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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">Richard Hamming</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 37 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-37" 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">37 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/%D8%B1%D9%8A%D8%AA%D8%B4%D8%A7%D8%B1%D8%AF_%D9%87%D8%A7%D9%85%D9%8A%D9%86%D8%BA" title="ريتشارد هامينغ – Arabic" lang="ar" hreflang="ar" data-title="ريتشارد هامينغ" 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/Ri%C3%A7ard_Hemminq" title="Riçard Hemminq – Azerbaijani" lang="az" hreflang="az" data-title="Riçard Hemminq" 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/%D8%B1%DB%8C%DA%86%D8%A7%D8%B1%D8%AF_%D9%87%D9%85%DB%8C%D9%86%D9%82" title="ریچارد همینق – South Azerbaijani" lang="azb" hreflang="azb" data-title="ریچارد همینق" 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%B0%E0%A6%BF%E0%A6%9A%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A1_%E0%A6%B9%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%82" title="রিচার্ড হ্যামিং – Bangla" lang="bn" hreflang="bn" data-title="রিচার্ড হ্যামিং" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Bosnian" lang="bs" hreflang="bs" data-title="Richard Hamming" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Catalan" lang="ca" hreflang="ca" data-title="Richard Hamming" 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/Richard_Hamming" title="Richard Hamming – Czech" lang="cs" hreflang="cs" data-title="Richard Hamming" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Richard_W._Hamming" title="Richard W. Hamming – Danish" lang="da" hreflang="da" data-title="Richard W. Hamming" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – German" lang="de" hreflang="de" data-title="Richard Hamming" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A1%CE%AF%CF%84%CF%83%CE%B1%CF%81%CE%BD%CF%84_%CE%A7%CE%AC%CE%BC%CE%B9%CE%BD%CE%B3%CE%BA" title="Ρίτσαρντ Χάμινγκ – Greek" lang="el" hreflang="el" data-title="Ρίτσαρντ Χάμινγκ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Spanish" lang="es" hreflang="es" data-title="Richard Hamming" 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/Richard_Hamming" title="Richard Hamming – Esperanto" lang="eo" hreflang="eo" data-title="Richard Hamming" 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/%D8%B1%DB%8C%DA%86%D8%A7%D8%B1%D8%AF_%D9%87%D9%85%DB%8C%D9%86%DA%AF" title="ریچارد همینگ – Persian" lang="fa" hreflang="fa" data-title="ریچارد همینگ" 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/Richard_Hamming" title="Richard Hamming – French" lang="fr" hreflang="fr" data-title="Richard Hamming" 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/%EB%A6%AC%EC%B2%98%EB%93%9C_%ED%95%B4%EB%B0%8D" title="리처드 해밍 – Korean" lang="ko" hreflang="ko" data-title="리처드 해밍" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Croatian" lang="hr" hreflang="hr" data-title="Richard Hamming" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Italian" lang="it" hreflang="it" data-title="Richard Hamming" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%99%D7%A6%27%D7%A8%D7%93_%D7%94%D7%9E%D7%99%D7%A0%D7%92" title="ריצ'רד המינג – Hebrew" lang="he" hreflang="he" data-title="ריצ'רד המינג" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%A9%E1%83%90%E1%83%A0%E1%83%93_%E1%83%B0%E1%83%90%E1%83%9B%E1%83%98%E1%83%9C%E1%83%92%E1%83%98" title="რიჩარდ ჰამინგი – Georgian" lang="ka" hreflang="ka" data-title="რიჩარდ ჰამინგი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Hungarian" lang="hu" hreflang="hu" data-title="Richard Hamming" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Malagasy" lang="mg" hreflang="mg" data-title="Richard Hamming" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%A9%E1%83%90%E1%83%A0%E1%83%93_%E1%83%B0%E1%83%94%E1%83%9B%E1%83%98%E1%83%9C%E1%83%92%E1%83%98" title="რიჩარდ ჰემინგი – Mingrelian" lang="xmf" hreflang="xmf" data-title="რიჩარდ ჰემინგი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B1%D9%8A%D8%AA%D8%B4%D8%A7%D8%B1%D8%AF_%D9%87%D8%A7%D9%85%D9%8A%D9%86%D8%AC" title="ريتشارد هامينج – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ريتشارد هامينج" 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/Richard_Hamming" title="Richard Hamming – Dutch" lang="nl" hreflang="nl" data-title="Richard Hamming" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AA%E3%83%81%E3%83%A3%E3%83%BC%E3%83%89%E3%83%BB%E3%83%8F%E3%83%9F%E3%83%B3%E3%82%B0" title="リチャード・ハミング – Japanese" lang="ja" hreflang="ja" data-title="リチャード・ハミング" 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/Richard_Hamming" title="Richard Hamming – Polish" lang="pl" hreflang="pl" data-title="Richard Hamming" 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/Richard_Hamming" title="Richard Hamming – Portuguese" lang="pt" hreflang="pt" data-title="Richard Hamming" 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/Richard_Hamming" title="Richard Hamming – Romanian" lang="ro" hreflang="ro" data-title="Richard Hamming" 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%A5%D1%8D%D0%BC%D0%BC%D0%B8%D0%BD%D0%B3,_%D0%A0%D0%B8%D1%87%D0%B0%D1%80%D0%B4_%D0%A3%D1%8D%D1%81%D0%BB%D0%B8" title="Хэмминг, Ричард Уэсли – Russian" lang="ru" hreflang="ru" data-title="Хэмминг, Ричард Уэсли" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Slovak" lang="sk" hreflang="sk" data-title="Richard Hamming" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B8%D1%87%D0%B0%D1%80%D0%B4_%D0%A5%D0%B5%D0%BC%D0%B8%D0%BD%D0%B3" title="Ричард Хеминг – Serbian" lang="sr" hreflang="sr" data-title="Ричард Хеминг" 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/Richard_Hamming" title="Richard Hamming – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Richard Hamming" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Finnish" lang="fi" hreflang="fi" data-title="Richard Hamming" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Swedish" lang="sv" hreflang="sv" data-title="Richard Hamming" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Richard_Hamming" title="Richard Hamming – Turkish" lang="tr" hreflang="tr" data-title="Richard Hamming" 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%A0%D1%96%D1%87%D0%B0%D1%80%D0%B4_%D0%93%D0%B5%D0%BC%D0%BC%D1%96%D0%BD%D0%B3" title="Річард Геммінг – Ukrainian" lang="uk" hreflang="uk" data-title="Річард Геммінг" 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/%E7%90%86%E6%9F%A5%E5%BE%B7%C2%B7%E8%A1%9B%E6%96%AF%E9%87%8C%C2%B7%E6%BC%A2%E6%98%8E" title="理查德·衛斯里·漢明 – Chinese" lang="zh" hreflang="zh" data-title="理查德·衛斯里·漢明" 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/Q92619#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit 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Click here for more information." src="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/19px-Symbol_support_vote.svg.png" decoding="async" width="19" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/29px-Symbol_support_vote.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/94/Symbol_support_vote.svg/39px-Symbol_support_vote.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span></div></div> </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">American mathematician and information theorist</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Richard_Hammond" title="Richard Hammond">Richard Hammond</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Richard Hamming</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Richard_Hamming.