CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Gisbert Hasenjaeger - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-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":"8042642b-8f89-4521-8e1b-18d3836c6051","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Gisbert_Hasenjaeger","wgTitle":"Gisbert Hasenjaeger","wgCurRevisionId":1248603025,"wgRevisionId":1248603025,"wgArticleId":41568237,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description is different from Wikidata","Articles with hCards","1919 births","2006 deaths","People from Hildesheim","University of Münster alumni","20th-century German mathematicians","German logicians","Mathematical logicians","German male writers","German cryptographers","German Army personnel of World War II","Academic staff of the University of Münster","Academic staff of the University of Bonn"],"wgPageViewLanguage":"en", "wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Gisbert_Hasenjaeger","wgRelevantArticleId":41568237,"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,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1527182","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","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.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</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.5"> <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/en/c/cc/Gisbert_Hasenjaeger_as_a_soldier_in_World_War_2.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="2118"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/en/c/cc/Gisbert_Hasenjaeger_as_a_soldier_in_World_War_2.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="1412"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="1130"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Gisbert Hasenjaeger - 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/Gisbert_Hasenjaeger"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Gisbert_Hasenjaeger&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/Gisbert_Hasenjaeger"> <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-Gisbert_Hasenjaeger rootpage-Gisbert_Hasenjaeger 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" > <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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Gisbert+Hasenjaeger" 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=Gisbert+Hasenjaeger" 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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Gisbert+Hasenjaeger" 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=Gisbert+Hasenjaeger" 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" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_life"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Personal life</span> </div> </a> <ul id="toc-Personal_life-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Work" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Work"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Work</span> </div> </a> <button aria-controls="toc-Work-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 Work subsection</span> </button> <ul id="toc-Work-sublist" class="vector-toc-list"> <li id="toc-Safety_Testing_the_Enigma_Machine" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Safety_Testing_the_Enigma_Machine"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Safety Testing the Enigma Machine</span> </div> </a> <ul id="toc-Safety_Testing_the_Enigma_Machine-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proof_of_Gödel's_completeness_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Proof_of_Gödel's_completeness_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Proof of Gödel's completeness theorem</span> </div> </a> <ul id="toc-Proof_of_Gödel's_completeness_theorem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Construction_of_Turing_Machines" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Construction_of_Turing_Machines"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Construction of Turing Machines</span> </div> </a> <button aria-controls="toc-Construction_of_Turing_Machines-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 Construction of Turing Machines subsection</span> </button> <ul id="toc-Construction_of_Turing_Machines-sublist" class="vector-toc-list"> <li id="toc-Comments_on_the_Enigma_Machine_weakness" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comments_on_the_Enigma_Machine_weakness"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Comments on the Enigma Machine weakness</span> </div> </a> <ul id="toc-Comments_on_the_Enigma_Machine_weakness-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </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" > <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">Gisbert Hasenjaeger</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 4 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-4" 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">4 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gisbert_Hasenjaeger" title="Gisbert Hasenjaeger – German" lang="de" hreflang="de" data-title="Gisbert Hasenjaeger" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%AF%DB%8C%D8%B3%D8%A8%D8%B1%D8%AA_%D9%87%D8%A7%D8%B2%D9%86%E2%80%8C%DB%8C%DA%AF%D8%B1" title="گیسبرت هازن‌یگر – Persian" lang="fa" hreflang="fa" data-title="گیسبرت هازن‌یگر" 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/Gisbert_Hasenjaeger" title="Gisbert Hasenjaeger – French" lang="fr" hreflang="fr" data-title="Gisbert Hasenjaeger" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Gisbert_Hasenjaeger" title="Gisbert Hasenjaeger – Portuguese" lang="pt" hreflang="pt" data-title="Gisbert Hasenjaeger" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</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/Q1527182#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/Gisbert_Hasenjaeger" 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:Gisbert_Hasenjaeger" 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/Gisbert_Hasenjaeger"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Gisbert_Hasenjaeger&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=Gisbert_Hasenjaeger&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/Gisbert_Hasenjaeger"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Gisbert_Hasenjaeger&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=Gisbert_Hasenjaeger&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/Gisbert_Hasenjaeger" 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/Gisbert_Hasenjaeger" 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="/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=Gisbert_Hasenjaeger&oldid=1248603025" 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=Gisbert_Hasenjaeger&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=Gisbert_Hasenjaeger&id=1248603025&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%2FGisbert_Hasenjaeger"><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%2FGisbert_Hasenjaeger"><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=Gisbert_Hasenjaeger&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=Gisbert_Hasenjaeger&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 id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1527182" 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 (1919–2006)</div> <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">Gisbert F. R. Hasenjaeger</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Gisbert_Hasenjaeger_as_a_soldier_in_World_War_2.