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Available in 30 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-30" 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">30 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A7%D9%86%D9%88%D9%8A%D9%84_%D8%A8%D9%84%D9%88%D9%85" title="مانويل بلوم – Arabic" lang="ar" hreflang="ar" data-title="مانويل بلوم" 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/Manuel_Bl%C3%BCm" title="Manuel Blüm – Azerbaijani" lang="az" hreflang="az" data-title="Manuel Blüm" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%D9%86%D9%88%D8%A6%D9%84_%D8%A8%D9%84%D9%88%D9%85" title="مانوئل بلوم – South Azerbaijani" lang="azb" hreflang="azb" data-title="مانوئل بلوم" 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%AE%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A8%E0%A7%81%E0%A6%AF%E0%A6%BC%E0%A7%87%E0%A6%B2_%E0%A6%AC%E0%A7%8D%E0%A6%B2%E0%A6%BE%E0%A6%AE" title="ম্যানুয়েল ব্লাম – Bangla" lang="bn" hreflang="bn" data-title="ম্যানুয়েল ব্লাম" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Catalan" lang="ca" hreflang="ca" data-title="Manuel Blum" 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/Manuel_Blum" title="Manuel Blum – Czech" lang="cs" hreflang="cs" data-title="Manuel Blum" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – German" lang="de" hreflang="de" data-title="Manuel Blum" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Spanish" lang="es" hreflang="es" data-title="Manuel Blum" 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/Manuel_Blum" title="Manuel Blum – Esperanto" lang="eo" hreflang="eo" data-title="Manuel Blum" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Basque" lang="eu" hreflang="eu" data-title="Manuel Blum" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A7%D9%86%D9%88%D8%A6%D9%84_%D8%A8%D9%84%D9%88%D9%85" title="مانوئل بلوم – Persian" lang="fa" hreflang="fa" data-title="مانوئل بلوم" 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/Manuel_Blum" title="Manuel Blum – French" lang="fr" hreflang="fr" data-title="Manuel Blum" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Indonesian" lang="id" hreflang="id" data-title="Manuel Blum" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Italian" lang="it" hreflang="it" data-title="Manuel Blum" 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%9E%D7%A0%D7%95%D7%90%D7%9C_%D7%91%D7%9C%D7%95%D7%9D" title="מנואל בלום – Hebrew" lang="he" hreflang="he" data-title="מנואל בלום" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AE%E0%B4%BE%E0%B4%A8%E0%B5%81%E0%B4%B5%E0%B5%BD_%E0%B4%AC%E0%B5%8D%E0%B4%B2%E0%B4%82" title="മാനുവൽ ബ്ലം – Malayalam" lang="ml" hreflang="ml" data-title="മാനുവൽ ബ്ലം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D8%A7%D9%86%D9%88%D9%8A%D9%84_%D8%A8%D9%84%D9%88%D9%85" title="مانويل بلوم – Egyptian Arabic" lang="arz" hreflang="arz" data-title="مانويل بلوم" 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/Manuel_Blum" title="Manuel Blum – Dutch" lang="nl" hreflang="nl" data-title="Manuel Blum" 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%9E%E3%83%8C%E3%82%A8%E3%83%AB%E3%83%BB%E3%83%96%E3%83%A9%E3%83%A0" title="マヌエル・ブラム – Japanese" lang="ja" hreflang="ja" data-title="マヌエル・ブラム" 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/Manuel_Blum" title="Manuel Blum – Polish" lang="pl" hreflang="pl" data-title="Manuel Blum" 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/Manuel_Blum" title="Manuel Blum – Portuguese" lang="pt" hreflang="pt" data-title="Manuel Blum" 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/Manuel_Blum" title="Manuel Blum – Romanian" lang="ro" hreflang="ro" data-title="Manuel Blum" 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%91%D0%BB%D1%8E%D0%BC,_%D0%9C%D0%B0%D0%BD%D1%83%D1%8D%D0%BB%D1%8C" title="Блюм, Мануэль – Russian" lang="ru" hreflang="ru" data-title="Блюм, Мануэль" 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/Manuel_Blum" title="Manuel Blum – Slovak" lang="sk" hreflang="sk" data-title="Manuel Blum" 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%9C%D0%B0%D0%BD%D1%83%D0%B5%D0%BB_%D0%91%D0%BB%D1%83%D0%BC" title="Мануел Блум – Serbian" lang="sr" hreflang="sr" data-title="Мануел Блум" 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/Manuel_Blum" title="Manuel Blum – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Manuel Blum" 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/Manuel_Blum" title="Manuel Blum – Finnish" lang="fi" hreflang="fi" data-title="Manuel Blum" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Manuel_Blum" title="Manuel