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/0/08/Richard_Hamming.jpg/220px-Richard_Hamming.jpg" decoding="async" width="220" height="288" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/0/08/Richard_Hamming.jpg 1.5x" data-file-width="276" data-file-height="361" /></a></span></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Richard Wesley Hamming</div><br /><span style="display:none">(<span class="bday">1915-02-11</span>)</span>February 11, 1915<br /><div style="display:inline" class="birthplace">Chicago, Illinois, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">January 7, 1998<span style="display:none">(1998-01-07)</span> (aged 82)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Monterey,_California" title="Monterey, California">Monterey, California</a>, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a> (B.S. 1937)<br /><a href="/wiki/University_of_Nebraska" class="mw-redirect" title="University of Nebraska">University of Nebraska</a> (M.A. 1939)<br /><a href="/wiki/University_of_Illinois_at_Urbana%E2%80%93Champaign" class="mw-redirect" title="University of Illinois at Urbana–Champaign">University of Illinois at Urbana–Champaign</a> (Ph.D. 1942)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><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><div class="hlist"><ul><li><a href="/wiki/Hamming_code" title="Hamming code">Hamming code</a></li><li><a href="/wiki/Hamming_window#Hamming_window" class="mw-redirect" title="Hamming window">Hamming window</a></li><li><a href="/wiki/Hamming_numbers" class="mw-redirect" title="Hamming numbers">Hamming numbers</a></li><li><a href="/wiki/Hamming_distance" title="Hamming distance">Hamming distance</a></li><li><a href="/wiki/Hamming_weight" title="Hamming weight">Hamming weight</a></li><li><a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a> <span style="font-size:85%;">(1968)</span><br /><a href="/wiki/IEEE_Emanuel_R._Piore_Award" title="IEEE Emanuel R. Piore Award">IEEE Emanuel R. Piore Award</a> <span style="font-size:85%;">(1979)</span><br /><a href="/wiki/Harold_Pender_Award" title="Harold Pender Award">Harold Pender Award</a> <small>(1981)</small> <br /> <a href="/wiki/IEEE_Richard_W._Hamming_Medal" title="IEEE Richard W. Hamming Medal">IEEE Hamming Medal</a> <small>(1988)</small></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">Mathematics</td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist"><ul><li><a href="/wiki/University_of_Louisville" title="University of Louisville">University of Louisville</a></li><li><a href="/wiki/Manhattan_Project" title="Manhattan Project">Manhattan Project</a> (Los Alamos Laboratory, <span style="font-size:85%;">(1945-1946)</span>)</li><li><a href="/wiki/Bell_Labs" title="Bell Labs">Bell Labs</a> <span style="font-size:85%;">(1946–1976)</span></li><li><a href="/wiki/Naval_Postgraduate_School" title="Naval Postgraduate School">Naval Postgraduate School</a> <span style="font-size:85%;">(1976–1998)</span></li></ul></div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i> Some Problems in the Boundary Value Theory of Linear Differential Equations </i> <span style="font-size:97%;">(1942)</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">Waldemar Trjitzinsky</td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Richard Wesley Hamming</b> (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for <a href="/wiki/Computer_engineering" title="Computer engineering">computer engineering</a> and telecommunications. His contributions include the <a href="/wiki/Hamming_code" title="Hamming code">Hamming code</a> (which makes use of a <a href="/wiki/Hamming_matrix" class="mw-redirect" title="Hamming matrix">Hamming matrix</a>), the <a href="/wiki/Hamming_window#Hamming_window" class="mw-redirect" title="Hamming window">Hamming window</a>, <a href="/wiki/Hamming_numbers" class="mw-redirect" title="Hamming numbers">Hamming numbers</a>, <a href="/wiki/Sphere-packing" class="mw-redirect" title="Sphere-packing">sphere-packing</a> (or <a href="/wiki/Hamming_bound" title="Hamming bound">Hamming bound</a>), <a href="/wiki/Hamming_graph" title="Hamming graph">Hamming graph</a> concepts, and the <a href="/wiki/Hamming_distance" title="Hamming distance">Hamming distance</a>. </p><p>Born in Chicago, Hamming attended <a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a>, <a href="/wiki/University_of_Nebraska" class="mw-redirect" title="University of Nebraska">University of Nebraska</a> and the <a href="/wiki/University_of_Illinois_at_Urbana%E2%80%93Champaign" class="mw-redirect" title="University of Illinois at Urbana–Champaign">University of Illinois at Urbana–Champaign</a>, where he wrote his doctoral thesis in mathematics under the supervision of <a href="/w/index.php?title=Waldemar_Trjitzinsky&action=edit&redlink=1" class="new" title="Waldemar Trjitzinsky (page does not exist)">Waldemar Trjitzinsky</a> (1901–1973). In April 1945, he joined the <a href="/wiki/Manhattan_Project" title="Manhattan Project">Manhattan Project</a> at the <a href="/wiki/Los_Alamos_Laboratory" class="mw-redirect" title="Los Alamos Laboratory">Los Alamos Laboratory</a>, where he programmed the <a href="/wiki/IBM" title="IBM">IBM</a> <a href="/wiki/Calculating_machines" class="mw-redirect" title="Calculating machines">calculating machines</a> that computed the solution to equations provided by the project's physicists. He left to join the <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Telephone Laboratories</a> in 1946. Over the next fifteen years, he was involved in nearly all of the laboratories' most prominent achievements. For his work, he received the <a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a> in 1968, being its third recipient.<sup id="cite_ref-TuringAward_1-0" class="reference"><a href="#cite_note-TuringAward-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>After retiring from the Bell Labs in 1976, Hamming took a position at the <a href="/wiki/Naval_Postgraduate_School" title="Naval Postgraduate School">Naval Postgraduate School</a> in <a href="/wiki/Monterey,_California" title="Monterey, California">Monterey, California</a>, where he worked as an <a href="/wiki/Adjunct_professor" title="Adjunct professor">adjunct professor</a> and <a href="/wiki/Senior_lecturer" title="Senior lecturer">senior lecturer</a> in <a href="/wiki/Computer_science" title="Computer science">computer science</a>, and devoted himself to teaching and writing books. He delivered his last lecture in December 1997, just a few weeks before he died from a heart attack on January 7, 1998. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_life">Early life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=1" title="Edit section: Early life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hamming was born in Chicago, Illinois, on February 11, 1915,<sup id="cite_ref-IEEE_2-0" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> the son of Richard J. Hamming, a credit manager, and Mabel G. Redfield.<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-0" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> His father was <a href="/wiki/Dutch_people" title="Dutch people">Dutch</a>, and his mother was a <a href="/wiki/Mayflower" title="Mayflower">Mayflower</a> descendant.<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> He grew up in Chicago, where he attended <a href="/wiki/Crane_High_School_(Chicago)" title="Crane High School (Chicago)">Crane Technical High School</a> and <a href="/wiki/Malcolm_X_College" title="Malcolm X College">Crane Junior College</a>.<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-1" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Hamming initially wanted to study engineering, but money was scarce during the <a href="/wiki/Great_Depression" title="Great Depression">Great Depression</a>, and the only scholarship offer he received came from the <a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a>, which had no engineering school. Instead, he became a science student, majoring in mathematics,<sup id="cite_ref-ACM_5-0" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and received his Bachelor of Science degree in 1937.<sup id="cite_ref-IEEE_2-1" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> He later considered this a fortunate turn of events. "As an engineer," he said, "I would have been the guy going down manholes instead of having the excitement of frontier research work."<sup id="cite_ref-IEEE_2-2" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>He went on to earn a Master of Arts degree from the <a href="/wiki/University_of_Nebraska" class="mw-redirect" title="University of Nebraska">University of Nebraska</a> in 1939, and then entered the <a href="/wiki/University_of_Illinois_at_Urbana%E2%80%93Champaign" class="mw-redirect" title="University of Illinois at Urbana–Champaign">University of Illinois at Urbana–Champaign</a>, where he wrote his doctoral thesis on <i>Some Problems in the Boundary Value Theory of Linear Differential Equations</i> under the supervision of <a href="/w/index.php?title=Waldemar_Trjitzinsky&action=edit&redlink=1" class="new" title="Waldemar Trjitzinsky (page does not exist)">Waldemar Trjitzinsky</a>.