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/c/cc/Gisbert_Hasenjaeger_as_a_soldier_in_World_War_2.jpg" decoding="async" width="200" height="353" class="mw-file-element" data-file-width="200" data-file-height="353" /></a></span><div class="infobox-caption">Picture of Gisbert Hasenjaeger in his identity papers during his time at <a href="/wiki/Oberkommando_der_Wehrmacht_Chiffrierabteilung" class="mw-redirect" title="Oberkommando der Wehrmacht Chiffrierabteilung">OKW/Chi</a></div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data">1 June 1919<br /><div style="display:inline" class="birthplace"><a href="/wiki/Hildesheim" title="Hildesheim">Hildesheim</a>, Germany</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">2 September 2006<span style="display:none">(2006-09-02)</span> (aged 87)<br /><div style="display:inline" class="deathplace"><a href="/wiki/M%C3%BCnster" title="Münster">Münster</a>, <a href="/wiki/Westphalia" title="Westphalia">Westphalia</a>, Germany</div></td></tr><tr><th scope="row" class="infobox-label">Citizenship</th><td class="infobox-data category"><a href="/wiki/Germans" title="Germans">German</a></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data"><a href="/wiki/University_of_M%C3%BCnster" title="University of Münster">Münster University</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data">Testing the <a href="/wiki/Enigma_machine" title="Enigma machine">Enigma</a> encryption machine for cryptographic weaknesses.<br />Developing a proof of the <a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">completeness</a> theorem in 1949.</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><br /><a href="/wiki/Logic" title="Logic">Logic</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_M%C3%BCnster" title="University of Münster">University of Münster</a><br /><a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a> <br /><a href="/wiki/Princeton_University" title="Princeton University">Princeton University</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/Heinrich_Scholz" title="Heinrich Scholz">Heinrich Scholz</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Dieter_R%C3%B6dding" title="Dieter Rödding">Dieter Rödding</a><br /><a href="/wiki/Ronald_Jensen" title="Ronald Jensen">Ronald Jensen</a><br />Peter Schroeder-Heister<sup id="cite_ref-mathgene_1-0" class="reference"><a href="#cite_note-mathgene-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Gisbert F. R. Hasenjaeger</b> (1 June 1919 – 2 September 2006) was a German <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> <a href="/wiki/Logic" title="Logic">logician</a>. Independently and simultaneously with <a href="/wiki/Leon_Henkin" title="Leon Henkin">Leon Henkin</a> in 1949, he developed a new proof of the <a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">completeness</a> theorem of <a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a> for <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a>.<sup id="cite_ref-Münster_2-0" class="reference"><a href="#cite_note-Münster-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Enc_3-0" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> He worked as an assistant to <a href="/wiki/Heinrich_Scholz" title="Heinrich Scholz">Heinrich Scholz</a> at Section IVa of <a href="/wiki/Oberkommando_der_Wehrmacht_Chiffrierabteilung" class="mw-redirect" title="Oberkommando der Wehrmacht Chiffrierabteilung">Oberkommando der Wehrmacht Chiffrierabteilung</a>, and was responsible for the security of the <a href="/wiki/Enigma_machine" title="Enigma machine">Enigma machine</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Personal_life">Personal life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=1" title="Edit section: Personal life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gisbert Hasenjaeger went to high school in <a href="/wiki/M%C3%BClheim" title="Mülheim">Mülheim</a>, where his father <a href="/w/index.php?title=Edwin_Renatus_Hasenjaeger&action=edit&redlink=1" class="new" title="Edwin Renatus Hasenjaeger (page does not exist)">Edwin Renatus Hasenjaeger</a><sup class="noprint" style="font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Edwin_Renatus_Hasenjaeger" class="extiw" title="de:Edwin Renatus Hasenjaeger">de</a>]</sup> was a lawyer and local politician. After completing school in 1936, Gisbert volunteered for labor service. He was drafted for military service in <a href="/wiki/World_War_II" title="World War II">World War II</a>, and fought as an artillerist in the <a href="/wiki/Eastern_Front_(World_War_II)" title="Eastern Front (World War II)">Russian campaign</a>, where he was badly wounded in January 1942. After his recovery, in October 1942, <a href="/wiki/Heinrich_Scholz" title="Heinrich Scholz">Heinrich Scholz</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> got him employment in the <a href="/wiki/Cipher_Department_of_the_High_Command_of_the_Wehrmacht" title="Cipher Department of the High Command of the Wehrmacht">Cipher Department of the High Command of the Wehrmacht</a> (OKW/Chi), where he was the youngest member at 24. He attended a <a href="/wiki/Cryptography" title="Cryptography">cryptography</a> training course by <a href="/wiki/Erich_H%C3%BCttenhain" title="Erich Hüttenhain">Erich Hüttenhain</a>, and was put into the recently founded Section IVa "Security check of own Encoding Procedures" under <a href="/wiki/Karl_Stein_(mathematician)" title="Karl Stein (mathematician)">Karl Stein</a>, who assigned him the security check of the <a href="/wiki/Enigma_machine" title="Enigma machine">Enigma machine</a>.<sup id="cite_ref-Heise_6-0" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Bauer.2000_7-0" class="reference"><a href="#cite_note-Bauer.2000-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> At the end of the war as OKW/Chi disintegrated, Hasenjaeger managed to escape <a href="/wiki/TICOM" title="TICOM">TICOM</a>, the United States effort to roundup and seize captured German intelligence people and material.