Blum – Turkish" lang="tr" hreflang="tr" data-title="Manuel Blum" 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%9C%D0%B0%D0%BD%D1%83%D0%B5%D0%BB%D1%8C_%D0%91%D0%BB%D1%83%D0%BC" title="Мануель Блум – Ukrainian" lang="uk" hreflang="uk" data-title="Мануель Блум" 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/%E6%9B%BC%E7%BA%BD%E5%B0%94%C2%B7%E5%B8%83%E5%8D%A2%E5%A7%86" title="曼纽尔·布卢姆 – Chinese" lang="zh" hreflang="zh" data-title="曼纽尔·布卢姆" 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/Q92626#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Manuel_Blum" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Venezuelan computer scientist</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">Manuel Blum</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Blum_manuel_lenore_avrim.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Blum_manuel_lenore_avrim.jpg/220px-Blum_manuel_lenore_avrim.jpg" decoding="async" width="220" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Blum_manuel_lenore_avrim.jpg/330px-Blum_manuel_lenore_avrim.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/77/Blum_manuel_lenore_avrim.jpg 2x" data-file-width="367" data-file-height="271" /></a></span><div class="infobox-caption">Manuel Blum (left) with his wife <a href="/wiki/Lenore_Blum" title="Lenore Blum">Lenore Blum</a> and their son <a href="/wiki/Avrim_Blum" title="Avrim Blum">Avrim Blum</a>, 1973</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none"> (<span class="bday">1938-04-26</span>) </span>26 April 1938<span class="noprint ForceAgeToShow"> (age 86)</span><br /><div style="display:inline" class="birthplace"><a href="/wiki/Caracas" title="Caracas">Caracas</a>, Venezuela</div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a> (<a href="/wiki/Bachelor_of_Science" title="Bachelor of Science">BS</a>, <a href="/wiki/M._S." class="mw-redirect" title="M. S.">MS</a>, <a href="/wiki/PhD" class="mw-redirect" title="PhD">PhD</a>)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Blum_complexity_axioms" class="mw-redirect" title="Blum complexity axioms">Blum complexity axioms</a><br /><a href="/wiki/Blum_integer" title="Blum integer">Blum integer</a><br /><a href="/wiki/Blum%27s_speedup_theorem" title="Blum's speedup theorem">Blum's speedup theorem</a><br /><a href="/wiki/Blum_Blum_Shub" title="Blum Blum Shub">Blum Blum Shub</a><br /><a href="/wiki/Blum%E2%80%93Goldwasser_cryptosystem" title="Blum–Goldwasser cryptosystem">Blum–Goldwasser cryptosystem</a><br /><a href="/wiki/Blum%E2%80%93Micali_algorithm" title="Blum–Micali algorithm">Blum–Micali algorithm</a><br /><a href="/wiki/CAPTCHA" title="CAPTCHA">CAPTCHA</a><br /><a href="/wiki/ReCAPTCHA" title="ReCAPTCHA">reCAPTCHA</a><br /><a href="/wiki/Commitment_scheme" title="Commitment scheme">Commitment scheme</a></td></tr><tr><th scope="row" class="infobox-label">Spouse</th><td class="infobox-data"><a href="/wiki/Lenore_Blum" title="Lenore Blum">Lenore Blum</a></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><a href="/wiki/Turing_Award" title="Turing Award">ACM's A.M. Turing Award, 1995</a><br />Distinguished Teaching Award, UC Berkeley, 1977<br />Sigma Xi's Monie A. Ferst Award, 1991<br />Herbert A.Simon Teaching award, 2007</td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Computer_science" title="Computer science">Computer science</a></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a><br /><a href="/wiki/Carnegie_Mellon_University" title="Carnegie Mellon University">Carnegie Mellon University</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i><a rel="nofollow" class="external text" href="http://dl.acm.org/citation.cfm?id=321395">A Machine-Independent Theory of the Complexity of Recursive Functions</a></i> <span style="font-size:97%;">(1964)</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"><a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a><sup id="cite_ref-mathgene_1-0" class="reference"><a href="#cite_note-mathgene-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><a href="/wiki/Leonard_Adleman" title="Leonard Adleman">Leonard Adleman</a><br /><a href="/wiki/Dana_Angluin" title="Dana Angluin">Dana Angluin</a><br /><a href="/wiki/Eric_Bach" title="Eric Bach">C. Eric Bach</a><br /><a href="/wiki/Shafi_Goldwasser" title="Shafi Goldwasser">Shafi Goldwasser</a><br /><a href="/wiki/Mor_Harchol-Balter" title="Mor Harchol-Balter">Mor Harchol-Balter</a><br /><a href="/wiki/Russell_Impagliazzo" title="Russell Impagliazzo">Russell Impagliazzo</a><br /><a href="/wiki/Silvio_Micali" title="Silvio Micali">Silvio Micali</a><br /><a href="/wiki/Gary_Miller_(professor)" class="mw-redirect" title="Gary Miller (professor)">Gary Miller</a><br /><a href="/wiki/Moni_Naor" title="Moni Naor">Moni Naor</a><br /><a href="/wiki/Ronitt_Rubinfeld" title="Ronitt Rubinfeld">Ronitt Rubinfeld</a><br /><a href="/wiki/Steven_Rudich" title="Steven Rudich">Steven Rudich</a><br /><a href="/wiki/Jeffrey_Shallit" title="Jeffrey Shallit">Jeffrey Shallit</a><br /><a href="/wiki/Michael_Sipser" title="Michael Sipser">Michael Sipser</a><br /><a href="/wiki/Umesh_Vazirani" title="Umesh Vazirani">Umesh Vazirani</a><br /><a href="/wiki/Vijay_Vazirani" title="Vijay Vazirani">Vijay Vazirani</a><br /><a href="/wiki/Luis_von_Ahn" title="Luis von Ahn">Luis von Ahn</a><br /><a href="/wiki/Ryan_Williams_(computer_scientist)" title="Ryan Williams (computer scientist)">Ryan Williams</a><sup id="cite_ref-mathgene_1-1" class="reference"><a href="#cite_note-mathgene-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/~mblum">www<wbr />.cs<wbr />.cmu<wbr />.edu<wbr />/~mblum</a></span></td></tr></tbody></table> <p><b>Manuel Blum</b> (born 26 April 1938) is a Venezuelan born American <a href="/wiki/Computer_scientist" title="Computer scientist">computer scientist</a> who received the Turing Award in 1995 "In recognition of his contributions to the foundations of <a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">computational complexity theory</a> and its application to <a href="/wiki/Cryptography" title="Cryptography">cryptography</a> and program checking".<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-dblp_3-0" class="reference"><a href="#cite_note-dblp-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-microsoft_4-0" class="reference"><a href="#cite_note-microsoft-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-doi10.1145/321386.321395_7-0" class="reference"><a href="#cite_note-doi10.1145/321386.321395-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Manuel_Blum&action=edit&section=1" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blum was born to a <a href="/wiki/Jewish" class="mw-redirect" title="Jewish">Jewish</a> family in Venezuela.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Blum was educated at <a href="/wiki/MIT" class="mw-redirect" title="MIT">MIT</a>, where he received his bachelor's degree and his master's degree in <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a> in 1959 and 1961 respectively. In MIT, he was recommended to <a href="/wiki/Warren_Sturgis_McCulloch" title="Warren Sturgis McCulloch">Warren S. McCulloch</a>, and they collaborated on some mathematical problems in neural networks.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-number_11-0" class="reference"><a href="#cite_note-number-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> He obtained a <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">Ph.D.</a> in <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> in 1964 supervised by <a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a>.<sup id="cite_ref-mathgene_1-2" class="reference"><a href="#cite_note-mathgene-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-doi10.1145/321386.321395_7-1" class="reference"><a href="#cite_note-doi10.1145/321386.321395-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Career">Career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Manuel_Blum&action=edit&section=2" title="Edit section: Career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blum worked as a professor of computer science at the <a href="/wiki/University_of_California,_Berkeley" title="University of California, Berkeley">University of California, Berkeley</a> until 2001. From 2001 to 2018, he was the Bruce Nelson Professor of Computer Science at <a href="/wiki/Carnegie_Mellon_University" title="Carnegie Mellon University">Carnegie Mellon University</a>, where his wife, <a href="/wiki/Lenore_Blum" title="Lenore Blum">Lenore Blum</a>,<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> was also a professor of Computer Science. </p><p>In 2002, he was elected to the <a href="/wiki/United_States_National_Academy_of_Sciences" class="mw-redirect" title="United States National Academy of Sciences">United States National Academy of Sciences</a>. In 2006, he was elected a member of the <a href="/wiki/National_Academy_of_Engineering" title="National Academy of Engineering">National Academy of Engineering</a> for contributions to abstract complexity theory, inductive inference, cryptographic protocols, and the theory and applications of program checkers. </p><p>In 2018 he and his wife Lenore resigned from Carnegie Mellon University to protest against sexism after a change in management structure of <a href="/w/index.php?title=Project_Olympus&action=edit&redlink=1" class="new" title="Project Olympus (page does not exist)">Project Olympus</a> led to sexist treatment of her as director and the exclusion of other women from project activities.