<sup id="cite_ref-ACM_5-1" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> His thesis was an extension of Trjitzinsky's work in that area. He looked at <a href="/wiki/Green%27s_function" title="Green's function">Green's function</a> and further developed <a href="/wiki/Jacob_Tamarkin" title="Jacob Tamarkin">Jacob Tamarkin</a>'s methods for obtaining <a href="/wiki/Characteristic_equation_(calculus)" title="Characteristic equation (calculus)">characteristic</a> solutions.<sup id="cite_ref-St_Andrews_6-0" class="reference"><a href="#cite_note-St_Andrews-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> While he was a graduate student, he discovered and read <a href="/wiki/George_Boole" title="George Boole">George Boole</a>'s <i><a href="/wiki/The_Laws_of_Thought" title="The Laws of Thought">The Laws of Thought</a></i>.<sup id="cite_ref-FOOTNOTEHamming1998643_7-0" class="reference"><a href="#cite_note-FOOTNOTEHamming1998643-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The University of Illinois at Urbana–Champaign awarded Hamming his Doctor of Philosophy in 1942, and he became an instructor in mathematics there. He married Wanda Little, a fellow student, on September 5, 1942,<sup id="cite_ref-ACM_5-2" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> immediately after she was awarded her own Master of Arts in English literature. They would remain married until his death, and had no children.<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-2" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In 1944, he became an assistant professor at the <a href="/wiki/J.B._Speed_School_of_Engineering" class="mw-redirect" title="J.B. Speed School of Engineering">J.B. Speed Scientific School</a> at the <a href="/wiki/University_of_Louisville" title="University of Louisville">University of Louisville</a> in <a href="/wiki/Louisville,_Kentucky" title="Louisville, Kentucky">Louisville, Kentucky</a>.<sup id="cite_ref-ACM_5-3" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Manhattan_Project">Manhattan Project</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=2" title="Edit section: Manhattan Project"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> With <a href="/wiki/World_War_II" title="World War II">World War II</a> still ongoing, Hamming left Louisville in April 1945 to work on the <a href="/wiki/Manhattan_Project" title="Manhattan Project">Manhattan Project</a> at the <a href="/wiki/Los_Alamos_Laboratory" class="mw-redirect" title="Los Alamos Laboratory">Los Alamos Laboratory</a>, in <a href="/wiki/Hans_Bethe" title="Hans Bethe">Hans Bethe</a>'s division, programming the <a href="/wiki/IBM" title="IBM">IBM</a> <a href="/wiki/Calculating_machines" class="mw-redirect" title="Calculating machines">calculating machines</a> that computed the solution to equations provided by the project's physicists. His wife Wanda soon followed, taking a job at Los Alamos as a <a href="/wiki/Human_computer" class="mw-redirect" title="Human computer">human computer</a>, working for Bethe and <a href="/wiki/Edward_Teller" title="Edward Teller">Edward Teller</a>.<sup id="cite_ref-ACM_5-4" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Hamming later recalled that:<style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p>Shortly before the first field test (you realize that no small scale experiment can be done—either you have a critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, "It is the probability that the test bomb will ignite the whole atmosphere." I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen—after all, there could be no experiments at the needed energy levels." He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, "What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?" I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, "Never mind, Hamming, no one will ever blame you."<sup id="cite_ref-FOOTNOTEHamming1998643_7-1" class="reference"><a href="#cite_note-FOOTNOTEHamming1998643-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p></blockquote> <p>Hamming remained at Los Alamos until 1946, when he accepted a post at the <a href="/wiki/Bell_Labs" title="Bell Labs">Bell Telephone Laboratories</a> (BTL). For the trip to New Jersey, he bought <a href="/wiki/Klaus_Fuchs" title="Klaus Fuchs">Klaus Fuchs</a>'s old car. When he later sold it just weeks before Fuchs was unmasked as a spy, the <a href="/wiki/FBI" class="mw-redirect" title="FBI">FBI</a> regarded the timing as suspicious enough to interrogate Hamming.<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-3" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Although Hamming described his role at Los Alamos as being that of a "computer janitor",<sup id="cite_ref-FOOTNOTEMorgan1998972_8-0" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998972-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> he saw <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulations</a> of experiments that would have been impossible to perform in a laboratory. "And when I had time to think about it," he later recalled, "I realized that it meant that science was going to be changed".<sup id="cite_ref-IEEE_2-3" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bell_Laboratories">Bell Laboratories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=3" title="Edit section: Bell Laboratories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hamming.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Hamming.jpg/240px-Hamming.jpg" decoding="async" width="240" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Hamming.jpg/360px-Hamming.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Hamming.jpg/480px-Hamming.jpg 2x" data-file-width="640" data-file-height="480" /></a><figcaption>A two-dimensional visualisation of the <a href="/wiki/Hamming_distance" title="Hamming distance">Hamming distance</a>. The color of each <a href="/wiki/Pixel" title="Pixel">pixel</a> indicates the <a href="/wiki/Hamming_distance" title="Hamming distance">Hamming distance</a> between the <a href="/wiki/Binary_representation" class="mw-redirect" title="Binary representation">binary representations</a> of its <i>x</i> and <i>y</i> coordinates, <a href="/wiki/Modulo_operation" class="mw-redirect" title="Modulo operation">modulo</a> 16, in the 16-color system.</figcaption></figure> <p>At the Bell Labs Hamming shared an office for a time with <a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a>. The Mathematical Research Department also included <a href="/wiki/John_Tukey" title="John Tukey">John Tukey</a> and Los Alamos veterans Donald Ling and <a href="/wiki/Brockway_McMillan" title="Brockway McMillan">Brockway McMillan</a>. Shannon, Ling, McMillan and Hamming came to call themselves the <a href="/wiki/Young_Turks_(Bell_Labs)" title="Young Turks (Bell Labs)">Young Turks</a>.<sup id="cite_ref-ACM_5-5" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> "We were first-class troublemakers," Hamming later recalled. "We did unconventional things in unconventional ways and still got valuable results. Thus management had to tolerate us and let us alone a lot of the time."<sup id="cite_ref-IEEE_2-4" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Although Hamming had been hired to work on <a href="/wiki/Elasticity_theory" class="mw-redirect" title="Elasticity theory">elasticity theory</a>, he still spent much of his time with the calculating machines.<sup id="cite_ref-FOOTNOTEMorgan1998972_8-1" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998972-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Before he went home on one Friday in 1947, he set the machines to perform a long and complex series of calculations over the weekend, only to find when he arrived on Monday morning that an error had occurred early in the process and the calculation had errored off.