<sup id="cite_ref-Heise_6-1" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>From the end of 1945, he studied mathematics and especially mathematical logic with <a href="/wiki/Heinrich_Scholz" title="Heinrich Scholz">Heinrich Scholz</a> at the <a href="/wiki/M%C3%BCnster_University" class="mw-redirect" title="Münster University">Westfälische Wilhelms-Universität</a> University in Münster. In 1950 received his doctorate <i>Topological studies on the semantics and syntax of an extended predicate calculus</i> and completed his habilitation in 1953.<sup id="cite_ref-Enc_3-1" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In Münster, Hasenjaeger worked as an assistant to Scholz and later co-author, to write the textbook <i>Fundamentals of Mathematical Logic</i> in <i>Springer's Grundlehren series</i> (Yellow series of Springer-Verlag), which he published in 1961 fully 6 years after Scholz's death. In 1962, he became a professor at the <a href="/wiki/University_of_Bonn" title="University of Bonn">University of Bonn</a>, where he was Director of the newly created Department of Logic.<sup id="cite_ref-Enc_3-2" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In 1962, Dr Hasenjaeger left Münster University to take a full professorship at Bonn University, where he became Director of the newly established Department of Logic and Basic Research. In 1964/65, he spent a year at <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a> at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> His doctoral students at Bonn included <a href="/wiki/Ronald_Jensen" title="Ronald Jensen">Ronald B. Jensen</a>, his most famous pupil.<sup id="cite_ref-Enc_3-3" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Hasenjaeger became professor emeritus in 1984.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=2" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Safety_Testing_the_Enigma_Machine">Safety Testing the Enigma Machine</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=3" title="Edit section: Safety Testing the Enigma Machine"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In October 1942, after starting work at <a href="/wiki/Oberkommando_der_Wehrmacht_Chiffrierabteilung" class="mw-redirect" title="Oberkommando der Wehrmacht Chiffrierabteilung">OKW/Chi</a>, Hasenjaeger was trained in cryptology, given by the mathematician, <a href="/wiki/Erich_H%C3%BCttenhain" title="Erich Hüttenhain">Erich Hüttenhain</a>, who was widely considered the most important German cryptologist of his time. Hasenjaeger was put into a newly formed department, whose principal responsibility was the defensive testing and security control of their own methods and devices.<sup id="cite_ref-Heise_6-2" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-TuringBook_10-0" class="reference"><a href="#cite_note-TuringBook-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Hasenjaeger was ordered, by the mathematician <a href="/wiki/Karl_Stein_(mathematician)" title="Karl Stein (mathematician)">Karl Stein</a> who was also conscripted at OKW/Chi, to examine the <a href="/wiki/Enigma_machine" title="Enigma machine">Enigma machine</a> for cryptologic weaknesses, while Stein was to examine the <a href="/wiki/Siemens_and_Halske_T52" title="Siemens and Halske T52">Siemens and Halske T52</a> and the <a href="/wiki/Lorenz_cipher" title="Lorenz cipher">Lorenz SZ-42</a>.<sup id="cite_ref-TuringBook_10-1" class="reference"><a href="#cite_note-TuringBook-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The Enigma machine that Hasenjaeger examined was a variation that worked with 3 rotors and had no plugboard. Germany sold this version to neutral countries to accrue foreign exchange. Hasenjaeger was presented with a 100 character encrypted message for analysis and found a weakness which enabled the identification of the correct wiring rotors and also the appropriate rotor positions, to decrypt the messages. Further success eluded him, however. He crucially failed to identify the most important weakness of the Enigma machine: the lack of fixed points (letters encrypting to themselves) due to the reflector. Hasenjaeger could take some comfort from the fact that even <a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a> missed this weakness. Instead, the honour was attributed to <a href="/wiki/Gordon_Welchman" title="Gordon Welchman">Gordon Welchman</a>, who used the knowledge to decrypt several hundred thousand Enigma messages during the war.<sup id="cite_ref-Heise_6-3" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-TuringBook_10-2" class="reference"><a href="#cite_note-TuringBook-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> In fact fixed points were earlier used by Polish codebreaker, Henryk Zygalski, as the basis for his method of attack on Enigma cipher, referred to by the Poles as "Zygalski sheets" (<a href="/wiki/Zygalski_sheets" title="Zygalski sheets">Zygalski sheets</a>) (płachty Zygalskiego) and by the British as the "Netz method". </p> <div class="mw-heading mw-heading3"><h3 id="Proof_of_Gödel's_completeness_theorem"><span id="Proof_of_G.C3.B6del.27s_completeness_theorem"></span>Proof of Gödel's completeness theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=4" title="Edit section: Proof of Gödel's completeness theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It was while Hasenjaeger was working at <a href="/wiki/M%C3%BCnster_University" class="mw-redirect" title="Münster University">Westfälische Wilhelms-Universität</a> University in Münster in the period between 1946 and 1953 that Hasenjaeger made a most amazing discovery - a <a href="/wiki/Mathematical_proof" title="Mathematical proof">proof</a> of <a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a>'s <a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">Gödel's completeness</a> <a href="/wiki/Theorem" title="Theorem">theorem</a> for full <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a> with identity and function symbols.<sup id="cite_ref-Enc_3-4" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Gödel's proof of 1930 for predicate logic did not automatically establish a procedure for the general case. When he had solved the problem in late 1949, he was frustrated to find that a young American mathematician <a href="/wiki/Leon_Henkin" title="Leon Henkin">Leon Henkin</a>, had also created a proof.<sup id="cite_ref-Enc_3-5" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Both construct from extension of a <a href="/wiki/Herbrand_structure" title="Herbrand structure">term model</a>, which is then the model for the initial theory. Although the Henkin proof was considered by Hasenjaeger and his peers to be more flexible, Hasenjaeger's is considered simpler and more transparent.