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Research">Research</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Manuel_Blum&action=edit&section=3" title="Edit section: Research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the 60s he developed an axiomatic complexity theory which was independent of concrete machine models. The theory is based on <a href="/wiki/G%C3%B6del_numbering" title="Gödel numbering">Gödel numberings</a> and the <a href="/wiki/Blum_axioms" title="Blum axioms">Blum axioms</a>. Even though the theory is not based on any machine model it yields concrete results like the <a href="/wiki/Compression_theorem" title="Compression theorem">compression theorem</a>, the <a href="/wiki/Gap_theorem" title="Gap theorem">gap theorem</a>, the honesty theorem and the <a href="/wiki/Blum_speedup_theorem" class="mw-redirect" title="Blum speedup theorem">Blum speedup theorem</a>. </p><p>Some of his other work includes a protocol for <a href="/wiki/Commitment_scheme#Coin_flipping" title="Commitment scheme">flipping a coin over a telephone</a>, <a href="/wiki/Median_of_medians" title="Median of medians">median of medians</a> (a linear time <a href="/wiki/Selection_algorithm" title="Selection algorithm">selection algorithm</a>), the <a href="/wiki/Blum_Blum_Shub" title="Blum Blum Shub">Blum Blum Shub</a> <a href="/wiki/Pseudorandom_number_generator" title="Pseudorandom number generator">pseudorandom number generator</a>, the <a href="/wiki/Blum%E2%80%93Goldwasser_cryptosystem" title="Blum–Goldwasser cryptosystem">Blum–Goldwasser cryptosystem</a>, and more recently <a href="/wiki/Captcha" class="mw-redirect" title="Captcha">CAPTCHAs</a>.<sup id="cite_ref-captcha_15-0" class="reference"><a href="#cite_note-captcha-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>Blum is also known as the advisor of many prominent researchers. Among his Ph.D. students are <a href="/wiki/Leonard_Adleman" title="Leonard Adleman">Leonard Adleman</a>, <a href="/wiki/Dana_Angluin" title="Dana Angluin">Dana Angluin</a>, <a href="/wiki/Shafi_Goldwasser" title="Shafi Goldwasser">Shafi Goldwasser</a>, <a href="/wiki/Mor_Harchol-Balter" title="Mor Harchol-Balter">Mor Harchol-Balter</a>, <a href="/wiki/Russell_Impagliazzo" title="Russell Impagliazzo">Russell Impagliazzo</a>, <a href="/wiki/Silvio_Micali" title="Silvio Micali">Silvio Micali</a>, <a href="/wiki/Gary_Miller_(professor)" class="mw-redirect" title="Gary Miller (professor)">Gary Miller</a>, <a href="/wiki/Moni_Naor" title="Moni Naor">Moni Naor</a>, <a href="/wiki/Steven_Rudich" title="Steven Rudich">Steven Rudich</a>, <a href="/wiki/Michael_Sipser" title="Michael Sipser">Michael Sipser</a>, <a href="/wiki/Ronitt_Rubinfeld" title="Ronitt Rubinfeld">Ronitt Rubinfeld</a>, <a href="/wiki/Umesh_Vazirani" title="Umesh Vazirani">Umesh Vazirani</a>, <a href="/wiki/Vijay_Vazirani" title="Vijay Vazirani">Vijay Vazirani</a>, <a href="/wiki/Luis_von_Ahn" title="Luis von Ahn">Luis von Ahn</a>, and <a href="/wiki/Ryan_Williams_(computer_scientist)" title="Ryan Williams (computer scientist)">Ryan Williams</a>.<sup id="cite_ref-mathgene_1-3" class="reference"><a href="#cite_note-mathgene-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Manuel_Blum&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/List_of_Venezuelans" title="List of Venezuelans">List of Venezuelans</a></li> <li><a href="/wiki/Graph_isomorphism_problem" title="Graph isomorphism problem">Graph isomorphism problem</a></li> <li><a href="/wiki/Non-interactive_zero-knowledge_proof" title="Non-interactive zero-knowledge proof">Non-interactive zero-knowledge proof</a></li> <li><a href="/wiki/Quantum_coin_flipping" title="Quantum coin flipping">Quantum coin flipping</a></li> <li><a href="/wiki/Pancake_sorting" title="Pancake sorting">Pancake sorting</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Manuel_Blum&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-mathgene-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-mathgene_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-mathgene_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-mathgene_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-mathgene_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=13373">Manuel Blum</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://wayback.archive-it.org/all/20120703013825/http://awards.acm.org/citation.cfm?id=4659082&srt=all&aw=140&ao=AMTURING&yr=1995">ACM Turing Award Citation</a>, retrieved 2010-01-24.