CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>William Kahan - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"8b3c8b1d-23b1-4661-ad79-b9931fbe9612","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"William_Kahan","wgTitle":"William Kahan","wgCurRevisionId":1275118506,"wgRevisionId":1275118506,"wgArticleId":303413,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description matches Wikidata","Articles with hCards","1933 births","Living people","20th-century Canadian mathematicians","21st-century Canadian mathematicians","Numerical analysts","Canadian computer scientists","Scientific computing researchers","UC Berkeley College of Engineering faculty","Turing Award laureates","1994 fellows of the Association for Computing Machinery","Scientists from Toronto","University of Toronto alumni", "Canadian expatriate academics in the United States","Jewish Canadian scientists"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"William_Kahan","wgRelevantArticleId":303413,"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":9000,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false, "wgWikibaseItemId":"Q92782","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","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.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.15"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/1200px-William_Kahan_2008.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="851"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/800px-William_Kahan_2008.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="567"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/640px-William_Kahan_2008.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="454"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="William Kahan - 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/William_Kahan"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=William_Kahan&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/William_Kahan"> <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-William_Kahan rootpage-William_Kahan skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=William+Kahan" 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=William+Kahan" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=William+Kahan" 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=William+Kahan" 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-Biography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Biography"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Biography</span> </div> </a> <ul id="toc-Biography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">3</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">William Kahan</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 28 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-28" 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">28 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%88%D9%84%D9%8A%D8%A7%D9%85_%D9%83%D8%A7%D9%87%D8%A7%D9%86" title="وليام كاهان – Arabic" lang="ar" hreflang="ar" data-title="وليام كاهان" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Vilyam_Morton_Kahan" title="Vilyam Morton Kahan – Azerbaijani" lang="az" hreflang="az" data-title="Vilyam Morton Kahan" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%88%DB%8C%D9%84%DB%8C%D8%A7%D9%85_%DA%A9%D8%A7%D9%87%D8%A7%D9%86" title="ویلیام کاهان – South Azerbaijani" lang="azb" hreflang="azb" data-title="ویلیام کاهان" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%89%E0%A6%87%E0%A6%B2%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%AE_%E0%A6%AE%E0%A6%B0%E0%A7%8D%E0%A6%9F%E0%A6%A8_%E0%A6%95%E0%A6%BE%E0%A6%B9%E0%A6%BE%E0%A6%A8" title="উইলিয়াম মর্টন কাহান – Bangla" lang="bn" hreflang="bn" data-title="উইলিয়াম মর্টন কাহান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/William_Kahan" title="William Kahan – Catalan" lang="ca" hreflang="ca" data-title="William Kahan" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/William_Kahan" title="William Kahan – Czech" lang="cs" hreflang="cs" data-title="William Kahan" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/William_Kahan" title="William Kahan – German" lang="de" hreflang="de" data-title="William Kahan" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/William_Kahan" title="William Kahan – Spanish" lang="es" hreflang="es" data-title="William Kahan" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/William_Kahan" title="William Kahan – Esperanto" lang="eo" hreflang="eo" data-title="William Kahan" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%DB%8C%D9%84%DB%8C%D8%A7%D9%85_%DA%A9%D8%A7%D9%87%D8%A7%D9%86" title="ویلیام کاهان – Persian" lang="fa" hreflang="fa" data-title="ویلیام کاهان" 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/William_Kahan" title="William Kahan – French" lang="fr" hreflang="fr" data-title="William Kahan" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%8C%EB%A6%AC%EC%97%84_%EC%B9%B4%ED%95%9C" title="윌리엄 카한 – Korean" lang="ko" hreflang="ko" data-title="윌리엄 카한" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/William_Kahan" title="William Kahan – Italian" lang="it" hreflang="it" data-title="William Kahan" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%88%D9%84%D9%8A%D8%A7%D9%85_%D9%83%D8%A7%D9%87%D8%A7%D9%86" title="وليام كاهان – Egyptian Arabic" lang="arz" hreflang="arz" data-title="وليام كاهان" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/William_Kahan" title="William Kahan – Dutch" lang="nl" hreflang="nl" data-title="William Kahan" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A3%E3%83%AA%E3%82%A2%E3%83%A0%E3%83%BB%E3%82%AB%E3%83%8F%E3%83%B3" title="ウィリアム・カハン – Japanese" lang="ja" hreflang="ja" data-title="ウィリアム・カハン" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/William_Kahan" title="William Kahan – Polish" lang="pl" hreflang="pl" data-title="William Kahan" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/William_Kahan" title="William