<sup id="cite_ref-Enc_3-6" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Hasenjaeger continued to refine his proof through to 1953 when he made a breakthrough. According to the mathematicians <a href="/wiki/Alfred_Tarski" title="Alfred Tarski">Alfred Tarski</a>, <a href="/wiki/Stephen_Cole_Kleene" title="Stephen Cole Kleene">Stephen Cole Kleene</a> and <a href="/wiki/Andrzej_Mostowski" title="Andrzej Mostowski">Andrzej Mostowski</a>, the <a href="/wiki/Arithmetical_hierarchy" title="Arithmetical hierarchy">Arithmetical hierarchy</a> of formulas is the set of arithmetical propositions that are true in the standard model, but not arithmetically definable. So, what does the concept of <a href="/wiki/Logical_truth" title="Logical truth">truth</a> for the term model mean, the results for the recursively <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatized</a> <a href="/wiki/Peano_axioms" title="Peano axioms">Peano arithmetic</a> from the Hasenjaeger method? The result was the <a href="/wiki/Truth_predicate" title="Truth predicate">truth predicate</a> is well arithmetically, it is even <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 \Delta _{2}^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta _{2}^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2647e336f34cacfba9934032137522052e8af0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.99ex; height:3.176ex;" alt="{\displaystyle \Delta _{2}^{0}}"></span>.<sup id="cite_ref-Enc_3-7" class="reference"><a href="#cite_note-Enc-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> So far down in the arithmetic hierarchy, and that goes for any recursively axiomatized (countable, consistent) theories. Even if you are true in all the <a href="/wiki/Natural_numbers" class="mw-redirect" title="Natural numbers">natural numbers</a> <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 \Pi _{1}^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi mathvariant="normal">Π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pi _{1}^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b3c0e79d8a5db977a9838be477eb3e30348937" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.797ex; height:3.176ex;" alt="{\displaystyle \Pi _{1}^{0}}"></span> formulas to the axioms. </p><p>This classic proof is a very early, original application of the arithmetic hierarchy theory to a general-logical problem. It appeared in 1953 in the <i><a href="/wiki/Journal_of_Symbolic_Logic" title="Journal of Symbolic Logic">Journal of Symbolic Logic</a></i>.<sup id="cite_ref-Symbolic_11-0" class="reference"><a href="#cite_note-Symbolic-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Construction_of_Turing_Machines">Construction of Turing Machines</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=5" title="Edit section: Construction of Turing Machines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1963, Hasenjaeger built a <a href="/wiki/Universal_Turing_machine" title="Universal Turing machine">Universal Turing machine</a> out of old telephone relays. Although Hasenjaeger's work on UTMs was largely unknown and he never published any details of the machinery during his lifetime, his family decided to donate the machine to the <a href="/wiki/Heinz_Nixdorf_Museum" class="mw-redirect" title="Heinz Nixdorf Museum">Heinz Nixdorf Museum</a> in <a href="/wiki/Paderborn" title="Paderborn">Paderborn</a>, <a href="/wiki/Germany" title="Germany">Germany</a>, after his death.<sup id="cite_ref-Heinz_12-0" class="reference"><a href="#cite_note-Heinz-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-UTM_13-0" class="reference"><a href="#cite_note-UTM-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In an academic paper presented at the <i>International Conference of History and Philosophy of Computing</i> in 2012.<sup id="cite_ref-Heinz_12-1" class="reference"><a href="#cite_note-Heinz-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Rainer Glaschick, Turlough Neary, Damien Woods, Niall Murphy had examined Hasenjaeger's UTM machine at the request of Hasenjaeger family and found that the UTM was remarkably small and efficiently <a href="/wiki/Turing_completeness" title="Turing completeness">universal</a>. Hasenjaeger UTM contained 3-tapes, 4 states, 2 symbols and was an evolution of ideas from <a href="/wiki/Edward_F._Moore" title="Edward F. Moore">Edward F. Moore</a>'s first universal machine and <a href="/wiki/Hao_Wang_(academic)" title="Hao Wang (academic)">Hao Wang</a>'s <a href="/wiki/Wang_B-machine" title="Wang B-machine">B-machine</a>. Hasenjaeger went on to build a small efficient Wang B-machine simulator. This was again proven by the team assembled by Rainer Glaschick to be efficiently <a href="/wiki/Turing_completeness" title="Turing completeness">universal</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Comments_on_the_Enigma_Machine_weakness">Comments on the Enigma Machine weakness</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=6" title="Edit section: Comments on the Enigma Machine weakness"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It was only in the 1970s that Hasenjaeger learned that the Enigma Machine had been so comprehensively broken.<sup id="cite_ref-Heise_6-4" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It impressed him that Alan Turing himself, considered one of the greatest mathematicians of the 20th century, had worked on breaking the device. The fact that the Germans had so comprehensively underestimated the weaknesses of the device, in contrast to Turing and Welchman's work, was seen by Hasenjaeger today as entirely positive. Hasenjaeger stated: </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>Would it not been so, then the war would have lasted probably longer and the first atomic bomb had not fallen on Japan, but on Germany.<sup id="cite_ref-Heise_6-5" class="reference"><a href="#cite_note-Heise-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p></blockquote> <style data-mw-deduplicate="TemplateStyles:r1259569809">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/28px-P_vip.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/41px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/69/P_vip.svg/55px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Biography" title="Portal:Biography">Biography portal</a></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=7" title="Edit section: Bibliography"><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="CITEREFSchmeh2009" class="citation journal cs1">Schmeh, Klaus (18 September 2009). "Enigma's Contemporary Witness: Gisbert Hasenjaeger". <i>Cryptologia</i>. <b>33</b> (4): 343–346. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01611190903186003">10.1080/01611190903186003</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:205487783">205487783</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cryptologia&rft.atitle=Enigma%27s+Contemporary+Witness%3A+Gisbert+Hasenjaeger&rft.volume=33&rft.issue=4&rft.pages=343-346&rft.date=2009-09-18&rft_id=info%3Adoi%2F10.1080%2F01611190903186003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205487783%23id-name%3DS2CID&rft.aulast=Schmeh&rft.aufirst=Klaus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=8" title="Edit section: 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-mathgene-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-mathgene_1-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=21245">Gisbert Hasenjaeger</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></span> </li> <li id="cite_note-Münster-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Münster_2-0">^</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://wwwmath.uni-muenster.de/historie/kapitel7.pdf">"Past Professors at Münster University"</a> <span class="cs1-format">(PDF)</span>. wwmath.uni-muenster.de<span class="reference-accessdate">. Retrieved <span class="nowrap">6 January</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Past+Professors+at+M%C3%BCnster+University&rft.pub=wwmath.uni-muenster.de&rft_id=http%3A%2F%2Fwwwmath.uni-muenster.de%2Fhistorie%2Fkapitel7.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-Enc-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Enc_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Enc_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Enc_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Enc_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Enc_3-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Enc_3-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Enc_3-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-Enc_3-7"><sup><i><b>h</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://web.archive.org/web/20120831193010/http://wwwmath.uni-muenster.de/logik/Veroeffentlichungen/etc/Hasenjaeger/haselaud.html">"Laudatio anläßlich der Erneuerung der Doktorurkunde"</a>. WWU Münster Mathematik: Logik. Archived from <a rel="nofollow" class="external text" href="http://wwwmath.uni-muenster.de/logik/Veroeffentlichungen/etc/Hasenjaeger/haselaud.html">the original</a> on 31 August 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">17 February</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Laudatio+anl%C3%A4%C3%9Flich+der+Erneuerung+der+Doktorurkunde&rft.pub=WWU+M%C3%BCnster+Mathematik%3A+Logik&rft_id=http%3A%2F%2Fwwwmath.uni-muenster.de%2Flogik%2FVeroeffentlichungen%2Fetc%2FHasenjaeger%2Fhaselaud.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmeh2009" class="citation journal cs1">Schmeh, Klaus (15 September 2009). "Enigma's Contemporary Witness: Gisbert Hasenjaeger". <i>Cryptologia</i>. <b>33</b> (4): 343–346. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01611190903186003">10.1080/01611190903186003</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0161-1194">0161-1194</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:205487783">205487783</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cryptologia&rft.atitle=Enigma%27s+Contemporary+Witness%3A+Gisbert+Hasenjaeger&rft.volume=33&rft.issue=4&rft.pages=343-346&rft.date=2009-09-15&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205487783%23id-name%3DS2CID&rft.issn=0161-1194&rft_id=info%3Adoi%2F10.1080%2F01611190903186003&rft.aulast=Schmeh&rft.aufirst=Klaus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Hasenjaeger knew Scholz since his school days and corresponded with him during his time as a <a href="/wiki/Conscription" title="Conscription">conscript</a>.</span> </li> <li id="cite_note-Heise-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Heise_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Heise_6-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Heise_6-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Heise_6-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Heise_6-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Heise_6-5"><sup><i><b>f</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.heise.de/tp/artikel/20/20750/1.html">"Enigma Contemporary Witness - Enigma Vulnerability Part 3"</a>. <i><a href="/wiki/Heise_Online" class="mw-redirect" title="Heise Online">Heise Online</a></i>. Klaus Schmeh. 29 August 2005<span class="reference-accessdate">. Retrieved <span class="nowrap">2 March</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Heise+Online&rft.atitle=Enigma+Contemporary+Witness+-+Enigma+Vulnerability+Part+3&rft.date=2005-08-29&rft_id=http%3A%2F%2Fwww.heise.de%2Ftp%2Fartikel%2F20%2F20750%2F1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-Bauer.2000-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bauer.2000_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFriedrich_L._Bauer2000" class="citation book cs1">Friedrich L. Bauer (2000). <i>Entzifferte Geheimnisse — Methoden und Maximen der Kryptologie</i> (3 ed.). Heidelberg: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-67931-8" title="Special:BookSources/978-3-540-67931-8"><bdi>978-3-540-67931-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Entzifferte+Geheimnisse+%26mdash%3B+Methoden+und+Maximen+der+Kryptologie&rft.place=Heidelberg&rft.edition=3&rft.pub=Springer&rft.date=2000&rft.isbn=978-3-540-67931-8&rft.au=Friedrich+L.+Bauer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span> Cited from <a href="https://de.wikipedia.org/wiki/Gisbert_Hasenjaeger#Einzelnachweise" class="extiw" title="de:Gisbert Hasenjaeger">German Wikipedia</a></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</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://www.ias.edu/scholars/gisbert-hasenjaeger">"IAS - Gisbert Hasenjeager"</a>. <i>www.ias.edu</i>. IAS<span class="reference-accessdate">. Retrieved <span class="nowrap">20 July</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.ias.edu&rft.atitle=IAS+-+Gisbert+Hasenjeager&rft_id=https%3A%2F%2Fwww.ias.edu%2Fscholars%2Fgisbert-hasenjaeger&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWirth2018" class="citation book cs1">Wirth, Claus-Peter (4 March 2018). <i>A Most Interesting Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and two CV of Gisbert Hasenjaeger</i>. Saarland University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Most+Interesting+Draft+for+Hilbert+and+Bernays%27+%22Grundlagen+der+Mathematik%22+that+never+found+its+way+into+any+publication%2C+and+two+CV+of+Gisbert+Hasenjaeger&rft.pub=Saarland+University&rft.date=2018-03-04&rft.aulast=Wirth&rft.aufirst=Claus-Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-TuringBook-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-TuringBook_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-TuringBook_10-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-TuringBook_10-2"><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 id="CITEREFCooperLeeuwen2013" class="citation book cs1">Cooper, S. Barry; Leeuwen, J. van (3 Jun 2013). <i>Alan Turing: His Work and Impact</i>. Elsevier Science. p. 936. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-386980-7" title="Special:BookSources/978-0-12-386980-7"><bdi>978-0-12-386980-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Alan+Turing%3A+His+Work+and+Impact&rft.pages=936&rft.pub=Elsevier+Science&rft.date=2013-06-03&rft.isbn=978-0-12-386980-7&rft.aulast=Cooper&rft.aufirst=S.+Barry&rft.au=Leeuwen%2C+J.+van&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-Symbolic-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Symbolic_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHasenjaeger1953" class="citation journal cs1">Hasenjaeger, G. (1953). "Eine Bemerkung zu Henkin's Beweis für die Vollständigkeit des Prädikatenkalküls der ersten Stufe". <i>Journal of Symbolic Logic</i>. <b>18</b> (1): 42–48. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2266326">10.2307/2266326</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2266326">2266326</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:45705695">45705695</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Symbolic+Logic&rft.atitle=Eine+Bemerkung+zu+Henkin%27s+Beweis+f%C3%BCr+die+Vollst%C3%A4ndigkeit+des+Pr%C3%A4dikatenkalk%C3%BCls+der+ersten+Stufe&rft.volume=18&rft.issue=1&rft.pages=42-48&rft.date=1953&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A45705695%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2266326%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2266326&rft.aulast=Hasenjaeger&rft.aufirst=G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span> Gödel proof.</span> </li> <li id="cite_note-Heinz-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Heinz_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Heinz_12-1"><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="CITEREFNearyWoodsMurphyGlaschick2014" class="citation journal cs1">Neary, Turlough; Woods, Damien; Murphy, Niall; Glaschick, Rainer (October 2014). "Wang's B machines are efficiently universal, as is Hasenjaeger's small universal electromechanical toy". <i>Journal of Complexity</i>. <b>30</b> (5): 634–646. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1304.0053">1304.0053</a></span>. <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/2013arXiv1304.0053N">2013arXiv1304.0053N</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.jco.2014.02.003">10.1016/j.jco.2014.02.003</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18828226">18828226</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Complexity&rft.atitle=Wang%27s+B+machines+are+efficiently+universal%2C+as+is+Hasenjaeger%27s+small+universal+electromechanical+toy&rft.volume=30&rft.issue=5&rft.pages=634-646&rft.date=2014-10&rft_id=info%3Aarxiv%2F1304.0053&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18828226%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.jco.2014.02.003&rft_id=info%3Abibcode%2F2013arXiv1304.0053N&rft.aulast=Neary&rft.aufirst=Turlough&rft.au=Woods%2C+Damien&rft.au=Murphy%2C+Niall&rft.au=Glaschick%2C+Rainer&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> <li id="cite_note-UTM-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-UTM_13-0">^</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/20140319025917/http://www.computing-conference.ugent.be/file/21">"Hasenjaeger's electromechanical small universal Turing machine is time efficient"</a>. Department of History and Philosophy Universiteit Gent. Archived from <a rel="nofollow" class="external text" href="http://www.computing-conference.ugent.be/file/21">the original</a> <span class="cs1-format">(PDF)</span> on 19 March 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">18 March</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Hasenjaeger%27s+electromechanical+small+universal+Turing+machine+is+time+efficient.&rft.pub=Department+of+History+and+Philosophy+Universiteit+Gent&rft_id=http%3A%2F%2Fwww.computing-conference.ugent.be%2Ffile%2F21&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGisbert+Hasenjaeger" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gisbert_Hasenjaeger&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Rebecca Ratcliffe: Searching for Security. The German Investigations into Enigma's security. In: Intelligence and National Security 14 (1999) Issue 1 (Special Issue) S.146–167.</li> <li>Rebecca Ratcliffe: How Statistics led the Germans to believe Enigma Secure and Why They Were Wrong: neglecting the practical Mathematics of Cipher machines Add:. Brian J. angle (eds.) The German Enigma Cipher Machine. Artech House: Boston, London of 2005.</li></ul> <div class="navbox-styles"><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><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" aria-labelledby="German_Signals_intelligence_organisations_before_1945" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><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:German_signal_intelligence_organisations_before_and_during_World_War_II" title="Template:German signal intelligence organisations before and during World War II"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:German_signal_intelligence_organisations_before_and_during_World_War_II&action=edit&redlink=1" class="new" title="Template talk:German signal intelligence organisations before and during World War II (page does not exist)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:German_signal_intelligence_organisations_before_and_during_World_War_II" title="Special:EditPage/Template:German signal intelligence organisations before and during World War II"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="German_Signals_intelligence_organisations_before_1945" style="font-size:114%;margin:0 4em">German <a href="/wiki/Signals_intelligence" title="Signals intelligence">Signals intelligence</a> organisations before 1945</div></th></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;"><div> <ul><li>The Type of organisation</li> <li>Name of organisation</li> <li>People</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:6.9em;text-align:left;">Military <abbr title="A German military organisation">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><i><a href="/wiki/Cipher_Department_of_the_High_Command_of_the_Wehrmacht" title="Cipher Department of the High Command of the Wehrmacht">Wehrmacht High Command Cipher