</span> </li> <li id="cite_note-dblp-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-dblp_3-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://dblp.org/pid/b/ManuelBlum">Manuel Blum</a> at <a href="/wiki/DBLP" title="DBLP">DBLP</a> Bibliography Server <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q92626#P2456" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span> </li> <li id="cite_note-microsoft-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-microsoft_4-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://academic.microsoft.com/v2/detail/648415">Manuel Blum</a> publications indexed by <a href="/wiki/MA_(identifier)" class="mw-redirect" title="MA (identifier)">Microsoft Academic</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBlumMicali1984" class="citation journal cs1"><a class="mw-selflink selflink">Blum, Manuel</a>; <a href="/wiki/Silvio_Micali" title="Silvio Micali">Micali, Silvio</a> (1984). <a rel="nofollow" class="external text" href="http://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Pseudo%20Randomness/How_To_Generate_Cryptographically_Strong_Sequences_Of_Pseudo-Random_Bits.pdf">"How to Generate Cryptographically Strong Sequences of Pseudorandom Bits"</a> <span class="cs1-format">(PDF)</span>. <i>SIAM Journal on Computing</i>. <b>13</b> (4): 850. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F0213053">10.1137/0213053</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:7008910">7008910</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Journal+on+Computing&rft.atitle=How+to+Generate+Cryptographically+Strong+Sequences+of+Pseudorandom+Bits&rft.volume=13&rft.issue=4&rft.pages=850&rft.date=1984&rft_id=info%3Adoi%2F10.1137%2F0213053&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7008910%23id-name%3DS2CID&rft.aulast=Blum&rft.aufirst=Manuel&rft.au=Micali%2C+Silvio&rft_id=http%3A%2F%2Fpeople.csail.mit.edu%2Fsilvio%2FSelected%2520Scientific%2520Papers%2FPseudo%2520Randomness%2FHow_To_Generate_Cryptographically_Strong_Sequences_Of_Pseudo-Random_Bits.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlumFloydPrattRivest1973" class="citation journal cs1"><a class="mw-selflink selflink">Blum, M.</a>; <a href="/wiki/Robert_W._Floyd" title="Robert W. Floyd">Floyd, R. W.</a>; <a href="/wiki/Vaughan_Pratt" title="Vaughan Pratt">Pratt, V. R.</a>; <a href="/wiki/Ron_Rivest" title="Ron Rivest">Rivest, R. L.</a>; <a href="/wiki/Robert_Tarjan" title="Robert Tarjan">Tarjan, R. E.</a> (August 1973). <a rel="nofollow" class="external text" href="http://people.csail.mit.edu/rivest/pubs/BFPRT73.pdf">"Time bounds for selection"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Computer and System Sciences</i>. <b>7</b> (4): 448–461. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0022-0000%2873%2980033-9">10.1016/S0022-0000(73)80033-9</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Computer+and+System+Sciences&rft.atitle=Time+bounds+for+selection&rft.volume=7&rft.issue=4&rft.pages=448-461&rft.date=1973-08&rft_id=info%3Adoi%2F10.1016%2FS0022-0000%2873%2980033-9&rft.aulast=Blum&rft.aufirst=M.&rft.au=Floyd%2C+R.+W.&rft.au=Pratt%2C+V.+R.&rft.au=Rivest%2C+R.+L.&rft.au=Tarjan%2C+R.+E.&rft_id=http%3A%2F%2Fpeople.csail.mit.edu%2Frivest%2Fpubs%2FBFPRT73.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-doi10.1145/321386.321395-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-doi10.1145/321386.321395_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-doi10.1145/321386.321395_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlum1967" class="citation journal cs1"><a class="mw-selflink selflink">Blum, Manuel</a> (1967). <a rel="nofollow" class="external text" href="http://port70.net/~nsz/articles/classic/blum_complexity_1976.pdf">"A Machine-Independent Theory of the Complexity of Recursive Functions"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Journal_of_the_ACM" title="Journal of the ACM">Journal of the ACM</a></i>. <b>14</b> (2): 322–336. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F321386.321395">10.1145/321386.321395</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:15710280">15710280</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+ACM&rft.atitle=A+Machine-Independent+Theory+of+the+Complexity+of+Recursive+Functions&rft.volume=14&rft.issue=2&rft.pages=322-336&rft.date=1967&rft_id=info%3Adoi%2F10.1145%2F321386.321395&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15710280%23id-name%3DS2CID&rft.aulast=Blum&rft.aufirst=Manuel&rft_id=http%3A%2F%2Fport70.net%2F~nsz%2Farticles%2Fclassic%2Fblum_complexity_1976.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlumBlumShub1986" class="citation journal cs1">Blum, L.; Blum, M.; Shub, M. (1986). "A Simple Unpredictable Pseudo-Random Number Generator". <i>SIAM Journal on Computing</i>. <b>15</b> (2): 364. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F0215025">10.1137/0215025</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Journal+on+Computing&rft.atitle=A+Simple+Unpredictable+Pseudo-Random+Number+Generator&rft.volume=15&rft.issue=2&rft.pages=364&rft.date=1986&rft_id=info%3Adoi%2F10.1137%2F0215025&rft.aulast=Blum&rft.aufirst=L.&rft.au=Blum%2C+M.&rft.au=Shub%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www-groups.dcs.st-and.ac.uk/history/Biographies/Blum.html">"Lenore Blum biography"</a>. <i>www-groups.dcs.st-and.ac.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 February</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www-groups.dcs.st-and.ac.uk&rft.atitle=Lenore+Blum+biography&rft_id=http%3A%2F%2Fwww-groups.dcs.st-and.ac.uk%2Fhistory%2FBiographies%2FBlum.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Blum, Manuel. "Properties of a neuron with many inputs." <i>Bionics Symposium: Living Prototypes--the Key to New Technology, 13-14-15 September 1960</i>. WADD technical report, 60-600. (1961)</span> </li> <li id="cite_note-number-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-number_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcCulloch1961" class="citation journal cs1">McCulloch, Warren (1961). <a rel="nofollow" class="external text" href="https://www.nsl.com/k/parry/mcculloch_what-is-a-number.pdf">"What is a number, that a man may know it, and a man, that he may know a Number"</a> <span class="cs1-format">(PDF)</span>. <i>General Semantics Bulletin</i> (26 & 27): 7–18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=General+Semantics+Bulletin&rft.atitle=What+is+a+number%2C+that+a+man+may+know+it%2C+and+a+man%2C+that+he+may+know+a+Number&rft.issue=26+%26+27&rft.pages=7-18&rft.date=1961&rft.aulast=McCulloch&rft.aufirst=Warren&rft_id=https%3A%2F%2Fwww.nsl.com%2Fk%2Fparry%2Fmcculloch_what-is-a-number.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.technologyreview.com/2023/10/24/1081478/manuel-blum-theoretical-computer-science-turing-award-academic-advisor/">"How this Turing Award–winning researcher became a legendary academic advisor"</a>. <i>MIT Technology Review</i><span class="reference-accessdate">. Retrieved <span class="nowrap">12 October</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MIT+Technology+Review&rft.atitle=How+this+Turing+Award%E2%80%93winning+researcher+became+a+legendary+academic+advisor&rft_id=https%3A%2F%2Fwww.technologyreview.com%2F2023%2F10%2F24%2F1081478%2Fmanuel-blum-theoretical-computer-science-turing-award-academic-advisor%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlumBlum1975" class="citation journal cs1">Blum, L.; Blum, M. (1975). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0019-9958%2875%2990261-2">"Toward a mathematical theory of inductive inference"</a>. <i>Information and Control</i>. <b>28</b> (2): 125. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0019-9958%2875%2990261-2">10.1016/S0019-9958(75)90261-2</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Information+and+Control&rft.atitle=Toward+a+mathematical+theory+of+inductive+inference&rft.volume=28&rft.issue=2&rft.pages=125&rft.date=1975&rft_id=info%3Adoi%2F10.1016%2FS0019-9958%2875%2990261-2&rft.aulast=Blum&rft.aufirst=L.&rft.au=Blum%2C+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252FS0019-9958%252875%252990261-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nextpittsburgh.com/features/lenore-blum-speaks-out-about-sexism-in-the-workplace/">"Lenore Blum shocked the community with her sudden resignation from CMU. Here she tells us why"</a>. 6 September 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Lenore+Blum+shocked+the+community+with+her+sudden+resignation+from+CMU.