Kahan – Portuguese" lang="pt" hreflang="pt" data-title="William Kahan" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/William_Kahan" title="William Kahan – Romanian" lang="ro" hreflang="ro" data-title="William Kahan" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D1%8D%D1%85%D1%8D%D0%BD,_%D0%A3%D0%B8%D0%BB%D1%8C%D1%8F%D0%BC_%D0%9C%D0%BE%D1%80%D1%82%D0%BE%D0%BD" title="Кэхэн, Уильям Мортон – Russian" lang="ru" hreflang="ru" data-title="Кэхэн, Уильям Мортон" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/William_Kahan" title="William Kahan – Simple English" lang="en-simple" hreflang="en-simple" data-title="William Kahan" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/William_Kahan" title="William Kahan – Slovak" lang="sk" hreflang="sk" data-title="William Kahan" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%88%DB%8C%D9%84%DB%8C%D8%A7%D9%85_%DA%A9%D8%A7%DA%BE%D8%A7%D9%86" title="ویلیام کاھان – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ویلیام کاھان" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B8%D0%BB%D0%B8%D1%98%D0%B0%D0%BC_%D0%9A%D0%BE%D0%BD" title="Вилијам Кон – Serbian" lang="sr" hreflang="sr" data-title="Вилијам Кон" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/William_Kahan" title="William Kahan – Serbo-Croatian" lang="sh" hreflang="sh" data-title="William Kahan" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/William_Kahan" title="William Kahan – Turkish" lang="tr" hreflang="tr" data-title="William Kahan" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%BB%D1%8C%D1%8F%D0%BC_%D0%9C%D0%BE%D1%80%D1%82%D0%BE%D0%BD_%D0%9A%D0%B5%D1%85%D0%B5%D0%BD" title="Вільям Мортон Кехен – Ukrainian" lang="uk" hreflang="uk" data-title="Вільям Мортон Кехен" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A8%81%E5%BB%89%C2%B7%E5%8D%A1%E9%9F%93" title="威廉·卡韓 – Chinese" lang="zh" hreflang="zh" data-title="威廉·卡韓" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q92782#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/William_Kahan" 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:William_Kahan" 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/William_Kahan"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=William_Kahan&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=William_Kahan&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/William_Kahan"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=William_Kahan&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=William_Kahan&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/William_Kahan" 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/William_Kahan" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=William_Kahan&oldid=1275118506" 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=William_Kahan&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=William_Kahan&id=1275118506&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%2FWilliam_Kahan"><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%2FWilliam_Kahan"><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=William_Kahan&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=William_Kahan&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:William_Kahan" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q92782" 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">Canadian mathematician and computer scientist</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">William Morton Kahan</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:William_Kahan_2008.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/220px-William_Kahan_2008.jpg" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/330px-William_Kahan_2008.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/William_Kahan_2008.jpg/440px-William_Kahan_2008.jpg 2x" data-file-width="3225" data-file-height="2287" /></a></span><div class="infobox-caption">Kahan in 2008</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none"> (<span class="bday">1933-06-05</span>) </span>June 5, 1933<span class="noprint ForceAgeToShow"> (age 91)</span><br /><div style="display:inline" class="birthplace"><a href="/wiki/Toronto" title="Toronto">Toronto, Ontario</a>, Canada</div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Toronto" title="University of Toronto">University of Toronto</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"> <ul><li><a href="/wiki/IEEE_754" title="IEEE 754">IEEE 754</a></li> <li><a href="/wiki/Kahan_summation_algorithm" title="Kahan summation algorithm">Kahan summation algorithm</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a> <small>(1989)</small></li> <li><a href="/wiki/IEEE_Emanuel_R._Piore_Award" title="IEEE Emanuel R. Piore Award">IEEE Emanuel R. Piore Award</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <span style="font-size:85%;">(2000)</span></li> <li><a href="/wiki/National_Academy_of_Engineering" title="National Academy of Engineering">National Academy of Engineering</a></li> <li><a href="/wiki/ACM_Fellow" title="ACM Fellow">ACM Fellow</a></li></ul> </div></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></li> <li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li></ul> </div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i> Gauss–Seidel Methods of Solving Large Systems of Linear Equations </i> <span style="font-size:97%;">(1958)</span></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">Byron Alexander Griffith</td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"><div class="plainlist"> <ul><li><a href="/wiki/James_Demmel" title="James Demmel">James Demmel</a></li></ul> </div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>William "Velvel" Morton Kahan</b> (born June 5, 1933) is a <a href="/wiki/Canadian" class="mw-redirect" title="Canadian">Canadian</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and <a href="/wiki/Computer_scientist" title="Computer scientist">computer scientist</a>, who is a professor emeritus at <a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a>. He received the <a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a> in 1989 for "his fundamental contributions to <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a>."