Bureau</a></i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Erich_Fellgiebel" title="Erich Fellgiebel">Erich Fellgiebel</a></li> <li><a href="/wiki/Albert_Praun" title="Albert Praun">Albert Praun</a></li> <li><a href="/wiki/Hugo_Kettler" title="Hugo Kettler">Hugo Kettler</a></li> <li><a href="/wiki/Wilhelm_Fenner" title="Wilhelm Fenner">Wilhelm Fenner</a></li> <li><a href="/wiki/Erich_H%C3%BCttenhain" title="Erich Hüttenhain">Erich Hüttenhain</a></li> <li><a href="/wiki/Peter_Novopashenny" title="Peter Novopashenny">Peter Novopashenny</a></li> <li><a href="/wiki/Walter_Fricke" title="Walter Fricke">Walter Fricke</a></li> <li><a href="/wiki/Karl_Stein_(mathematician)" title="Karl Stein (mathematician)">Karl Stein</a></li> <li><a href="/wiki/Wolfgang_Franz_(mathematician)" title="Wolfgang Franz (mathematician)">Wolfgang Franz</a></li> <li><a class="mw-selflink selflink">Gisbert Hasenjaeger</a></li> <li><a href="/wiki/Heinrich_Scholz" title="Heinrich Scholz">Heinrich Scholz</a></li> <li><a href="/wiki/Werner_Liebknecht" title="Werner Liebknecht">Werner Liebknecht</a></li> <li><a href="/wiki/Gottfried_K%C3%B6the" title="Gottfried Köthe">Gottfried Köthe</a></li> <li><a href="/wiki/Ernst_Witt" title="Ernst Witt">Ernst Witt</a></li> <li><a href="/wiki/Helmut_Grunsky" title="Helmut Grunsky">Helmut Grunsky</a></li> <li><a href="/wiki/Georg_Hamel" title="Georg Hamel">Georg Hamel</a></li> <li><a href="/wiki/Georg_Aumann" title="Georg Aumann">Georg Aumann</a></li> <li><a href="/wiki/Oswald_Teichm%C3%BCller" title="Oswald Teichmüller">Oswald Teichmüller</a></li> <li><a href="/wiki/Alexander_Aigner" title="Alexander Aigner">Alexander Aigner</a></li> <li><a href="/wiki/Werner_Weber_(mathematician)" title="Werner Weber (mathematician)">Werner Weber</a></li> <li><a href="/wiki/Otto_Leiberich" title="Otto Leiberich">Otto Leiberich</a></li> <li><a href="/wiki/Otto_Buggisch" title="Otto Buggisch">Otto Buggisch</a></li> <li><a href="/wiki/Fritz_Menzer" title="Fritz Menzer">Fritz Menzer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><a href="/wiki/General_der_Nachrichtenaufkl%C3%A4rung" title="General der Nachrichtenaufklärung">General der Nachrichtenaufklärung</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Erich_Fellgiebel" title="Erich Fellgiebel">Erich Fellgiebel</a></li> <li><a href="/wiki/Fritz_Thiele" title="Fritz Thiele">Fritz Thiele</a></li> <li><a href="/wiki/Wilhelm_Gimmler" title="Wilhelm Gimmler">Wilhelm Gimmler</a></li> <li><a href="/wiki/Hugo_Kettler" title="Hugo Kettler">Hugo Kettler</a></li> <li><a href="/wiki/Friedrich_Boetzel" title="Friedrich Boetzel">Fritz Boetzel</a></li> <li><a href="/wiki/Otto_Buggisch" title="Otto Buggisch">Otto Buggisch</a></li> <li><a href="/wiki/Fritz_Menzer" title="Fritz Menzer">Fritz Menzer</a></li> <li><a href="/wiki/Herbert_von_Denffer" title="Herbert von Denffer">Herbert von Denffer</a></li> <li><a href="/wiki/Ludwig_F%C3%B6ppl" title="Ludwig Föppl">Ludwig Föppl</a></li> <li><a href="/wiki/Horst_Schubert" title="Horst Schubert">Horst Schubert</a></li> <li><a href="/wiki/Friedrich_B%C3%B6hm" title="Friedrich Böhm">Friedrich Böhm</a></li> <li><a href="/wiki/Bruno_von_Freytag-L%C3%B6ringhoff" title="Bruno von Freytag-Löringhoff">Bruno von Freytag-Löringhoff</a></li> <li><a href="/wiki/Johannes_Marquart" title="Johannes Marquart">Johannes Marquart</a></li> <li><a href="/wiki/Willi_Rinow" title="Willi Rinow">Willi Rinow</a></li> <li><a href="/wiki/Rudolf_Kochend%C3%B6rffer" title="Rudolf Kochendörffer">Rudolf Kochendörffer</a></li> <li><a href="/wiki/Hans_Pietsch_(mathematician)" title="Hans Pietsch (mathematician)">Hans Pietsch</a></li> <li><a href="/wiki/Guido_Hoheisel" title="Guido Hoheisel">Guido Hoheisel</a></li> <li><a href="/wiki/Hans-Peter_Luzius" title="Hans-Peter Luzius">Hans-Peter Luzius</a></li> <li><a href="/wiki/Wilhelm_Vauck" title="Wilhelm Vauck">Wilhelm Vauck</a></li> <li><a href="/wiki/Rudolf_Bailovic" title="Rudolf Bailovic">Rudolf Bailovic</a></li> <li><a href="/wiki/Alfred_Kneschke" title="Alfred Kneschke">Alfred Kneschke</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><i><a href="/wiki/Luftnachrichten_Abteilung_350" title="Luftnachrichten Abteilung 350">Luftnachrichten Abteilung 350</a></i></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wolfgang_Martini" title="Wolfgang Martini">Wolfgang Martini</a></li> <li><a href="/wiki/Ferdinand_Voegele" title="Ferdinand Voegele">Ferdinand Voegele</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><i><a href="/wiki/B-Dienst" title="B-Dienst">B-Dienst</a></i></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kurt_Fricke" title="Kurt Fricke">Kurt Fricke</a></li> <li><a href="/wiki/Ludwig_Stummel" title="Ludwig Stummel">Ludwig Stummel</a></li> <li><a href="/wiki/Heinz_Bonatz" title="Heinz Bonatz">Heinz Bonatz</a></li> <li><a href="/wiki/Wilhelm_Tranow" title="Wilhelm Tranow">Wilhelm Tranow</a></li> <li><a href="/wiki/Erhard_Maertens" title="Erhard Maertens">Erhard Maertens</a></li> <li><a href="/wiki/Fritz_Krauss" title="Fritz Krauss">Fritz Krauss</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><i><a href="/wiki/Abwehr" title="Abwehr">Abwehr</a></i> <abbr title="The Abwehr didn't have its own cryptanalyts instead relying on the four others agencies for intelligence.">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wilhelm_Canaris" title="Wilhelm Canaris">Wilhelm Canaris</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:6.9em;text-align:left;">Civilian <abbr title="A German civilian operation">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Pers_Z_S" scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><a href="/wiki/Pers_Z_S" title="Pers Z S">Pers Z S</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Curt_Selchow" title="Curt Selchow">Curt Selchow</a></li> <li><a href="/wiki/Horst_Hauthal" title="Horst Hauthal">Horst Hauthal</a></li> <li><a href="/wiki/Rudolf_Schauffler" title="Rudolf Schauffler">Rudolf Schauffler</a></li> <li><a href="/wiki/Johannes_Benzing" title="Johannes Benzing">Johannes Benzing</a></li> <li><a href="/wiki/Otfried_Deubner" title="Otfried Deubner">Otfried Deubner</a></li> <li><a href="/wiki/Hans_Rohrbach" title="Hans Rohrbach">Hans Rohrbach</a></li> <li><a href="/wiki/Helmut_Grunsky" title="Helmut Grunsky">Helmut Grunsky</a></li> <li><a href="/wiki/Erika_Pannwitz" title="Erika Pannwitz">Erika Pannwitz</a></li> <li><a href="/wiki/Karl_Schr%C3%B6ter" title="Karl Schröter">Karl Schröter</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><a href="/wiki/Research_Office_of_the_Reich_Air_Ministry" title="Research Office of the Reich Air Ministry">Research Office of the Reich Air Ministry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hermann_G%C3%B6ring" title="Hermann Göring">Hermann Göring</a></li> <li><a href="/wiki/Gottfried_Schapper" title="Gottfried Schapper">Gottfried Schapper</a></li> <li><a href="/wiki/Hans_Schimpf" title="Hans Schimpf">Hans Schimpf</a></li> <li><a href="/wiki/Prince_Christoph_of_Hesse" title="Prince Christoph of Hesse">Prince Christoph of Hesse</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:6.9em;text-align:left;">Training <abbr title="Signal intelligence and cipher training organisations">(?)