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<span>Career</span> </div> </a> <ul id="toc-Career-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Personal_life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Personal_life"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Personal life</span> </div> </a> <ul id="toc-Personal_life-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Legacy</span> </div> </a> <ul id="toc-Legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Works" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Works"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Works</span> </div> </a> <ul id="toc-Works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gallery" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gallery"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Gallery</span> </div> </a> <ul id="toc-Gallery-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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">János Bolyai</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 47 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-47" 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">47 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%AC%D8%A7%D9%86%D9%88%D8%B3_%D8%A8%D9%88%D9%84%D9%8A%D8%A7%D9%8A" title="جانوس بولياي – Arabic" lang="ar" hreflang="ar" data-title="جانوس بولياي" 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/Yano%C5%9F_Boyyay" title="Yanoş Boyyay – Azerbaijani" lang="az" hreflang="az" data-title="Yanoş Boyyay" 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/%DB%8C%D8%A7%D9%86%D9%88%D8%B4_%D8%A8%D9%88%DB%8C%D9%88%DB%8C%DB%8C" title="یانوش بویویی – South Azerbaijani" lang="azb" hreflang="azb" data-title="یانوش بویویی" 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%87%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A8%E0%A7%8B%E0%A6%B6_%E0%A6%AC%E0%A6%B2%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%87" title="ইয়ানোশ বলিয়ই – Bangla" lang="bn" hreflang="bn" data-title="ইয়ানোশ বলিয়ই" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AF%D0%BD%D0%B0%D1%88_%D0%91%D0%BE%D1%8F%D1%96" title="Янаш Бояі – Belarusian" lang="be" hreflang="be" data-title="Янаш Бояі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%AF%D0%BD%D0%BE%D1%88_%D0%91%D0%BE%D1%8F%D0%B9" title="Янош Бояй – Bulgarian" lang="bg" hreflang="bg" data-title="Янош Бояй" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Catalan" lang="ca" hreflang="ca" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Czech" lang="cs" hreflang="cs" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – German" lang="de" hreflang="de" data-title="János Bolyai" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Estonian" lang="et" hreflang="et" data-title="János Bolyai" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B9%CE%AC%CE%BD%CE%BF%CF%82_%CE%9C%CF%80%CF%8C%CE%B9%CE%B3%CE%B9%CE%B1%CF%8A" title="Γιάνος Μπόιγιαϊ – Greek" lang="el" hreflang="el" data-title="Γιάνος Μπόιγιαϊ" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Spanish" lang="es" hreflang="es" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Esperanto" lang="eo" hreflang="eo" data-title="János Bolyai" 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/%DB%8C%D8%A7%D9%86%D9%88%D8%B4_%D8%A8%D9%88%DB%8C%D8%A7%DB%8C%DB%8C" title="یانوش بویایی – Persian" lang="fa" hreflang="fa" data-title="یانوش بویایی" 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/J%C3%A1nos_Bolyai" title="János Bolyai – French" lang="fr" hreflang="fr" data-title="János Bolyai" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Galician" lang="gl" hreflang="gl" data-title="János Bolyai" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B4%EC%97%AC%EC%9D%B4_%EC%95%BC%EB%85%B8%EC%8B%9C" title="보여이 야노시 – Korean" lang="ko" hreflang="ko" data-title="보여이 야노시" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%85%D5%A1%D5%B6%D5%B8%D5%B7_%D4%B2%D5%B8%D5%B5%D5%A1%D5%B5%D5%AB" title="Յանոշ Բոյայի – Armenian" lang="hy" hreflang="hy" data-title="Յանոշ Բոյայի" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Indonesian" lang="id" hreflang="id" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Italian" lang="it" hreflang="it" data-title="János Bolyai" 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%99%D7%90%D7%A0%D7%95%D7%A9_%D7%91%D7%95%D7%99%D7%90%D7%99" title="יאנוש בויאי – Hebrew" lang="he" hreflang="he" data-title="יאנוש