<sup id="cite_ref-TuringAward_2-0" class="reference"><a href="#cite_note-TuringAward-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=William_Kahan&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Born to a <a href="/wiki/History_of_the_Jews_in_Canada" title="History of the Jews in Canada">Canadian Jewish</a> family,<sup id="cite_ref-TuringAward_2-1" class="reference"><a href="#cite_note-TuringAward-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> he attended the <a href="/wiki/University_of_Toronto" title="University of Toronto">University of Toronto</a>, where he received his bachelor's degree in 1954, his master's degree in 1956, and his Ph.D. in 1958, all in the field of mathematics. Kahan is now emeritus professor of mathematics and of electrical engineering and computer sciences (EECS) at the <a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a>. </p><p>Kahan was the primary architect behind the <a href="/wiki/IEEE_754-1985" title="IEEE 754-1985">IEEE 754-1985</a> standard for <a href="/wiki/Floating-point" class="mw-redirect" title="Floating-point">floating-point</a> computation (and its radix-independent follow-on, <a href="/wiki/IEEE_854-1987" title="IEEE 854-1987">IEEE 854</a>). He has been called "The Father of Floating Point", since he was instrumental in creating the original IEEE 754 specification.<sup id="cite_ref-TuringAward_2-2" class="reference"><a href="#cite_note-TuringAward-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Kahan continued his contributions to the <a href="/wiki/IEEE_754_revision" class="mw-redirect" title="IEEE 754 revision">IEEE 754 revision</a> that led to the current <a href="/wiki/IEEE_754-2008" class="mw-redirect" title="IEEE 754-2008">IEEE 754 standard</a>. </p><p>In the 1980s he developed the program "paranoia", a benchmark that tests for a wide range of potential floating-point bugs.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> He also developed the <a href="/wiki/Kahan_summation_algorithm" title="Kahan summation algorithm">Kahan summation algorithm</a>, an important algorithm for minimizing error introduced when adding a sequence of finite-precision <a href="/wiki/Floating-point_number" class="mw-redirect" title="Floating-point number">floating-point numbers</a>. He coined the term <a href="/wiki/Rounding#Table-maker's_dilemma" title="Rounding">"Table-maker's dilemma"</a> for the unknown cost of correctly rounding <a href="/wiki/Transcendental_function" title="Transcendental function">transcendental functions</a> to some preassigned number of digits.<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><p>The <a href="/w/index.php?title=Davis%E2%80%93Kahan%E2%80%93Weinberger_dilation_theorem&action=edit&redlink=1" class="new" title="Davis–Kahan–Weinberger dilation theorem (page does not exist)">Davis–Kahan–Weinberger dilation theorem</a> is one of the landmark results in the dilation theory of <a href="/wiki/Hilbert_space" title="Hilbert space">Hilbert space</a> operators and has found applications in many different areas.<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> </p><p>He is an outspoken advocate of better education of the general computing population about floating-point issues and regularly denounces decisions in the design of computers and programming languages that he believes would impair good floating-point computations.<sup id="cite_ref-kahan_java_6-0" class="reference"><a href="#cite_note-kahan_java-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-kahan_interview_7-0" class="reference"><a href="#cite_note-kahan_interview-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><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> </p><p>When <a href="/wiki/Hewlett-Packard" title="Hewlett-Packard">Hewlett-Packard</a> (HP) introduced the original <a href="/wiki/HP-35" title="HP-35">HP-35</a> pocket scientific calculator, its numerical accuracy in evaluating transcendental functions for some arguments was not optimal. HP worked extensively with Kahan to enhance the accuracy of the algorithms, which led to major improvements. This was documented at the time in the <i><a href="/wiki/Hewlett-Packard_Journal" title="Hewlett-Packard Journal">Hewlett-Packard Journal</a></i>.<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><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He also contributed substantially to the design of the algorithms in the <a href="/wiki/HP_Voyager_series" class="mw-redirect" title="HP Voyager series">HP Voyager series</a> and wrote part of their intermediate and advanced manuals. </p><p>Kahan was named an <a href="/wiki/ACM_Fellow" title="ACM Fellow">ACM Fellow</a> in 1994, and inducted into the <a href="/wiki/National_Academy_of_Engineering" title="National Academy of Engineering">National Academy of Engineering</a> in 2005.<sup id="cite_ref-TuringAward_2-3" class="reference"><a href="#cite_note-TuringAward-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=William_Kahan&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Intel_8087" title="Intel 8087">Intel 8087</a></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=William_Kahan&action=edit&section=3" 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"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101124232834/http://ieee.org/documents/piore_rl.pdf">"IEEE Emanuel R. Piore Award Recipients"</a> <span class="cs1-format">(PDF)</span>. <a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a>. Archived from <a rel="nofollow" class="external text" href="http://www.ieee.org/documents/piore_rl.pdf">the original</a> <span class="cs1-format">(PDF)</span> on November 24, 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">March 20,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=IEEE+Emanuel+R.