><a href="/wiki/Category:Academic_staff_of_ETH_Zurich" title="Category:Academic staff of ETH Zurich">Academic staff of ETH Zurich</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_Bonn" title="Category:Academic staff of the University of Bonn">Academic staff of the University of Bonn</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_G%C3%B6ttingen" title="Category:Academic staff of the University of Göttingen">Academic staff of the University of Göttingen</a></li><li><a href="/wiki/Category:Deaths_from_appendicitis" title="Category:Deaths from appendicitis">Deaths from appendicitis</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_Russian-language_sources_(ru)" title="Category:CS1 Russian-language sources (ru)">CS1 Russian-language sources (ru)</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_April_2017" title="Category:Use dmy dates from April 2017">Use dmy dates from April 2017</a></li><li><a href="/wiki/Category:Biography_with_signature" title="Category:Biography with signature">Biography with signature</a></li><li><a href="/wiki/Category:Articles_with_hCards" title="Category:Articles with hCards">Articles with hCards</a></li><li><a href="/wiki/Category:Pages_with_German_IPA" title="Category:Pages with German IPA">Pages with German IPA</a></li><li><a href="/wiki/Category:Commons_category_link_from_Wikidata" title="Category:Commons category link from Wikidata">Commons category link from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 30 December 2024, at 20:58<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Hermann_Minkowski&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" lang="en" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Hermann Minkowski</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>62 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5f467697bf-tc97h","wgBackendResponseTime":114,"wgPageParseReport":{"limitreport":{"cputime":"0.889","walltime":"1.208","ppvisitednodes":{"value":4833,"limit":1000000},"postexpandincludesize":{"value":108344,"limit":2097152},"templateargumentsize":{"value":6961,"limit":2097152},"expansiondepth":{"value":14,"limit":100},"expensivefunctioncount":{"value":5,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":127132,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 1081.814 1 -total"," 20.93% 226.388 1 Template:Infobox_scientist"," 13.71% 148.320 1 Template:Reflist"," 11.46% 123.976 1 Template:Special_relativity_sidebar"," 11.21% 121.237 1 Template:Sidebar_with_collapsible_lists"," 10.82% 117.036 1 Template:IPA"," 9.09% 98.390 6 Template:Cite_journal"," 7.45% 80.547 4 Template:Sister_project"," 7.21% 77.966 4 Template:Side_box"," 6.85% 74.090 1 Template:Short_description"]},"scribunto":{"limitreport-timeusage":{"value":"0.620","limit":"10.000"},"limitreport-memusage":{"value":26883013,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\n"},"cachereport":{"origin":"mw-web.eqiad.main-775cfc968-ksrtm","timestamp":"20250211195831","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Hermann Minkowski","url":"https:\/\/en.wikipedia.org\/wiki\/Hermann_Minkowski","sameAs":"http:\/\/www.wikidata.org\/entity\/Q57246","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q57246","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-03-08T17:42:38Z","dateModified":"2024-12-30T20:58:12Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/3\/35\/De_Raum_zeit_Minkowski_Bild_%28cropped%29.jpg","headline":"German mathematician and physicist (1864\u20131909)"}</script> </body> </html>