בויאי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%BE%D0%BB%D1%8C%D1%8F%D0%B9_%D0%AF%D0%BD%D0%BE%D1%88" title="Больяй Янош – Kazakh" lang="kk" hreflang="kk" data-title="Больяй Янош" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/J%C4%81no%C5%A1s_Bojai" title="Jānošs Bojai – Latvian" lang="lv" hreflang="lv" data-title="Jānošs Bojai" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://hu.wikipedia.org/wiki/Bolyai_J%C3%A1nos" title="Bolyai János – Hungarian" lang="hu" hreflang="hu" data-title="Bolyai János" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%88%D0%B0%D0%BD%D0%BE%D1%88_%D0%91%D0%BE%D1%98%D0%B0%D0%B8" title="Јанош Бојаи – Macedonian" lang="mk" hreflang="mk" data-title="Јанош Бојаи" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D8%A7%D9%86%D9%88%D8%B3_%D8%A8%D9%88%D9%84%D9%8A%D8%A7%D9%89" title="جانوس بولياى – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جانوس بولياى" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Dutch" lang="nl" hreflang="nl" data-title="János Bolyai" 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%9C%E3%83%BC%E3%83%A4%E3%82%A4%E3%83%BB%E3%83%A4%E3%83%BC%E3%83%8E%E3%82%B7%E3%83%A5" title="ボーヤイ・ヤーノシュ – Japanese" lang="ja" hreflang="ja" data-title="ボーヤイ・ヤーノシュ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Janos_Bolyai" title="Janos Bolyai – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Janos Bolyai" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="János Bolyai" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Bolyay_Yanosh" title="Bolyay Yanosh – Uzbek" lang="uz" hreflang="uz" data-title="Bolyay Yanosh" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/J%C3%A0nos_Bolyai" title="Jànos Bolyai – Piedmontese" lang="pms" hreflang="pms" data-title="Jànos Bolyai" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Polish" lang="pl" hreflang="pl" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Portuguese" lang="pt" hreflang="pt" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Romanian" lang="ro" hreflang="ro" data-title="János Bolyai" 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%BE%D0%B9%D1%8F%D0%B8,_%D0%AF%D0%BD%D0%BE%D1%88" title="Бойяи, Янош – Russian" lang="ru" hreflang="ru" data-title="Бойяи, Янош" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Simple English" lang="en-simple" hreflang="en-simple" data-title="János Bolyai" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Slovak" lang="sk" hreflang="sk" data-title="János Bolyai" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/J%C3%A1nos_Bolyai" title="János Bolyai – Slovenian" lang="sl" hreflang="sl" data-title="János Bolyai" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Jano%C5%A1_Boljaj" title="Janoš Boljaj – Serbian" lang="sr" hreflang="sr" data-title="Janoš Boljaj" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Serbo-Croatian" lang="sh" hreflang="sh" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Finnish" lang="fi" hreflang="fi" data-title="János Bolyai" 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/J%C3%A1nos_Bolyai" title="János Bolyai – Swedish" lang="sv" hreflang="sv" data-title="János Bolyai" 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 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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">"Bolyai" redirects here. For the lunar crater, see <a href="/wiki/Bolyai_(crater)" title="Bolyai (crater)">Bolyai (crater)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">The native form of this <a href="/wiki/Personal_name" title="Personal name">personal name</a> is <i>Bolyai János</i>. This article uses <a href="/wiki/Personal_name#Western_name_order" title="Personal name">Western name order</a> when mentioning individuals.</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">János Bolyai</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Bolyai_J%C3%A1nos_(M%C3%A1rkos_Ferenc_festm%C3%A9nye).