+Piore+Award+Recipients&rft.pub=IEEE&rft_id=http%3A%2F%2Fwww.ieee.org%2Fdocuments%2Fpiore_rl.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> <li id="cite_note-TuringAward-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-TuringAward_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-TuringAward_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-TuringAward_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-TuringAward_2-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaigh1989" class="citation web cs1">Haigh, Thomas (1989). <a rel="nofollow" class="external text" href="https://amturing.acm.org/award_winners/kahan_1023746.cfm">"William ("Velvel") Morton Kahan"</a>. <i>A. M. Turing Award</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2017-05-27</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=A.+M.+Turing+Award&rft.atitle=William+%28%22Velvel%22%29+Morton+Kahan&rft.date=1989&rft.aulast=Haigh&rft.aufirst=Thomas&rft_id=https%3A%2F%2Famturing.acm.org%2Faward_winners%2Fkahan_1023746.cfm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKarpinski1985" class="citation cs2">Karpinski, Richard (1985), <a rel="nofollow" class="external text" href="https://archive.org/stream/byte-magazine-1985-02/1985_02_BYTE_10-02_Computing_and_the_Sciences#page/n222/mode/1up">"Paranoia: A floating-point benchmark"</a>, <i>Byte Magazine</i>, <b>10</b> (2): <span class="nowrap">223–</span>235</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Byte+Magazine&rft.atitle=Paranoia%3A+A+floating-point+benchmark&rft.volume=10&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E223-%3C%2Fspan%3E235&rft.date=1985&rft.aulast=Karpinski&rft.aufirst=Richard&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Fbyte-magazine-1985-02%2F1985_02_BYTE_10-02_Computing_and_the_Sciences%23page%2Fn222%2Fmode%2F1up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" 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="CITEREFKahan" class="citation web cs1">Kahan, William. <a rel="nofollow" class="external text" href="http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT">"A Logarithm Too Clever by Half"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2008-11-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Logarithm+Too+Clever+by+Half&rft.aulast=Kahan&rft.aufirst=William&rft_id=http%3A%2F%2Fwww.cs.berkeley.edu%2F~wkahan%2FLOG10HAF.TXT&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisKahanWeinberger1982" class="citation journal cs1">Davis, Chandler; Kahan, W. M.; Weinberger, H. F. (1982). "Norm-Preserving Dilations and Their Applications to Optimal Error Bounds". <i>SIAM Journal on Numerical Analysis</i>. <b>19</b> (3): <span class="nowrap">445–</span>469. <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/1982SJNA...19..445D">1982SJNA...19..445D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F0719029">10.1137/0719029</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10338.dmlcz%2F128534">10338.dmlcz/128534</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Journal+on+Numerical+Analysis&rft.atitle=Norm-Preserving+Dilations+and+Their+Applications+to+Optimal+Error+Bounds&rft.volume=19&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E445-%3C%2Fspan%3E469&rft.date=1982&rft_id=info%3Ahdl%2F10338.dmlcz%2F128534&rft_id=info%3Adoi%2F10.1137%2F0719029&rft_id=info%3Abibcode%2F1982SJNA...19..445D&rft.aulast=Davis&rft.aufirst=Chandler&rft.au=Kahan%2C+W.+M.&rft.au=Weinberger%2C+H.+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> <li id="cite_note-kahan_java-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-kahan_java_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKahan1998" class="citation web cs1">Kahan, William (1 March 1998). <a rel="nofollow" class="external text" href="http://people.eecs.berkeley.edu/~wkahan/JAVAhurt.pdf">"How Java's Floating-Point Hurts Everyone Everywhere"</a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=How+Java%27s+Floating-Point+Hurts+Everyone+Everywhere&rft.date=1998-03-01&rft.aulast=Kahan&rft.aufirst=William&rft_id=http%3A%2F%2Fpeople.eecs.berkeley.edu%2F~wkahan%2FJAVAhurt.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> <li id="cite_note-kahan_interview-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-kahan_interview_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHaigh2016" class="citation web cs1">Haigh, Thomas (March 2016). <a rel="nofollow" class="external text" href="http://history.siam.org/%5C/pdfs2/Kahan_final.pdf">"An interview with William M. Kahan"</a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=An+interview+with+William+M.+Kahan&rft.date=2016-03&rft.aulast=Haigh&rft.aufirst=Thomas&rft_id=http%3A%2F%2Fhistory.siam.org%2F%255C%2Fpdfs2%2FKahan_final.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></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 id="CITEREFKahan2004" class="citation web cs1">Kahan, William (31 July 2004). <a rel="nofollow" class="external text" href="http://people.eecs.berkeley.edu/~wkahan/MxMulEps.pdf">"Matlab's Loss is Nobody's Gain"</a> <span class="cs1-format">(PDF)</span><span class="reference-accessdate">. Retrieved <span class="nowrap">1 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Matlab%27s+Loss+is+Nobody%27s+Gain&rft.date=2004-07-31&rft.aulast=Kahan&rft.aufirst=William&rft_id=http%3A%2F%2Fpeople.eecs.berkeley.edu%2F~wkahan%2FMxMulEps.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" 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="CITEREFKahan1979" class="citation journal cs1">Kahan, William M. (December 1979). <a rel="nofollow" class="external text" href="http://hparchive.com/Journals/HPJ-1979-12.pdf">"Personal Calculator Has Key to Solve Any Equation <i>f</i>(<i>x</i>) = 0"</a> <span class="cs1-format">(PDF)</span>. <i>Hewlett-Packard Journal</i>. <b>30</b> (12): <span class="nowrap">20–</span>26<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Hewlett-Packard+Journal&rft.atitle=Personal+Calculator+Has+Key+to+Solve+Any+Equation+f%28x%29+%3D+0&rft.volume=30&rft.issue=12&rft.pages=%3Cspan+class%3D%22nowrap%22%3E20-%3C%2Fspan%3E26&rft.date=1979-12&rft.aulast=Kahan&rft.aufirst=William+M.