<sup id="cite_ref-Additional_Materials_9-0" class="reference"><a href="#cite_note-Additional_Materials-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Digital machines manipulated information as sequences of zeroes and ones, units of information that Tukey would christen "<a href="/wiki/Bit" title="Bit">bits</a>".<sup id="cite_ref-FOOTNOTEShannon1948379_10-0" class="reference"><a href="#cite_note-FOOTNOTEShannon1948379-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> If a single bit in a sequence was wrong, then the whole sequence would be. To detect this, a <a href="/wiki/Parity_bit" title="Parity bit">parity bit</a> was used to verify the correctness of each sequence. "If the computer can tell when an error has occurred," Hamming reasoned, "surely there is a way of telling where the error is so that the computer can correct the error itself."<sup id="cite_ref-Additional_Materials_9-1" class="reference"><a href="#cite_note-Additional_Materials-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Hamming set himself the task of solving this problem,<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-4" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> which he realised would have an enormous range of applications. Each bit can only be a zero or a one, so if you know which bit is wrong, then it can be corrected. In a landmark paper published in 1950, he introduced a concept of the number of positions in which two code words differ, and therefore how many changes are required to transform one <a href="/wiki/Code_word_(communication)" title="Code word (communication)">code word</a> into another, which is today known as the <a href="/wiki/Hamming_distance" title="Hamming distance">Hamming distance</a>.<sup id="cite_ref-FOOTNOTEMorgan1998973–975_11-0" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998973–975-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Hamming thereby created a family of mathematical <a href="/wiki/Error-correcting_code" class="mw-redirect" title="Error-correcting code">error-correcting codes</a>, which are called <a href="/wiki/Hamming_code" title="Hamming code">Hamming codes</a>. This not only solved an important problem in telecommunications and computer science, it opened up a whole new field of study.<sup id="cite_ref-FOOTNOTEMorgan1998973–975_11-1" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998973–975-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEHamming1950147–160_12-0" class="reference"><a href="#cite_note-FOOTNOTEHamming1950147–160-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Hamming_bound" title="Hamming bound">Hamming bound</a>, also known as the sphere-packing or volume bound is a limit on the parameters of an arbitrary <a href="/wiki/Block_code" title="Block code">block code</a>. It is from an interpretation in terms of <a href="/wiki/Sphere_packing" title="Sphere packing">sphere packing</a> in the Hamming distance into the <a href="/wiki/Space_(mathematics)" title="Space (mathematics)">space</a> of all possible words. It gives an important limitation on the <a href="/wiki/Efficiency" title="Efficiency">efficiency</a> with which any error-correcting code can utilize the space in which its code words are embedded. A code which attains the Hamming bound is said to be a perfect code. Hamming codes are perfect codes.<sup id="cite_ref-FOOTNOTELingXing200482–88_13-0" class="reference"><a href="#cite_note-FOOTNOTELingXing200482–88-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEPless198221–24_14-0" class="reference"><a href="#cite_note-FOOTNOTEPless198221–24-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Returning to <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a>, Hamming studied means of numerically integrating them. A popular approach at the time was Milne's Method, attributed to <a href="/wiki/Edward_Arthur_Milne" title="Edward Arthur Milne">Arthur Milne</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This had the drawback of being unstable, so that under certain conditions the result could be swamped by roundoff noise. Hamming developed an improved version, the Hamming predictor-corrector. This was in use for many years, but has since been superseded by the <a href="/wiki/Linear_multistep_method" title="Linear multistep method">Adams method</a>.<sup id="cite_ref-FOOTNOTEMorgan1998975_16-0" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998975-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> He did extensive research into digital <a href="/wiki/Filter_(signal_processing)" title="Filter (signal processing)">filters</a>, devising a new filter, the <a href="/wiki/Hamming_window" class="mw-redirect" title="Hamming window">Hamming window</a>, and eventually writing an entire book on the subject, <i>Digital Filters</i> (1977).<sup id="cite_ref-FOOTNOTEMorgan1998976–977_17-0" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998976–977-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>During the 1950s, he programmed one of the earliest computers, the <a href="/wiki/IBM_650" title="IBM 650">IBM 650</a>, and with <a href="/wiki/Ruth_A._Weiss" title="Ruth A. Weiss">Ruth A. Weiss</a> developed the <a href="/wiki/L2_(programming_language)" class="mw-redirect" title="L2 (programming language)">L2 programming language</a>, one of the earliest computer languages, in 1956. It was widely used within the Bell Labs, and also by external users, who knew it as Bell 2. It was superseded by <a href="/wiki/Fortran" title="Fortran">Fortran</a> when the Bell Labs' IBM 650 were replaced by the <a href="/wiki/IBM_704" title="IBM 704">IBM 704</a> in 1957.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>In <i>A Discipline of Programming</i> (1976), <a href="/wiki/Edsger_Dijkstra" class="mw-redirect" title="Edsger Dijkstra">Edsger Dijkstra</a> attributed to Hamming the problem of efficiently finding <a href="/wiki/Regular_numbers" class="mw-redirect" title="Regular numbers">regular numbers</a>.<sup id="cite_ref-FOOTNOTEDijkstra1976129–134_19-0" class="reference"><a href="#cite_note-FOOTNOTEDijkstra1976129–134-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The problem became known as "Hamming's problem", and the regular numbers are often referred to as Hamming numbers in Computer Science, although he did not discover them.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>Throughout his time at Bell Labs, Hamming avoided management responsibilities. He was promoted to management positions several times, but always managed to make these only temporary. "I knew in a sense that by avoiding management," he later recalled, "I was not doing my duty by the organization. That is one of my biggest failures."<sup id="cite_ref-IEEE_2-5" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Later_life">Later life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=4" title="Edit section: Later life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> Hamming served as president of the <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a> from 1958 to 1960.<sup id="cite_ref-FOOTNOTEMorgan1998972_8-2" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998972-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> In 1960, he predicted that one day half of the Bell Labs budget would be spent on computing. None of his colleagues thought that it would ever be so high, but his forecast actually proved to be too low.<sup id="cite_ref-FOOTNOTEMorgan1998977_21-0" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998977-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> His philosophy on scientific computing appeared as the motto of his <i>Numerical Methods for Scientists and Engineers</i> (1962): <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>The purpose of computing is insight, not numbers.<sup id="cite_ref-FOOTNOTEHamming1962vii,_276,_395_22-0" class="reference"><a href="#cite_note-FOOTNOTEHamming1962vii,_276,_395-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p></blockquote> <p>In later life, Hamming became interested in teaching. Between 1960 and 1976, when he left Bell Labs, he held visiting or adjunct professorships at <a href="/wiki/Stanford_University" title="Stanford University">Stanford University</a>, <a href="/wiki/Stevens_Institute_of_Technology" title="Stevens Institute of Technology">Stevens Institute of Technology</a>, the <a href="/wiki/City_College_of_New_York" title="City College of New York">City College of New York</a>, the <a href="/wiki/University_of_California_at_Irvine" class="mw-redirect" title="University of California at Irvine">University of California at Irvine</a> and <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a>.