+Here+she+tells+us+why&rft.date=2018-09-06&rft_id=https%3A%2F%2Fwww.nextpittsburgh.com%2Ffeatures%2Flenore-blum-speaks-out-about-sexism-in-the-workplace%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AManuel+Blum" class="Z3988"></span></span> </li> <li id="cite_note-captcha-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-captcha_15-0">^</a></b></span> <span class="reference-text">Von Ahn, Luis; Blum, Manuel; Hopper, Nicholas J.; Langford, John (May 2003). "<a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007/3-540-39200-9_18.pdf">CAPTCHA: Using Hard AI Problems for Security</a>". Proceedings of the <a href="/wiki/International_Conference_on_the_Theory_and_Applications_of_Cryptographic_Techniques" class="mw-redirect" title="International Conference on the Theory and Applications of Cryptographic Techniques">International Conference on the Theory and Applications of Cryptographic Techniques</a> (EUROCRYPT 2003).</span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol 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M. Turing Award</a> <a href="/wiki/Laureate" title="Laureate">laureates</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Alan_Perlis" title="Alan Perlis">Alan Perlis</a> (1966)</span></li> <li><span class="nowrap"><a href="/wiki/Maurice_Wilkes" title="Maurice Wilkes">Maurice Vincent Wilkes</a> (1967)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_Hamming" title="Richard Hamming">Richard Hamming</a> (1968)</span></li> <li><span class="nowrap"><a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a> (1969)</span></li> <li><span class="nowrap"><a href="/wiki/James_H._Wilkinson" title="James H. Wilkinson">James H. Wilkinson</a> (1970)</span></li> <li><span class="nowrap"><a href="/wiki/John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a> (1971)</span></li> <li><span class="nowrap"><a href="/wiki/Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Edsger W. Dijkstra</a> (1972)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_Bachman" title="Charles Bachman">Charles Bachman</a> (1973)</span></li> <li><span class="nowrap"><a href="/wiki/Donald_Knuth" title="Donald Knuth">Donald Knuth</a> (1974)</span></li> <li><span class="nowrap"><a href="/wiki/Allen_Newell" title="Allen Newell">Allen Newell</a>; <a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a> (1975)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_O._Rabin" title="Michael O. Rabin">Michael O. Rabin</a>; <a href="/wiki/Dana_Scott" title="Dana Scott">Dana Scott</a> (1976)</span></li> <li><span class="nowrap"><a href="/wiki/John_Backus" title="John Backus">John Backus</a> (1977)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_W._Floyd" title="Robert W. Floyd">Robert W. Floyd</a> (1978)</span></li> <li><span class="nowrap"><a href="/wiki/Kenneth_E._Iverson" title="Kenneth E. Iverson">Kenneth E. Iverson</a> (1979)</span></li> <li><span class="nowrap"><a href="/wiki/Tony_Hoare" title="Tony Hoare">Tony Hoare</a> (1980)</span></li> <li><span class="nowrap"><a href="/wiki/Edgar_F._Codd" title="Edgar F. Codd">Edgar F. Codd</a> (1981)</span></li> <li><span class="nowrap"><a href="/wiki/Stephen_Cook" title="Stephen Cook">Stephen Cook</a> (1982)</span></li> <li><span class="nowrap"><a href="/wiki/Ken_Thompson" title="Ken Thompson">Ken Thompson</a>; <a href="/wiki/Dennis_Ritchie" title="Dennis Ritchie">Dennis Ritchie</a> (1983)</span></li> <li><span class="nowrap"><a href="/wiki/Niklaus_Wirth" title="Niklaus Wirth">Niklaus Wirth</a> (1984)</span></li> <li><span class="nowrap"><a href="/wiki/Richard_M._Karp" title="Richard M. Karp">Richard Karp</a> (1985)</span></li> <li><span class="nowrap"><a href="/wiki/John_Hopcroft" title="John Hopcroft">John Hopcroft</a>; <a href="/wiki/Robert_Tarjan" title="Robert Tarjan">Robert Tarjan</a> (1986)</span></li> <li><span class="nowrap"><a href="/wiki/John_Cocke_(computer_scientist)" title="John Cocke (computer scientist)">John Cocke</a> (1987)</span></li> <li><span class="nowrap"><a href="/wiki/Ivan_Sutherland" title="Ivan Sutherland">Ivan Sutherland</a> (1988)</span></li> <li><span class="nowrap"><a 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 class="mw-selflink selflink">Manuel Blum</a> (1995)</span></li> <li><span class="nowrap"><a href="/wiki/Amir_Pnueli" title="Amir Pnueli">Amir Pnueli</a> (1996)</span></li> <li><span class="nowrap"><a href="/wiki/Douglas_Engelbart" title="Douglas Engelbart">Douglas Engelbart</a> (1997)</span></li> <li><span class="nowrap"><a href="/wiki/Jim_Gray_(computer_scientist)" title="Jim Gray (computer scientist)">Jim Gray</a> (1998)</span></li> <li><span class="nowrap"><a href="/wiki/Fred_Brooks" title="Fred