&rft_id=http%3A%2F%2Fhparchive.com%2FJournals%2FHPJ-1979-12.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKahan1980" class="citation journal cs1">Kahan, William M. (August 1980). <a rel="nofollow" class="external text" href="http://hparchive.com/Journals/HPJ-1980-08.pdf">"Handheld Calculator Evaluates Integrals"</a> <span class="cs1-format">(PDF)</span>. <i>Hewlett-Packard Journal</i>. <b>31</b> (8): <span class="nowrap">23–</span>32<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Hewlett-Packard+Journal&rft.atitle=Handheld+Calculator+Evaluates+Integrals&rft.volume=31&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E23-%3C%2Fspan%3E32&rft.date=1980-08&rft.aulast=Kahan&rft.aufirst=William+M.&rft_id=http%3A%2F%2Fhparchive.com%2FJournals%2FHPJ-1980-08.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AWilliam+Kahan" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=William_Kahan&action=edit&section=4" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://people.eecs.berkeley.edu/~wkahan/">William Kahan's home page</a></li> <li><a rel="nofollow" class="external text" href="http://history.siam.org/pdfs2/Kahan_final.pdf">An oral history of William Kahan</a>, Revision 1.1, March, 2016</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=16049">William Kahan</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://www.ddj.com/architect/184410314">A Conversation with William Kahan, Dr. Dobb's Journal </a>, November 1, 1997</li> <li><a rel="nofollow" class="external text" href="http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html">An Interview with the Old Man of Floating-Point</a>, February 20, 1998</li> <li><a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/2954891_IEEE_754_An_Interview_with_William_Kahan">IEEE 754 An Interview with William Kahan</a> April, 1998</li> <li><a rel="nofollow" class="external text" href="http://www.netlib.org/paranoia/index.html">Paranoia source code in multiple languages</a></li> <li><a rel="nofollow" class="external text" href="http://www.cs.unc.edu/~ibr/projects/paranoia/">Paranoia for modern graphics processing units (GPUs)</a></li> <li><a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/30711">754-1985 - IEEE Standard for Binary Floating-Point Arithmetic</a>, 1985, Superseded by <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/4610935/">IEEE Std 754-2008</a></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="A._M._Turing_Award_laureates58" 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"><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:Turing_Award_laureates" title="Template:Turing Award laureates"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Turing_Award_laureates" title="Template talk:Turing Award laureates"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Turing_Award_laureates" title="Special:EditPage/Template:Turing Award laureates"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="A._M._Turing_Award_laureates58" style="font-size:114%;margin:0 4em"><a href="/wiki/Turing_Award" title="Turing Award">A. M. Turing Award</a> <a href="/wiki/Laureate" title="Laureate">laureates</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Alan_Perlis" title="Alan Perlis">Alan Perlis</a> (1966)</span></li> <li><span class="nowrap"><a href="/wiki/Maurice_Wilkes" title="Maurice Wilkes">Maurice Vincent Wilkes</a> (1967)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_Hamming" title="Richard Hamming">Richard Hamming</a> (1968)</span></li> <li><span class="nowrap"><a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a> (1969)</span></li> <li><span class="nowrap"><a href="/wiki/James_H._Wilkinson" title="James H. Wilkinson">James H. Wilkinson</a> (1970)</span></li> <li><span class="nowrap"><a href="/wiki/John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a> (1971)</span></li> <li><span class="nowrap"><a href="/wiki/Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Edsger W. Dijkstra</a> (1972)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Bachman" title="Charles Bachman">Charles Bachman</a> (1973)</span></li> <li><span class="nowrap"><a href="/wiki/Donald_Knuth" title="Donald Knuth">Donald Knuth</a> (1974)</span></li> <li><span class="nowrap"><a href="/wiki/Allen_Newell" title="Allen Newell">Allen Newell</a>; <a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a> (1975)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_O._Rabin" title="Michael O. Rabin">Michael O. Rabin</a>; <a href="/wiki/Dana_Scott" title="Dana Scott">Dana Scott</a> (1976)</span></li> <li><span class="nowrap"><a href="/wiki/John_Backus" title="John Backus">John Backus</a> (1977)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_W._Floyd" title="Robert W. Floyd">Robert W. Floyd</a> (1978)</span></li> <li><span class="nowrap"><a href="/wiki/Kenneth_E._Iverson" title="Kenneth E. Iverson">Kenneth E. Iverson</a> (1979)</span></li> <li><span class="nowrap"><a href="/wiki/Tony_Hoare" title="Tony Hoare">Tony Hoare</a> (1980)</span></li> <li><span class="nowrap"><a href="/wiki/Edgar_F._Codd" title="Edgar F. Codd">Edgar F. Codd</a> (1981)</span></li> <li><span class="nowrap"><a href="/wiki/Stephen_Cook" title="Stephen Cook">Stephen Cook</a> (1982)</span></li> <li><span class="nowrap"><a href="/wiki/Ken_Thompson" title="Ken Thompson">Ken Thompson</a>; <a href="/wiki/Dennis_Ritchie" title="Dennis Ritchie">Dennis Ritchie</a> (1983)</span></li> <li><span class="nowrap"><a href="/wiki/Niklaus_Wirth" title="Niklaus Wirth">Niklaus Wirth</a> (1984)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_M._Karp" title="Richard