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Bolyai_J%C3%A1nos_%28M%C3%A1rkos_Ferenc_festm%C3%A9nye%29.jpg/200px-Bolyai_J%C3%A1nos_%28M%C3%A1rkos_Ferenc_festm%C3%A9nye%29.jpg" decoding="async" width="200" height="320" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Bolyai_J%C3%A1nos_%28M%C3%A1rkos_Ferenc_festm%C3%A9nye%29.jpg/300px-Bolyai_J%C3%A1nos_%28M%C3%A1rkos_Ferenc_festm%C3%A9nye%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d8/Bolyai_J%C3%A1nos_%28M%C3%A1rkos_Ferenc_festm%C3%A9nye%29.jpg 2x" data-file-width="400" data-file-height="639" /></a></span><div class="infobox-caption">Portrait of J. Bolyai by Ferenc Márkos (2012)<sup id="cite_ref-amsNotices_1-0" class="reference"><a href="#cite_note-amsNotices-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1802-12-15</span>)</span>15 December 1802<br /><div style="display:inline" class="birthplace">Klausenburg, <a href="/wiki/Principality_of_Transylvania_(1711%E2%80%931867)" title="Principality of Transylvania (1711–1867)">Transylvania</a> (now <a href="/wiki/Cluj-Napoca" title="Cluj-Napoca">Cluj-Napoca</a>, <a href="/wiki/Romania" title="Romania">Romania</a>)</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">27 January 1860<span style="display:none">(1860-01-27)</span> (aged 57)<br /><div style="display:inline" class="deathplace">Neumarkt am Mieresch, <a href="/wiki/Austrian_Empire" title="Austrian Empire">Austrian Empire</a> (now <a href="/wiki/T%C3%A2rgu_Mure%C8%99" title="Târgu Mureș">Târgu Mureș</a>, Romania)</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><a href="/wiki/Hungarians" title="Hungarians">Hungarian</a></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data"><a href="/wiki/Theresian_Military_Academy" title="Theresian Military Academy">TherMilAk</a> (<a href="/wiki/Diploma" title="Diploma">diploma</a>, 1822)</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">Non-Euclidean geometry</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></td></tr><tr><th scope="row" class="infobox-label">Academic advisors</th><td class="infobox-data"><a href="/wiki/Farkas_Bolyai" title="Farkas Bolyai">Farkas Bolyai</a></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bolyai-arck%C3%A9p.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Bolyai-arck%C3%A9p.JPG/220px-Bolyai-arck%C3%A9p.JPG" decoding="async" width="220" height="315" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Bolyai-arck%C3%A9p.JPG/330px-Bolyai-arck%C3%A9p.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Bolyai-arck%C3%A9p.JPG/440px-Bolyai-arck%C3%A9p.JPG 2x" data-file-width="939" data-file-height="1344" /></a><figcaption>János Bolyai; artwork by Attila Zsigmond<sup id="cite_ref-amsNotices_1-1" class="reference"><a href="#cite_note-amsNotices-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Janos_Bolyai_memorial_plaque.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Janos_Bolyai_memorial_plaque.jpg/220px-Janos_Bolyai_memorial_plaque.jpg" decoding="async" width="220" height="433" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Janos_Bolyai_memorial_plaque.jpg/330px-Janos_Bolyai_memorial_plaque.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Janos_Bolyai_memorial_plaque.jpg/440px-Janos_Bolyai_memorial_plaque.jpg 2x" data-file-width="1167" data-file-height="2298" /></a><figcaption>Memorial plaque of János Bolyai in <a href="/wiki/Olomouc" title="Olomouc">Olomouc</a>, <a href="/wiki/Czech_Republic" title="Czech Republic">Czech Republic</a></figcaption></figure> <p><b>János Bolyai</b> (<style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">Hungarian:</span> <span class="IPA nowrap" lang="hu-Latn-fonipa"><a href="/wiki/Help:IPA/Hungarian" title="Help:IPA/Hungarian">[ˈjaːnoʃ<span class="wrap"> </span>ˈboːjɒi]</a></span>; 15 December 1802 – 27 January 1860) or <b>Johann Bolyai</b>,<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> was a <a href="/wiki/Hungarian_people" class="mw-redirect" title="Hungarian people">Hungarian</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> who developed <a href="/wiki/Absolute_geometry" title="Absolute geometry">absolute geometry</a>—a geometry that includes both <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a> and <a href="/wiki/Hyperbolic_geometry" title="Hyperbolic geometry">hyperbolic geometry</a>. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </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=J%C3%A1nos_Bolyai&action=edit&section=1" title="Edit section: Early life"><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:Bolyai_Janos_szulohaza.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Bolyai_Janos_szulohaza.jpg/220px-Bolyai_Janos_szulohaza.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Bolyai_Janos_szulohaza.jpg/330px-Bolyai_Janos_szulohaza.