</abbr></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><a href="/wiki/General_der_Nachrichtenaufkl%C3%A4rung_Training_Referat" title="General der Nachrichtenaufklärung Training Referat">GdNA Training Referat</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i> </i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:left; font-weight: normal;"><a href="/wiki/Heer_and_Luftwaffe_Signals_School" title="Heer and Luftwaffe Signals School">Heer and Luftwaffe Signals School</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i> </i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align: center;;font-weight: normal;"><div> <ul><li><b><a href="/wiki/German_Radio_Intelligence_Operations_during_World_War_II" class="mw-redirect" title="German Radio Intelligence Operations during World War II">German Radio Intelligence Operations during World War II</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></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/Q1527182#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" 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/Q1527182#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" 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/Q1527182#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/0000000109978978">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/91872544">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJh4wvcqMY9bvYKjBhhPwC">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/1022914154">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n84088111">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb17227124v">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb17227124v">BnF data</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=mzk2013773779&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p070129339">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007350239305171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14721207">Belgium</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://www.mathgenealogy.org/id.php?id=21245">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:hasenjaeger.gisbert">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/40/5606">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/82125">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://www.deutsche-biographie.de/pnd1022914154.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/1022914154">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/082110662">IdRef</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" 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=Gisbert_Hasenjaeger&oldid=1248603025">https://en.wikipedia.org/w/index.php?title=Gisbert_Hasenjaeger&oldid=1248603025</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:1919_births" title="Category:1919 births">1919 births</a></li><li><a href="/wiki/Category:2006_deaths" title="Category:2006 deaths">2006 deaths</a></li><li><a href="/wiki/Category:People_from_Hildesheim" title="Category:People from Hildesheim">People from Hildesheim</a></li><li><a href="/wiki/Category:University_of_M%C3%BCnster_alumni" title="Category:University of Münster alumni">University of Münster alumni</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_logicians" title="Category:German logicians">German logicians</a></li><li><a href="/wiki/Category:Mathematical_logicians" title="Category:Mathematical logicians">Mathematical logicians</a></li><li><a href="/wiki/Category:German_male_writers" title="Category:German male writers">German male writers</a></li><li><a href="/wiki/Category:German_cryptographers" title="Category:German cryptographers">German cryptographers</a></li><li><a href="/wiki/Category:German_Army_personnel_of_World_War_II" title="Category:German Army personnel of World War II">German Army personnel of World War II</a></li><li><a href="/wiki/Category:Academic_staff_of_the_University_of_M%C3%BCnster" title="Category:Academic staff of the University of Münster">Academic staff of the University of Münster</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></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><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_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_with_hCards" title="Category:Articles with hCards">Articles with hCards</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 September 2024, at 13:34<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=Gisbert_Hasenjaeger&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" 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-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-6d94db5ff4-kbvgk","wgBackendResponseTime":199,"wgPageParseReport":{"limitreport":{"cputime":"0.491","walltime":"0.648","ppvisitednodes":{"value":3080,"limit":1000000},"postexpandincludesize":{"value":74676,"limit":2097152},"templateargumentsize":{"value":3467,"limit":2097152},"expansiondepth":{"value":11,"limit":100},"expensivefunctioncount":{"value":3,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":63276,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 544.309 1 -total"," 25.15% 136.880 1 Template:Infobox_scientist"," 19.35% 105.317 4 Template:Cite_journal"," 18.30% 99.593 4 Template:Navbox"," 18.06% 98.284 1 Template:German_signal_intelligence_organisations_before_and_during_World_War_II"," 16.68% 90.799 1 Template:Reflist"," 10.70% 58.238 1 Template:Short_description"," 6.43% 35.008 2 Template:Pagetype"," 5.75% 31.294 1 Template:Infobox"," 4.41% 24.020 5 Template:Cite_web"]},"scribunto":{"limitreport-timeusage":{"value":"0.326","limit":"10.000"},"limitreport-memusage":{"value":7121468,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-847495b4dd-9ktdk","timestamp":"20241128134250","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Gisbert Hasenjaeger","url":"https:\/\/en.wikipedia.org\/wiki\/Gisbert_Hasenjaeger","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1527182","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1527182","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":"2014-01-06T22:27:47Z","dateModified":"2024-09-30T13:34:21Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/en\/c\/cc\/Gisbert_Hasenjaeger_as_a_soldier_in_World_War_2.jpg","headline":"German mathematician (1919-2006)"}</script> </body> </html>