M. Karp">Richard Karp</a> (1985)</span></li> <li><span class="nowrap"><a href="/wiki/John_Hopcroft" title="John Hopcroft">John Hopcroft</a>; <a href="/wiki/Robert_Tarjan" title="Robert Tarjan">Robert Tarjan</a> (1986)</span></li> <li><span class="nowrap"><a href="/wiki/John_Cocke_(computer_scientist)" title="John Cocke (computer scientist)">John Cocke</a> (1987)</span></li> <li><span class="nowrap"><a href="/wiki/Ivan_Sutherland" title="Ivan Sutherland">Ivan Sutherland</a> (1988)</span></li> <li><span class="nowrap"><a class="mw-selflink selflink">William Kahan</a> (1989)</span></li> <li><span class="nowrap"><a href="/wiki/Fernando_J._Corbat%C3%B3" title="Fernando J. Corbató">Fernando J. Corbató</a> (1990)</span></li> <li><span class="nowrap"><a href="/wiki/Robin_Milner" title="Robin Milner">Robin Milner</a> (1991)</span></li> <li><span class="nowrap"><a href="/wiki/Butler_Lampson" title="Butler Lampson">Butler Lampson</a> (1992)</span></li> <li><span class="nowrap"><a href="/wiki/Juris_Hartmanis" title="Juris Hartmanis">Juris Hartmanis</a>; <a href="/wiki/Richard_E._Stearns" title="Richard E. Stearns">Richard E. Stearns</a> (1993)</span></li> <li><span class="nowrap"><a href="/wiki/Edward_Feigenbaum" title="Edward Feigenbaum">Edward Feigenbaum</a>; <a href="/wiki/Raj_Reddy" title="Raj Reddy">Raj Reddy</a> (1994)</span></li> <li><span class="nowrap"><a href="/wiki/Manuel_Blum" title="Manuel Blum">Manuel Blum</a> (1995)</span></li> <li><span class="nowrap"><a href="/wiki/Amir_Pnueli" title="Amir Pnueli">Amir Pnueli</a> (1996)</span></li> <li><span class="nowrap"><a href="/wiki/Douglas_Engelbart" title="Douglas Engelbart">Douglas Engelbart</a> (1997)</span></li> <li><span class="nowrap"><a href="/wiki/Jim_Gray_(computer_scientist)" title="Jim Gray (computer scientist)">Jim Gray</a> (1998)</span></li> <li><span class="nowrap"><a href="/wiki/Fred_Brooks" title="Fred Brooks">Fred Brooks</a> (1999)</span></li> <li><span class="nowrap"><a href="/wiki/Andrew_Yao" title="Andrew Yao">Andrew Yao</a> (2000)</span></li> <li><span class="nowrap"><a href="/wiki/Ole-Johan_Dahl" title="Ole-Johan Dahl">Ole-Johan Dahl</a>; <a href="/wiki/Kristen_Nygaard" title="Kristen Nygaard">Kristen Nygaard</a> (2001)</span></li> <li><span class="nowrap"><a href="/wiki/Ron_Rivest" title="Ron Rivest">Ron Rivest</a>; <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a>; <a href="/wiki/Leonard_Adleman" title="Leonard Adleman">Leonard Adleman</a> (2002)</span></li> <li><span class="nowrap"><a href="/wiki/Alan_Kay" title="Alan Kay">Alan Kay</a> (2003)</span></li> <li><span class="nowrap"><a href="/wiki/Vint_Cerf" title="Vint Cerf">Vint Cerf</a>; <a href="/wiki/Robert_Kahn_(computer_scientist)" title="Robert Kahn (computer scientist)">Bob Kahn</a> (2004)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Naur" title="Peter Naur">Peter Naur</a> (2005)</span></li> <li><span class="nowrap"><a href="/wiki/Frances_Allen" title="Frances Allen">Frances Allen</a> (2006)</span></li> <li><span class="nowrap"><a href="/wiki/Edmund_M._Clarke" title="Edmund M. Clarke">Edmund M. Clarke</a>; <a href="/wiki/E._Allen_Emerson" title="E. Allen Emerson">E. Allen Emerson</a>; <a href="/wiki/Joseph_Sifakis" title="Joseph Sifakis">Joseph Sifakis</a> (2007)</span></li> <li><span class="nowrap"><a href="/wiki/Barbara_Liskov" title="Barbara Liskov">Barbara Liskov</a> (2008)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_P._Thacker" title="Charles P. Thacker">Charles P. Thacker</a> (2009)</span></li> <li><span class="nowrap"><a href="/wiki/Leslie_Valiant" title="Leslie Valiant">Leslie G. Valiant</a> (2010)</span></li> <li><span class="nowrap"><a href="/wiki/Judea_Pearl" title="Judea Pearl">Judea Pearl</a> (2011)</span></li> <li><span class="nowrap"><a href="/wiki/Shafi_Goldwasser" title="Shafi Goldwasser">Shafi Goldwasser</a>; <a href="/wiki/Silvio_Micali" title="Silvio Micali">Silvio Micali</a> (2012)</span></li> <li><span class="nowrap"><a href="/wiki/Leslie_Lamport" title="Leslie Lamport">Leslie Lamport</a> (2013)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_Stonebraker" title="Michael Stonebraker">Michael Stonebraker</a> (2014)</span></li> <li><span class="nowrap"><a href="/wiki/Martin_Hellman" title="Martin Hellman">Martin Hellman</a>; <a href="/wiki/Whitfield_Diffie" title="Whitfield Diffie">Whitfield Diffie</a> (2015)</span></li> <li><span class="nowrap"><a href="/wiki/Tim_Berners-Lee" title="Tim Berners-Lee">Tim Berners-Lee</a> (2016)</span></li> <li><span class="nowrap"><a href="/wiki/John_L._Hennessy" title="John L. Hennessy">John L. Hennessy</a>; <a href="/wiki/David_Patterson_(computer_scientist)" title="David Patterson (computer scientist)">David Patterson</a> (2017)</span></li> <li><span class="nowrap"><a href="/wiki/Yoshua_Bengio" title="Yoshua Bengio">Yoshua Bengio</a>; <a href="/wiki/Geoffrey_Hinton" title="Geoffrey Hinton">Geoffrey Hinton</a>; <a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a> (2018)</span></li> <li><span class="nowrap"><a href="/wiki/Edwin_Catmull" title="Edwin Catmull">Ed Catmull</a>; <a href="/wiki/Pat_Hanrahan" title="Pat Hanrahan">Pat Hanrahan</a> (2019)</span></li> <li><span class="nowrap"><a href="/wiki/Alfred_Aho" title="Alfred Aho">Alfred Aho</a>; <a href="/wiki/Jeffrey_Ullman" title="Jeffrey Ullman">Jeffrey Ullman</a> (2020) </span></li> <li><span class="nowrap"><a href="/wiki/Jack_Dongarra" title="Jack Dongarra">Jack Dongarra</a> (2021)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Metcalfe" title="Robert Metcalfe">Robert Metcalfe</a> (2022)</span></li> <li><span class="nowrap"><a href="/wiki/Avi_Wigderson" title="Avi Wigderson">Avi Wigderson</a> (2023)</span></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" aria-labelledby="John_von_Neumann_Lecturers55" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:John_von_Neumann_Lecturers" title="Template:John von Neumann Lecturers"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:John_von_Neumann_Lecturers" title="Template