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Bolyai_Janos_szulohaza.jpg/440px-Bolyai_Janos_szulohaza.jpg 2x" data-file-width="1280" data-file-height="960" /></a><figcaption>The house in <a href="/wiki/Cluj-Napoca" title="Cluj-Napoca">Cluj-Napoca</a> where János Bolyai was born</figcaption></figure> <p>Bolyai was born in the town of Kolozsvár, <a href="/wiki/Grand_Principality_of_Transylvania" class="mw-redirect" title="Grand Principality of Transylvania">Grand Principality of Transylvania</a> (now <a href="/wiki/Cluj-Napoca" title="Cluj-Napoca">Cluj-Napoca</a> in <a href="/wiki/Romania" title="Romania">Romania</a>), the son of Zsuzsanna Benkő and the well-known mathematician <a href="/wiki/Farkas_Bolyai" title="Farkas Bolyai">Farkas Bolyai</a>. </p><p>By the age of 13, he had mastered <a href="/wiki/Calculus" title="Calculus">calculus</a> and other forms of <a href="/wiki/Analytical_mechanics" title="Analytical mechanics">analytical mechanics</a>, receiving instruction from his father. He studied at the <a href="/wiki/Theresian_Military_Academy" title="Theresian Military Academy">Imperial and Royal Military Academy</a> (TherMilAk) in <a href="/wiki/Vienna" title="Vienna">Vienna</a> from 1818 to 1822, and Bolyai received his commission as sub-lieutenant. At the age of 21, he was already a lieutenant, at the age of 22, a first lieutenant and at the age of 24, a captain.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <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=J%C3%A1nos_Bolyai&action=edit&section=2" title="Edit section: Career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bolyai became so obsessed with <a href="/wiki/Euclid" title="Euclid">Euclid</a>'s <a href="/wiki/Parallel_postulate" title="Parallel postulate">parallel postulate</a> that his father, who had pursued the same subject for many years, wrote to him in 1820: "You must not attempt this approach to parallels. I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life. I entreat you, leave the science of parallels alone...Learn from my example."<sup id="cite_ref-Ellenberg_5-0" class="reference"><a href="#cite_note-Ellenberg-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>János, however, persisted in his quest and eventually came to the conclusion that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on its negation. In 1823, he wrote to his father: "I have discovered such wonderful things that I was amazed...out of nothing I have created a strange new universe."<sup id="cite_ref-Ellenberg_5-1" class="reference"><a href="#cite_note-Ellenberg-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tóth_1965_6-0" class="reference"><a href="#cite_note-Tóth_1965-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Between 1820 and 1823 he had prepared a treatise on <a href="/wiki/Parallel_lines" class="mw-redirect" title="Parallel lines">parallel lines</a> that he called <a href="/wiki/Absolute_geometry" title="Absolute geometry">absolute geometry</a>. Bolyai's work was published in 1832 as an appendix to a mathematics textbook by his father. </p><p><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a>, on reading the Appendix, wrote in a letter, "I regard this young <a href="/wiki/Geometer" class="mw-redirect" title="Geometer">geometer</a> Bolyai as a genius of the first order."<sup id="cite_ref-St_Andrews_7-0" class="reference"><a href="#cite_note-St_Andrews-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> To his old friend Farkas Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years."<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><sup id="cite_ref-Ellenberg_5-2" class="reference"><a href="#cite_note-Ellenberg-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-St_Andrews_7-1" class="reference"><a href="#cite_note-St_Andrews-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tóth_1965_6-1" class="reference"><a href="#cite_note-Tóth_1965-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Indeed, Gauss had disclosed his discovery of a consistent non-Euclidean geometry in a letter in 1827, and in 1829 wrote that he feared backlash if he published about it.<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> János suspected that Gauss had been secretly informed about his discoveries by his father, causing a rift between him and his father.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> He later bitterly complained about Gauss's attitude.