Brooks">Fred Brooks</a> (1999)</span></li> <li><span class="nowrap"><a href="/wiki/Andrew_Yao" title="Andrew Yao">Andrew Yao</a> (2000)</span></li> <li><span class="nowrap"><a href="/wiki/Ole-Johan_Dahl" title="Ole-Johan Dahl">Ole-Johan Dahl</a>; <a href="/wiki/Kristen_Nygaard" title="Kristen Nygaard">Kristen Nygaard</a> (2001)</span></li> <li><span class="nowrap"><a href="/wiki/Ron_Rivest" title="Ron Rivest">Ron Rivest</a>; <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a>; <a href="/wiki/Leonard_Adleman" title="Leonard Adleman">Leonard Adleman</a> (2002)</span></li> <li><span class="nowrap"><a href="/wiki/Alan_Kay" title="Alan Kay">Alan Kay</a> (2003)</span></li> <li><span class="nowrap"><a href="/wiki/Vint_Cerf" title="Vint Cerf">Vint Cerf</a>; <a href="/wiki/Robert_Kahn_(computer_scientist)" title="Robert Kahn (computer scientist)">Bob Kahn</a> (2004)</span></li> <li><span class="nowrap"><a href="/wiki/Peter_Naur" title="Peter Naur">Peter Naur</a> (2005)</span></li> <li><span class="nowrap"><a href="/wiki/Frances_Allen" title="Frances Allen">Frances Allen</a> (2006)</span></li> <li><span class="nowrap"><a href="/wiki/Edmund_M._Clarke" title="Edmund M. Clarke">Edmund M. Clarke</a>; <a href="/wiki/E._Allen_Emerson" title="E. Allen Emerson">E. Allen Emerson</a>; <a href="/wiki/Joseph_Sifakis" title="Joseph Sifakis">Joseph Sifakis</a> (2007)</span></li> <li><span class="nowrap"><a href="/wiki/Barbara_Liskov" title="Barbara Liskov">Barbara Liskov</a> (2008)</span></li> <li><span class="nowrap"><a href="/wiki/Charles_P._Thacker" title="Charles P. Thacker">Charles P. Thacker</a> (2009)</span></li> <li><span class="nowrap"><a href="/wiki/Leslie_Valiant" title="Leslie Valiant">Leslie G. Valiant</a> (2010)</span></li> <li><span class="nowrap"><a href="/wiki/Judea_Pearl" title="Judea Pearl">Judea Pearl</a> (2011)</span></li> <li><span class="nowrap"><a href="/wiki/Shafi_Goldwasser" title="Shafi Goldwasser">Shafi Goldwasser</a>; <a href="/wiki/Silvio_Micali" title="Silvio Micali">Silvio Micali</a> (2012)</span></li> <li><span class="nowrap"><a href="/wiki/Leslie_Lamport" title="Leslie Lamport">Leslie Lamport</a> (2013)</span></li> <li><span class="nowrap"><a href="/wiki/Michael_Stonebraker" title="Michael Stonebraker">Michael Stonebraker</a> (2014)</span></li> <li><span class="nowrap"><a href="/wiki/Martin_Hellman" title="Martin Hellman">Martin Hellman</a>; <a href="/wiki/Whitfield_Diffie" title="Whitfield Diffie">Whitfield Diffie</a> (2015)</span></li> <li><span class="nowrap"><a href="/wiki/Tim_Berners-Lee" title="Tim Berners-Lee">Tim Berners-Lee</a> (2016)</span></li> <li><span class="nowrap"><a href="/wiki/John_L._Hennessy" title="John L. Hennessy">John L. Hennessy</a>; <a href="/wiki/David_Patterson_(computer_scientist)" title="David Patterson (computer scientist)">David Patterson</a> (2017)</span></li> <li><span class="nowrap"><a href="/wiki/Yoshua_Bengio" title="Yoshua Bengio">Yoshua Bengio</a>; <a href="/wiki/Geoffrey_Hinton" title="Geoffrey Hinton">Geoffrey Hinton</a>; <a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a> (2018)</span></li> <li><span class="nowrap"><a href="/wiki/Edwin_Catmull" title="Edwin Catmull">Ed Catmull</a>; <a href="/wiki/Pat_Hanrahan" title="Pat Hanrahan">Pat Hanrahan</a> (2019)</span></li> <li><span class="nowrap"><a href="/wiki/Alfred_Aho" title="Alfred Aho">Alfred Aho</a>; <a href="/wiki/Jeffrey_Ullman" title="Jeffrey Ullman">Jeffrey Ullman</a> (2020) </span></li> <li><span class="nowrap"><a href="/wiki/Jack_Dongarra" title="Jack Dongarra">Jack Dongarra</a> (2021)</span></li> <li><span class="nowrap"><a href="/wiki/Robert_Metcalfe" title="Robert Metcalfe">Robert Metcalfe</a> (2022)</span></li> <li><span class="nowrap"><a href="/wiki/Avi_Wigderson" title="Avi Wigderson">Avi Wigderson</a> (2023)</span></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q92626#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q92626#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q92626#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=13373">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dl.acm.org/profile/81100159946">Association for Computing Machinery</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:blum.manuel">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/b/ManuelBlum">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/213414">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6z73c12">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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