talk:John von Neumann Lecturers"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:John_von_Neumann_Lecturers" title="Special:EditPage/Template:John von Neumann Lecturers"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="John_von_Neumann_Lecturers55" style="font-size:114%;margin:0 4em"><a href="/wiki/John_von_Neumann_Lecture" class="mw-redirect" title="John von Neumann Lecture">John von Neumann Lecturers</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Lars_Ahlfors" title="Lars Ahlfors">Lars Ahlfors</a> <small>(1960)</small></li> <li><a href="/wiki/Mark_Kac" title="Mark Kac">Mark Kac</a><small> (1961)</small></li> <li><a href="/wiki/Jean_Leray" title="Jean Leray">Jean Leray</a><small> (1962)</small></li> <li><a href="/wiki/Stanislaw_Ulam" class="mw-redirect" title="Stanislaw Ulam">Stanislaw Ulam</a> <small>(1963)</small></li> <li><a href="/wiki/Solomon_Lefschetz" title="Solomon Lefschetz">Solomon Lefschetz</a> <small>(1964)</small></li> <li><a href="/wiki/Freeman_Dyson" title="Freeman Dyson">Freeman Dyson</a> <small>(1965)</small></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Eugene Wigner</a> <small>(1966)</small></li> <li><a href="/wiki/Chia-Chiao_Lin" title="Chia-Chiao Lin">Chia-Chiao Lin</a> <small>(1967)</small></li> <li><a href="/wiki/Peter_Lax" title="Peter Lax">Peter Lax</a> <small>(1968)</small></li> <li><a href="/wiki/George_F._Carrier" title="George F. Carrier">George F. Carrier</a> <small>(1969)</small></li> <li><a href="/wiki/James_H._Wilkinson" title="James H. Wilkinson">James H. Wilkinson</a> <small>(1970)</small></li> <li><a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Paul Samuelson</a> <small>(1971)</small></li> <li><a href="/wiki/Jule_Gregory_Charney" title="Jule Gregory Charney">Jule Charney</a> <small>(1974)</small></li> <li><a href="/wiki/James_Lighthill" title="James Lighthill">James Lighthill</a> <small>(1975)</small></li> <li><a href="/wiki/Ren%C3%A9_Thom" title="René Thom">René Thom</a> <small>(1976)</small></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a> <small>(1977)</small></li> <li><a href="/wiki/Peter_Henrici_(mathematician)" title="Peter Henrici (mathematician)">Peter Henrici</a> <small>(1978)</small></li> <li><a href="/wiki/Kurt_Otto_Friedrichs" title="Kurt Otto Friedrichs">Kurt O. Friedrichs</a> <small>(1979)</small></li> <li><a href="/wiki/Keith_Stewartson" title="Keith Stewartson">Keith Stewartson</a> <small>(1980)</small></li> <li><a href="/wiki/Garrett_Birkhoff" title="Garrett Birkhoff">Garrett Birkhoff</a> <small>(1981)</small></li> <li><a href="/wiki/David_Slepian" title="David Slepian">David Slepian</a> <small>(1982)</small></li> <li><a href="/wiki/Joseph_Keller" title="Joseph Keller">Joseph B. Keller</a> <small>(1983)</small></li> <li><a href="/wiki/J%C3%BCrgen_Moser" title="Jürgen Moser">Jürgen Moser</a> <small>(1984)</small></li> <li><a href="/wiki/John_Tukey" title="John Tukey">John W. Tukey</a> <small>(1985)</small></li> <li><a href="/wiki/Jacques-Louis_Lions" title="Jacques-Louis Lions">Jacques-Louis Lions</a> <small>(1986)</small></li> <li><a href="/wiki/Richard_M._Karp" title="Richard M. Karp">Richard M. Karp</a> <small>(1987)</small></li> <li><a href="/wiki/Germund_Dahlquist" title="Germund Dahlquist">Germund Dahlquist</a> <small>(1988)</small></li> <li><a href="/wiki/Stephen_Smale" title="Stephen Smale">Stephen Smale</a> <small>(1989)</small></li> <li><a href="/wiki/Andrew_Majda" title="Andrew Majda">Andrew Majda</a> <small>(1990)</small></li> <li><a href="/wiki/R._Tyrrell_Rockafellar" title="R. Tyrrell Rockafellar">R. Tyrrell Rockafellar</a> <small>(1992)</small></li> <li><a href="/wiki/Martin_David_Kruskal" title="Martin David Kruskal">Martin D. Kruskal</a> <small>(1994)</small></li> <li><a href="/wiki/Carl_R._de_Boor" title="Carl R. de Boor">Carl de Boor</a> <small>(1996)</small></li> <li><a class="mw-selflink selflink">William Kahan</a> <small>(1997)</small></li> <li><a href="/wiki/Olga_Ladyzhenskaya" title="Olga Ladyzhenskaya">Olga Ladyzhenskaya</a> <small>(1998)</small></li> <li><a href="/wiki/Charles_S._Peskin" title="Charles S. Peskin">Charles S. Peskin</a> <small>(1999)</small></li> <li><a href="/wiki/Persi_Diaconis" title="Persi Diaconis">Persi Diaconis</a> <small>(2000)</small></li> <li><a href="/wiki/David_Donoho" title="David Donoho">David Donoho</a> <small>(2001)</small></li> <li><a href="/wiki/Eric_Lander" title="Eric Lander">Eric Lander</a> <small>(2002)</small></li> <li><a href="/wiki/Heinz-Otto_Kreiss" title="Heinz-Otto Kreiss">Heinz-Otto Kreiss</a> <small>(2003)</small></li> <li><a href="/wiki/Alan_C._Newell" title="Alan C. Newell">Alan C. Newell</a> <small>(2004)</small></li> <li><a href="/wiki/Jerrold_E._Marsden" title="Jerrold E. Marsden">Jerrold E. Marsden</a> <small>(2005)</small></li> <li><a href="/wiki/George_C._Papanicolaou" title="George C. Papanicolaou">George C. Papanicolaou</a> <small>(2006)</small></li> <li><a href="/wiki/Nancy_Kopell" title="Nancy Kopell">Nancy Kopell</a> <small>(2007)</small></li> <li><a href="/wiki/David_Gottlieb_(mathematician)" title="David Gottlieb (mathematician)">David Gottlieb</a> <small>(2008)</small></li> <li><a href="/wiki/Franco_Brezzi" title="Franco Brezzi">Franco Brezzi</a> <small>(2009)</small></li> <li><a href="/wiki/Bernd_Sturmfels" title="Bernd Sturmfels">Bernd Sturmfels</a> <small>(2010)</small></li> <li><a href="/wiki/Ingrid_Daubechies" title="Ingrid Daubechies">Ingrid Daubechies</a> <small>(2011)</small></li> <li><a href="/wiki/John_M._Ball" title="John M. Ball">John M. Ball</a> <small>(2012)</small></li> <li><a href="/wiki/Stanley_Osher" title="Stanley Osher">Stanley Osher</a> <small>(2013)</small></li> <li><a href="/wiki/Leslie_Greengard" title="Leslie Greengard">Leslie Greengard</a> <small>(2014)</small></li> <li><a href="/wiki/Jennifer_Tour_Chayes" title="Jennifer Tour Chayes">Jennifer Tour Chayes</a> <small>(2015)</small></li> <li><a