<sup id="cite_ref-FOOTNOTECarnes2005220–221TveitoBruasetLysne200959_23-0" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221TveitoBruasetLysne200959-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> As a Young Turk, Hamming had resented older scientists who had used up space and resources that would have been put to much better use by the young Turks. Looking at a commemorative poster of the Bell Labs' valued achievements, he noted that he had worked on or been associated with nearly all of those listed in the first half of his career at Bell Labs, but none in the second. He therefore resolved to retire in 1976, after thirty years.<sup id="cite_ref-IEEE_2-6" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>In 1976 he moved to the <a href="/wiki/Naval_Postgraduate_School" title="Naval Postgraduate School">Naval Postgraduate School</a> in <a href="/wiki/Monterey,_California" title="Monterey, California">Monterey, California</a>, where he worked as an <a href="/wiki/Adjunct_professor" title="Adjunct professor">adjunct professor</a> and <a href="/wiki/Senior_lecturer" title="Senior lecturer">senior lecturer</a> in <a href="/wiki/Computer_science" title="Computer science">computer science</a>.<sup id="cite_ref-FOOTNOTECarnes2005220–221_3-5" class="reference"><a href="#cite_note-FOOTNOTECarnes2005220–221-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> He gave up research, and concentrated on teaching and writing books.<sup id="cite_ref-ACM_5-6" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> He noted that: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The way mathematics is currently taught it is exceedingly dull. In the calculus book we are currently using on my campus, I found no single problem whose answer I felt the student would care about! The problems in the text have the dignity of solving a crossword puzzle – hard to be sure, but the result is of no significance in life.<sup id="cite_ref-ACM_5-7" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p></blockquote> <p>Hamming attempted to rectify the situation with a new text, <i>Methods of Mathematics Applied to Calculus, Probability, and Statistics</i> (1985).<sup id="cite_ref-ACM_5-8" class="reference"><a href="#cite_note-ACM-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In 1993, he remarked that "when I left BTL, I knew that that was the end of my scientific career. When I retire from here, in another sense, it's really the end."<sup id="cite_ref-IEEE_2-7" class="reference"><a href="#cite_note-IEEE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> And so it proved. He became <a href="/wiki/Professor_Emeritus" class="mw-redirect" title="Professor Emeritus">Professor Emeritus</a> in June 1997,<sup id="cite_ref-obit_24-0" class="reference"><a href="#cite_note-obit-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> and delivered his last lecture in December 1997, just a few weeks before his death from a heart attack on January 7, 1998.<sup id="cite_ref-FOOTNOTEMorgan1998972_8-3" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998972-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> He was survived by his wife Wanda.<sup id="cite_ref-obit_24-1" class="reference"><a href="#cite_note-obit-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Hamming's final recorded lecture series<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> is maintained by <a href="/wiki/Naval_Postgraduate_School" title="Naval Postgraduate School">Naval Postgraduate School</a> along with ongoing work<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> that preserves his insights and extends his legacy. </p> <div class="mw-heading mw-heading2"><h2 id="Awards_and_professional_recognition">Awards and professional recognition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=5" title="Edit section: Awards and professional recognition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Turing_Award" title="Turing Award">Turing Award</a>, <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a>, 1968.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></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-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><br /> 1979 <i>"For introduction of error correcting codes, pioneering work in operating systems and programming languages, and the advancement of numerical computation."</i> <br /></li> <li>Member of the <a href="/wiki/National_Academy_of_Engineering" title="National Academy of Engineering">National Academy of Engineering</a>, 1980.<sup id="cite_ref-NAE_29-0" class="reference"><a href="#cite_note-NAE-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Harold_Pender_Award" title="Harold Pender Award">Harold Pender Award</a>, <a href="/wiki/University_of_Pennsylvania" title="University of Pennsylvania">University of Pennsylvania</a>, 1981.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/IEEE_Richard_W._Hamming_Medal" title="IEEE Richard W. Hamming Medal">IEEE Richard W. Hamming Medal</a>, 1988.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li>Fellow of the <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a>, 1994.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Eduard_Rhein_Award" class="mw-redirect" title="Eduard Rhein Award">Basic Research Award</a>, <a href="/wiki/Eduard_Rhein_Foundation" title="Eduard Rhein Foundation">Eduard Rhein Foundation</a>, 1996.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li></ul> <p>The <a href="/wiki/IEEE_Richard_W._Hamming_Medal" title="IEEE Richard W. Hamming Medal">IEEE Richard W. Hamming Medal</a>, named after him, is an award given annually by the <a href="/wiki/Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">Institute of Electrical and Electronics Engineers</a> (IEEE), for "exceptional contributions to <a href="/wiki/Information_sciences" class="mw-redirect" title="Information sciences">information sciences</a>, <a href="/wiki/Information_systems" class="mw-redirect" title="Information systems">systems</a> and <a href="/wiki/Information_technology" title="Information technology">technology</a>", and he was the first recipient of this medal.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> The reverse side of the medal depicts a Hamming parity check matrix for a Hamming error-correcting code.<sup id="cite_ref-FOOTNOTEMorgan1998972_8-4" class="reference"><a href="#cite_note-FOOTNOTEMorgan1998972-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=6" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation book cs1">Hamming, Richard W. (1962). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/numericalmethods0000hamm"><i>Numerical Methods for Scientists and Engineers</i></a></span>. New York: McGraw-Hill.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+Methods+for+Scientists+and+Engineers&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=1962&rft.aulast=Hamming&rft.aufirst=Richard+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnumericalmethods0000hamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span>; <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Numerical_Methods_for_Scientists_and_Eng.html?id=Y3YSCmWBVwoC">second edition 1973</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1968" class="citation book cs1">— (1968). <i>Calculus and the Computer Revolution</i>. Boston: Houghton-Mifflin.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+and+the+Computer+Revolution&rft.place=Boston&rft.pub=Houghton-Mifflin&rft.date=1968&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1971" class="citation book cs1">— (1971). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoap0000hamm"><i>Introduction To Applied Numerical Analysis</i></a></span>. New York: McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780070258891" title="Special:BookSources/9780070258891"><bdi>9780070258891</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+To+Applied+Numerical+Analysis&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=1971&rft.isbn=9780070258891&rft.aulast=Hamming&rft.aufirst=Richard+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoap0000hamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span>; Hemisphere Pub. Corp reprint 1989; <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Introduction_to_Applied_Numerical_Analys.html?id=osnZ9eiO-ngC">Dover reprint 2012</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1972" class="citation book cs1">— (1972). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/computerssociety0000hamm"><i>Computers and Society</i></a></span>. New York: McGraw-Hill.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computers+and+Society&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=1972&rft.aulast=Hamming&rft.aufirst=Richard+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcomputerssociety0000hamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1977" class="citation book cs1">— (1977). <i>Digital Filters</i>. Englewood Cliffs, New Jersey: Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-212571-0" title="Special:BookSources/978-0-13-212571-0"><bdi>978-0-13-212571-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Filters&rft.place=Englewood+Cliffs%2C+New+Jersey&rft.pub=Prentice+Hall&rft.date=1977&rft.isbn=978-0-13-212571-0&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span>; second edition 1983; <a rel="nofollow" class="external text" href="https://books.google.com/books/about/Digital_Filters.html?id=GQv9UOdeW9cC">third edition 1989</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1980" class="citation book cs1">— (1980). <i>The Unreasonable Effectiveness of Mathematics</i>. Washington, D.C.: The American Mathematical Monthly.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Unreasonable+Effectiveness+of+Mathematics&rft.place=Washington%2C+D.C.&rft.pub=The+American+Mathematical+Monthly&rft.date=1980&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1980" class="citation book cs1">— (1980). <i>Coding and Information Theory</i>. Englewood Cliffs, New Jersey: Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-139139-0" title="Special:BookSources/978-0-13-139139-0"><bdi>978-0-13-139139-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Coding+and+Information+Theory&rft.place=Englewood+Cliffs%2C+New+Jersey&rft.pub=Prentice+Hall&rft.date=1980&rft.isbn=978-0-13-139139-0&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span>; second edition 1986.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1985" class="citation book cs1">— (1985). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/methodsofmathema0000hamm"><i>Methods of Mathematics Applied to Calculus, Probability, and Statistics</i></a></span>. Englewood Cliffs, New Jersey: Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-578899-8" title="Special:BookSources/978-0-13-578899-8"><bdi>978-0-13-578899-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Methods+of+Mathematics+Applied+to+Calculus%2C+Probability%2C+and+Statistics&rft.place=Englewood+Cliffs%2C+New+Jersey&rft.pub=Prentice+Hall&rft.date=1985&rft.isbn=978-0-13-578899-8&rft.aulast=Hamming&rft.aufirst=Richard+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmethodsofmathema0000hamm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1991" class="citation book cs1">— (1991). <i>The Art of Probability for Scientists and Engineers</i>. Redwood City, California: Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-51058-4" title="Special:BookSources/978-0-201-51058-4"><bdi>978-0-201-51058-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Art+of+Probability+for+Scientists+and+Engineers&rft.place=Redwood+City%2C+California&rft.pub=Addison-Wesley&rft.date=1991&rft.isbn=978-0-201-51058-4&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1997" class="citation book cs1">— (1997). <i><a href="/wiki/The_Art_of_Doing_Science_and_Engineering" title="The Art of Doing Science and Engineering">The Art of Doing Science and Engineering</a>: Learning to Learn</i>. Australia: Gordon and Breach. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-5699-500-3" title="Special:BookSources/978-90-5699-500-3"><bdi>978-90-5699-500-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Art+of+Doing+Science+and+Engineering%3A+Learning+to+Learn&rft.place=Australia&rft.pub=Gordon+and+Breach&rft.date=1997&rft.isbn=978-90-5699-500-3&rft.aulast=Hamming&rft.aufirst=Richard+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Lectures">Lectures</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=7" title="Edit section: Lectures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1991 - <a rel="nofollow" class="external text" href="https://library.ucsd.edu/dc/object/bb4096852z">You and Your Research</a>. Lecture sponsored by the Dept. of Electrical and Computer engineering, University of California, San Diego. Electrical and Computer Engineering Distinguished Lecture Series. Digital Object Made Available by Special Collections & Archives, UC San Diego.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Richard_Hamming&action=edit&section=8" title="Edit section: Notes"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-TuringAward-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-TuringAward_1-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://amturing.acm.org/award_winners/hamming_1000652.cfm">"A.M. Turing Award, Richard W. Hamming"</a>. <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a><span class="reference-accessdate">. Retrieved <span class="nowrap">August 1,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A.M.+Turing+Award%2C+Richard+W.+Hamming&rft.pub=Association+for+Computing+Machinery&rft_id=https%3A%2F%2Famturing.acm.org%2Faward_winners%2Fhamming_1000652.cfm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></span> </li> <li id="cite_note-IEEE-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-IEEE_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-IEEE_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-IEEE_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-IEEE_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-IEEE_2-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-IEEE_2-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-IEEE_2-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-IEEE_2-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140903102828/https://www.computer.org/computer-pioneers/hamming.html">"Computer Pioneers – Richard Wesley Hamming"</a>. <a href="/wiki/IEEE_Computer_Society" title="IEEE Computer Society">IEEE Computer Society</a>. Archived from <a rel="nofollow" class="external text" href="http://computer.org/computer-pioneers/hamming.html">the original</a> on September 3, 2014<span class="reference-accessdate">. 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Retrieved <span class="nowrap">February 5,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ACM+Fellows+%E2%80%93+H&rft.pub=Association+for+Computing+Machinery&rft_id=http%3A%2F%2Ffellows.acm.org%2Fhomepage.cfm%3Falpha%3DH%26srt%3Dalpha&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110718233021/http://www.eduard-rhein-stiftung.de/html/Preistraeger_e.html">"Award Winners (chronological)"</a>. <a href="/wiki/Eduard_Rhein_Foundation" title="Eduard Rhein Foundation">Eduard Rhein Foundation</a>. 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Archived from <a rel="nofollow" class="external text" href="http://www.ieee.org/about/awards/medals/hamming.html">the original</a> on April 7, 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">February 5,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=IEEE+Richard+W.+Hamming+Medal&rft.pub=IEEE&rft_id=http%3A%2F%2Fwww.ieee.org%2Fabout%2Fawards%2Fmedals%2Fhamming.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></span> </li> </ol></div> <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=Richard_Hamming&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarnes2005" class="citation book cs1">Carnes, Mark C. (2005). <i>American National Biography. Supplement 2</i>. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-522202-9" title="Special:BookSources/978-0-19-522202-9"><bdi>978-0-19-522202-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=American+National+Biography.+Supplement+2.&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=2005&rft.isbn=978-0-19-522202-9&rft.aulast=Carnes&rft.aufirst=Mark+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDijkstra1976" class="citation book cs1"><a href="/wiki/Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Dijkstra, Edsger W.</a> (1976). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/disciplineofprog0000dijk"><i>A Discipline of Programming</i></a></span>. Englewood Cliffs, New Jersey: Prentice-Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-215871-8" title="Special:BookSources/978-0-13-215871-8"><bdi>978-0-13-215871-8</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">September 2,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Discipline+of+Programming&rft.place=Englewood+Cliffs%2C+New+Jersey&rft.pub=Prentice-Hall&rft.date=1976&rft.isbn=978-0-13-215871-8&rft.aulast=Dijkstra&rft.aufirst=Edsger+W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fdisciplineofprog0000dijk&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1950" class="citation journal cs1">Hamming, Richard W. (1950). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060525060427/http://www.caip.rutgers.edu/~bushnell/dsdwebsite/hamming.pdf">"Error detecting and error correcting codes"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Bell_System_Technical_Journal" class="mw-redirect" title="Bell System Technical Journal">Bell System Technical Journal</a></i>. <b>29</b> (2): <span class="nowrap">147–</span>160. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fj.1538-7305.1950.tb00463.x">10.1002/j.1538-7305.1950.tb00463.x</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10945%2F46756">10945/46756</a>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0035935">0035935</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:61141773">61141773</a>. Archived from <a rel="nofollow" class="external text" href="http://www.caip.rutgers.edu/~bushnell/dsdwebsite/hamming.pdf">the original</a> <span class="cs1-format">(PDF)</span> on May 25, 2006.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bell+System+Technical+Journal&rft.atitle=Error+detecting+and+error+correcting+codes&rft.volume=29&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E147-%3C%2Fspan%3E160&rft.date=1950&rft_id=info%3Ahdl%2F10945%2F46756&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D0035935%23id-name%3DMR&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A61141773%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1002%2Fj.1538-7305.1950.tb00463.x&rft.aulast=Hamming&rft.aufirst=Richard+W.&rft_id=http%3A%2F%2Fwww.caip.rutgers.edu%2F~bushnell%2Fdsdwebsite%2Fhamming.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1962" class="citation book cs1">Hamming, Richard (1962). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/numericalmethods00hamm_0"><i>Numerical Methods for Scientists and Engineers</i></a></span>. New York: McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-65241-2" title="Special:BookSources/978-0-486-65241-2"><bdi>978-0-486-65241-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+Methods+for+Scientists+and+Engineers&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=1962&rft.isbn=978-0-486-65241-2&rft.aulast=Hamming&rft.aufirst=Richard&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnumericalmethods00hamm_0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1980" class="citation journal cs1">Hamming, Richard (1980). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070203151259/http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html">"The Unreasonable Effectiveness of Mathematics"</a>. <i><a href="/wiki/American_Mathematical_Monthly" class="mw-redirect" title="American Mathematical Monthly">American Mathematical Monthly</a></i>. <b>87</b> (2): <span class="nowrap">81–</span>90. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2321982">10.2307/2321982</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/10945%2F55827">10945/55827</a></span>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2321982">2321982</a>. Archived from <a rel="nofollow" class="external text" href="http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html">the original</a> on February 3, 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">September 12,</span> 2006</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Mathematical+Monthly&rft.atitle=The+Unreasonable+Effectiveness+of+Mathematics&rft.volume=87&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E81-%3C%2Fspan%3E90&rft.date=1980&rft_id=info%3Ahdl%2F10945%2F55827&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2321982%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F2321982&rft.aulast=Hamming&rft.aufirst=Richard&rft_id=http%3A%2F%2Fwww.dartmouth.edu%2F~matc%2FMathDrama%2Freading%2FHamming.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamming1998" class="citation journal cs1">Hamming, Richard (August–September 1998). <a rel="nofollow" class="external text" href="https://www.dropbox.com/s/xf0efns895cw98x/1998-hamming.pdf">"Mathematics on a Distant Planet"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/American_Mathematical_Monthly" class="mw-redirect" title="American Mathematical Monthly">American Mathematical Monthly</a></i>. <b>105</b> (7): <span class="nowrap">640–</span>650. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2589247">10.2307/2589247</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2589247">2589247</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Mathematical+Monthly&rft.atitle=Mathematics+on+a+Distant+Planet&rft.volume=105&rft.issue=7&rft.pages=%3Cspan+class%3D%22nowrap%22%3E640-%3C%2Fspan%3E650&rft.date=1998-08%2F1998-09&rft_id=info%3Adoi%2F10.2307%2F2589247&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2589247%23id-name%3DJSTOR&rft.aulast=Hamming&rft.aufirst=Richard&rft_id=https%3A%2F%2Fwww.dropbox.com%2Fs%2Fxf0efns895cw98x%2F1998-hamming.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLingXing2004" class="citation book cs1">Ling, San; Xing, Chaoping (2004). <i>Coding Theory: a First Course</i>. Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-82191-9" title="Special:BookSources/978-0-521-82191-9"><bdi>978-0-521-82191-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Coding+Theory%3A+a+First+Course&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-0-521-82191-9&rft.aulast=Ling&rft.aufirst=San&rft.au=Xing%2C+Chaoping&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorgan1998" class="citation journal cs1">Morgan, Samuel P. (September 1998). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/199808/mem-morgan.pdf">"Richard Wesley Hamming (1915–1998)"</a> <span class="cs1-format">(PDF)</span>. <i>Notices of the AMS</i>. <b>45</b> (8): <span class="nowrap">972–</span>977. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0002-9920">0002-9920</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20040215065757/http://www.ams.org/notices/199808/mem-morgan.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on February 15, 2004<span class="reference-accessdate">. Retrieved <span class="nowrap">August 30,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notices+of+the+AMS&rft.atitle=Richard+Wesley+Hamming+%281915%E2%80%931998%29&rft.volume=45&rft.issue=8&rft.pages=%3Cspan+class%3D%22nowrap%22%3E972-%3C%2Fspan%3E977&rft.date=1998-09&rft.issn=0002-9920&rft.aulast=Morgan&rft.aufirst=Samuel+P.&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F199808%2Fmem-morgan.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPless1982" class="citation book cs1"><a href="/wiki/Vera_Pless" title="Vera Pless">Pless, Vera</a> (1982). <a href="/wiki/Introduction_to_the_Theory_of_Error-Correcting_Codes" title="Introduction to the Theory of Error-Correcting Codes"><i>Introduction to the Theory of Error-Correcting Codes</i></a>. New York: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-08684-0" title="Special:BookSources/978-0-471-08684-0"><bdi>978-0-471-08684-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+the+Theory+of+Error-Correcting+Codes&rft.place=New+York&rft.pub=Wiley&rft.date=1982&rft.isbn=978-0-471-08684-0&rft.aulast=Pless&rft.aufirst=Vera&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShannon1948" class="citation journal cs1">Shannon, Claude (July 1948). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150328051218/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf">"A Mathematical Theory of Communication"</a> <span class="cs1-format">(PDF)</span>. <i>The Bell System Technical Journal</i>. <b>27</b> (3): <span class="nowrap">379–</span>423, <span class="nowrap">623–</span>656. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fj.1538-7305.1948.tb01338.x">10.1002/j.1538-7305.1948.tb01338.x</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/11858%2F00-001M-0000-002C-4314-2">11858/00-001M-0000-002C-4314-2</a></span>. Archived from <a rel="nofollow" class="external text" href="http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf">the original</a> <span class="cs1-format">(PDF)</span> on March 28, 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">September 2,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Bell+System+Technical+Journal&rft.atitle=A+Mathematical+Theory+of+Communication&rft.volume=27&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E379-%3C%2Fspan%3E423%2C+%3Cspan+class%3D%22nowrap%22%3E623-%3C%2Fspan%3E656&rft.date=1948-07&rft_id=info%3Ahdl%2F11858%2F00-001M-0000-002C-4314-2&rft_id=info%3Adoi%2F10.1002%2Fj.1538-7305.1948.tb01338.x&rft.aulast=Shannon&rft.aufirst=Claude&rft_id=http%3A%2F%2Fcm.bell-labs.com%2Fcm%2Fms%2Fwhat%2Fshannonday%2Fshannon1948.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTveitoBruasetLysne2009" class="citation book cs1">Tveito, Aslak; Bruaset, Are Magnus; Lysne, Olav (2009). <i>Simula Research Laboratory: By Thinking Constantly about it</i>. New York: Springer Science & Business Media. p. 59. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-01156-6" title="Special:BookSources/978-3-642-01156-6"><bdi>978-3-642-01156-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Simula+Research+Laboratory%3A+By+Thinking+Constantly+about+it&rft.place=New+York&rft.pages=59&rft.pub=Springer+Science+%26+Business+Media&rft.date=2009&rft.isbn=978-3-642-01156-6&rft.aulast=Tveito&rft.aufirst=Aslak&rft.au=Bruaset%2C+Are+Magnus&rft.au=Lysne%2C+Olav&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li></ul> <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=Richard_Hamming&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><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="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Richard_Hamming" class="extiw" title="q:Special:Search/Richard Hamming">Richard Hamming</a></b></i>.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" class="mw-redirect" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Hamming.html">"Richard Hamming"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Richard+Hamming&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FHamming.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARichard+Hamming" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=4556">Richard Hamming</a> at the 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Reed">Irving S. Reed</a> (1989)</span></li> <li><span class="nowrap"><a href="/wiki/Dennis_Ritchie" title="Dennis Ritchie">Dennis Ritchie</a> / <a href="/wiki/Ken_Thompson" title="Ken Thompson">Ken Thompson</a> (1990)</span></li> <li><span class="nowrap"><a href="/wiki/Elwyn_Berlekamp" title="Elwyn Berlekamp">Elwyn Berlekamp</a> (1991)</span></li> <li><span class="nowrap"><a href="/wiki/Lotfi_A._Zadeh" title="Lotfi A. Zadeh">Lotfi A. Zadeh</a> (1992)</span></li> <li><span class="nowrap"><a href="/wiki/Jorma_Rissanen" title="Jorma Rissanen">Jorma Rissanen</a> (1993)</span></li> <li><span class="nowrap"><a href="/wiki/Gottfried_Ungerboeck" title="Gottfried Ungerboeck">Gottfried Ungerboeck</a> (1994)</span></li> <li><span class="nowrap"><a href="/wiki/Yaakov_Ziv" class="mw-redirect" title="Yaakov Ziv">Jacob Ziv</a> (1995)</span></li> <li><span class="nowrap"><a href="/wiki/Mark_Semenovich_Pinsker" class="mw-redirect" title="Mark Semenovich Pinsker">Mark Semenovich Pinsker</a> (1996)</span></li> <li><span class="nowrap"><a href="/wiki/Thomas_M._Cover" title="Thomas M. Cover">Thomas M. Cover</a> (1997)</span></li> <li><span class="nowrap"><a href="/wiki/David_D._Clark" title="David D. Clark">David D. Clark</a> (1998)</span></li> <li><span class="nowrap"><a href="/wiki/David_A._Huffman" title="David A. Huffman">David A. Huffman</a> (1999)</span></li> <li><span class="nowrap"><a href="/wiki/Solomon_W._Golomb" title="Solomon W. Golomb">Solomon W. Golomb</a> (2000)</span></li> <li><span class="nowrap"><a href="/wiki/Alexander_G._Fraser" title="Alexander G. Fraser">Alexander G. Fraser</a> (2001)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Elias" title="Peter Elias">Peter Elias</a> (2002)</span></li> <li><span class="nowrap"><a href="/wiki/Claude_Berrou" title="Claude Berrou">Claude Berrou</a> / <a href="/wiki/Alain_Glavieux" title="Alain Glavieux">Alain Glavieux</a> (2003)</span></li> <li><span class="nowrap"><a href="/wiki/Jack_Wolf" title="Jack Wolf">Jack K. Wolf</a> (2004)</span></li> <li><span class="nowrap"><a href="/wiki/Neil_Sloane" title="Neil Sloane">Neil Sloane</a> (2005)</span></li> <li><span class="nowrap"><a href="/wiki/Vladimir_Levenshtein" title="Vladimir Levenshtein">Vladimir Levenshtein</a> (2006)</span></li> <li><span class="nowrap"><a href="/wiki/Abraham_Lempel" title="Abraham Lempel">Abraham Lempel</a> (2007)</span></li> <li><span class="nowrap"><a href="/wiki/Sergio_Verd%C3%BA" title="Sergio Verdú">Sergio Verdú</a> (2008)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Franaszek" title="Peter Franaszek">Peter Franaszek</a> (2009)</span></li> <li><span class="nowrap"><a href="/wiki/Whitfield_Diffie" title="Whitfield Diffie">Whitfield Diffie</a> / <a href="/wiki/Martin_Hellman" title="Martin Hellman">Martin Hellman</a> / <a href="/wiki/Ralph_Merkle" title="Ralph Merkle">Ralph Merkle</a> (2010)</span></li> <li><span class="nowrap"><a href="/wiki/Toby_Berger" title="Toby Berger">Toby Berger</a> (2011)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_Luby" title="Michael Luby">Michael Luby</a> / <a href="/wiki/Amin_Shokrollahi" title="Amin Shokrollahi">Amin Shokrollahi</a> (2012)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Calderbank" title="Robert Calderbank">Robert Calderbank</a> (2013)</span></li> <li><span class="nowrap">Thomas Richardson / <a href="/wiki/R%C3%BCdiger_Urbanke" title="Rüdiger Urbanke">Rüdiger Urbanke</a> (2014)</span></li> <li><span class="nowrap"><a href="/wiki/Imre_Csisz%C3%A1r" title="Imre Csiszár">Imre Csiszár</a> (2015)</span></li> <li><span class="nowrap"><a href="/wiki/Abbas_El_Gamal" title="Abbas El Gamal">Abbas El Gamal</a> (2016)</span></li> <li><span class="nowrap"><a href="/wiki/Shlomo_Shamai" title="Shlomo Shamai">Shlomo Shamai</a> (2017)</span></li> <li><span class="nowrap"><a href="/wiki/Erdal_Ar%C4%B1kan" title="Erdal Arıkan">Erdal Arıkan</a> (2018)</span></li> <li><span class="nowrap"><a href="/wiki/David_Tse" title="David Tse">David Tse</a> (2019)</span></li> <li><span class="nowrap"><a href="/wiki/Cynthia_Dwork" title="Cynthia Dwork">Cynthia Dwork</a> (2020)</span></li> <li><span class="nowrap"><a href="/wiki/Raymond_W._Yeung" title="Raymond W. Yeung">Raymond Yeung</a> (2021)</span></li> <li><span class="nowrap"><a href="/wiki/Madhu_Sudan" title="Madhu Sudan">Madhu Sudan</a> (2022)</span></li> <li><span class="nowrap"><a href="/wiki/Frank_Kschischang" title="Frank Kschischang">Frank Kschischang</a> (2023)</span></li> <li><span class="nowrap">Alexander Barg (2024)</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="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"><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: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 class="mw-selflink selflink">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 href="/wiki/William_Kahan" title="William Kahan">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> 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