href="/wiki/Donald_Knuth" title="Donald Knuth">Donald Knuth</a> <small>(2016)</small></li> <li><a href="/wiki/Bernard_J._Matkowsky" title="Bernard J. Matkowsky">Bernard J. Matkowsky</a> <small>(2017)</small></li> <li><a href="/wiki/Charles_F._Van_Loan" title="Charles F. Van Loan">Charles F. Van Loan</a> <small>(2018)</small></li> <li><a href="/wiki/Margaret_H._Wright" title="Margaret H. Wright">Margaret H. Wright</a> <small>(2019)</small></li> <li><a href="/wiki/Nick_Trefethen" title="Nick Trefethen">Nick Trefethen</a> <small>(2020)</small></li> <li><a href="/wiki/Chi-Wang_Shu" title="Chi-Wang Shu">Chi-Wang Shu</a> <small>(2021)</small></li> <li><a href="/wiki/Leah_Keshet" title="Leah Keshet">Leah Keshet</a> <small>(2022)</small></li> <li><a href="/wiki/Yousef_Saad" title="Yousef Saad">Yousef Saad</a> <small>(2023)</small></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-label="Navbox992" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: Academics <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q92782#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></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=16049">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dl.acm.org/profile/81100645838">Association for Computing Machinery</a></span><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://dl.acm.org/profile/81503674907">2</a></span></li></ul></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.scopus.com/authid/detail.uri?authorId=6603570125">Scopus</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:kahan.william-m">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/k/WilliamKahan">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/96750">MathSciNet</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=William_Kahan&oldid=1275118506">https://en.wikipedia.org/w/index.php?title=William_Kahan&oldid=1275118506</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:1933_births" title="Category:1933 births">1933 births</a></li><li><a href="/wiki/Category:Living_people" title="Category:Living people">Living people</a></li><li><a href="/wiki/Category:20th-century_Canadian_mathematicians" title="Category:20th-century Canadian mathematicians">20th-century Canadian mathematicians</a></li><li><a href="/wiki/Category:21st-century_Canadian_mathematicians" title="Category:21st-century Canadian mathematicians">21st-century Canadian mathematicians</a></li><li><a href="/wiki/Category:Numerical_analysts" title="Category:Numerical analysts">Numerical analysts</a></li><li><a href="/wiki/Category:Canadian_computer_scientists" title="Category:Canadian computer scientists">Canadian computer scientists</a></li><li><a href="/wiki/Category:Scientific_computing_researchers" title="Category:Scientific computing researchers">Scientific computing researchers</a></li><li><a href="/wiki/Category:UC_Berkeley_College_of_Engineering_faculty" title="Category:UC Berkeley College of Engineering faculty">UC Berkeley College of Engineering faculty</a></li><li><a href="/wiki/Category:Turing_Award_laureates" title="Category:Turing Award laureates">Turing Award laureates</a></li><li><a href="/wiki/Category:1994_fellows_of_the_Association_for_Computing_Machinery" title="Category:1994 fellows of the Association for Computing Machinery">1994 fellows of the Association for Computing Machinery</a></li><li><a href="/wiki/Category:Scientists_from_Toronto" title="Category:Scientists from Toronto">Scientists from Toronto</a></li><li><a href="/wiki/Category:University_of_Toronto_alumni" title="Category:University of Toronto alumni">University of Toronto alumni</a></li><li><a href="/wiki/Category:Canadian_expatriate_academics_in_the_United_States" title="Category:Canadian expatriate academics in the United States">Canadian expatriate academics in the United States</a></li><li><a href="/wiki/Category:Jewish_Canadian_scientists" title="Category:Jewish Canadian scientists">Jewish Canadian scientists</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_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches 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 11 February 2025, at 04:27<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=William_Kahan&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" lang="en" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">William Kahan</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>28 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-68d95c4d5-b75fq","wgBackendResponseTime":121,"wgPageParseReport":{"limitreport":{"cputime":"0.378","walltime":"0.499","ppvisitednodes":{"value":2648,"limit":1000000},"postexpandincludesize":{"value":61851,"limit":2097152},"templateargumentsize":{"value":4570,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":61010,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 437.555 1 -total"," 32.59% 142.610 1 Template:Infobox_scientist"," 27.57% 120.644 1 Template:Reflist"," 19.59% 85.717 6 Template:Cite_web"," 18.06% 79.022 1 Template:Turing_award"," 17.53% 76.703 2 Template:Navbox"," 12.96% 56.697 1 Template:Short_description"," 7.90% 34.553 2 Template:Pagetype"," 7.28% 31.851 1 Template:Birth_date_and_age"," 6.54% 28.598 1 Template:Infobox"]},"scribunto":{"limitreport-timeusage":{"value":"0.255","limit":"10.000"},"limitreport-memusage":{"value":6988659,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-7878cd4448-pzwqs","timestamp":"20250211203942","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"William Kahan","url":"https:\/\/en.wikipedia.org\/wiki\/William_Kahan","sameAs":"http:\/\/www.wikidata.org\/entity\/Q92782","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q92782","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-08-24T04:11:02Z","dateModified":"2025-02-11T04:27:39Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/f\/fb\/William_Kahan_2008.jpg","headline":"Canadian mathematician and computer scientist"}</script> </body> </html>