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>In 1848 Bolyai learned that <a href="/wiki/Nikolai_Ivanovich_Lobachevsky" class="mw-redirect" title="Nikolai Ivanovich Lobachevsky">Nikolai Ivanovich Lobachevsky</a> had published a piece of work similar to his appendix in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained only <a href="/wiki/Hyperbolic_geometry" title="Hyperbolic geometry">hyperbolic geometry</a>. Working independently, Bolyai and Lobachevsky pioneered the investigation of <a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean geometry</a>. </p><p>In addition to his work in geometry, Bolyai developed a rigorous geometric concept of <a href="/wiki/Complex_numbers" class="mw-redirect" title="Complex numbers">complex numbers</a> as ordered pairs of <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">real numbers</a>. Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died. These can now be found in the <a href="/wiki/Teleki_Library" title="Teleki Library">Teleki-Bolyai Library</a> in <a href="/wiki/T%C3%A2rgu_Mure%C8%99" title="Târgu Mureș">Târgu Mureș</a>, where Bolyai died. His grave lies in the Lutheran Cemetery in Târgu Mureș.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Personal_life">Personal life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&section=3" title="Edit section: Personal life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>He was an accomplished linguist, speaking several foreign <a href="/wiki/Language" title="Language">languages</a> beside his native Hungarian, these being <a href="/wiki/German_language" title="German language">German</a>, <a href="/wiki/Latin" title="Latin">Latin</a>, <a href="/wiki/French_language" title="French language">French</a>, <a href="/wiki/Italian_language" title="Italian language">Italian</a> and <a href="/wiki/Romanian_language" title="Romanian language">Romanian</a>. He learned the violin and performed in Vienna.<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> </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>It is related of him that he was challenged by thirteen officers of his garrison, a thing not unlikely to happen considering how differently he thought from everyone else. He fought them all in succession—making it his only condition that he should be allowed to play on his violin for an interval between meeting each opponent. He disarmed or wounded all his antagonists. It can be easily imagined that a temperament such as his was not one congenial to his military superiors. He was retired in 1833.<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></blockquote> <p>No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.<sup id="cite_ref-amsNotices_1-2" class="reference"><a href="#cite_note-amsNotices-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Legacy">Legacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&section=4" title="Edit section: Legacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Babe%C8%99-Bolyai_University" title="Babeș-Bolyai University">Babeș-Bolyai University</a> in <a href="/wiki/Cluj-Napoca" title="Cluj-Napoca">Cluj-Napoca</a>, that was established in 1959, bears his name, as does the professional society of Hungarian mathematicians, the <a href="/wiki/J%C3%A1nos_Bolyai_Mathematical_Institute" title="János Bolyai Mathematical Institute">János Bolyai Mathematical Institute</a>, at the <a href="/wiki/University_of_Szeged" title="University of Szeged">University of Szeged</a>. There is also a mathematical award given out every five years, named the <a href="/wiki/Bolyai_Prize" title="Bolyai Prize">Bolyai Prize</a>. Bolyai is a minor character in the 1969 science-fiction/fantasy story <a href="/wiki/Operation_Chaos_(novel)" title="Operation Chaos (novel)">"Operation Changeling"</a>, where his unique abilities allow the protagonists to navigate the non-Euclidean geometry of <a href="/wiki/Hell" title="Hell">Hell</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2022)">citation needed</span></a></i>]</sup> </p><p>The crater <a href="/wiki/Bolyai_(crater)" title="Bolyai (crater)">Bolyai</a> on the <a href="/wiki/Moon" title="Moon">Moon</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> and <a href="/wiki/1441_Bolyai" title="1441 Bolyai">1441 Bolyai</a>, a <a href="/wiki/Minor_planet" title="Minor planet">minor planet</a> discovered in 1937, are also named after him. </p><p>Several primary and secondary schools in the <a href="/wiki/Pannonian_Basin" title="Pannonian Basin">Carpathian Basin</a> also bear Bolyai's name; for instance, Bolyai János Műszaki Szakközépiskola in <a href="/wiki/Budapest" title="Budapest">Budapest</a>, Bolyai János Gyakorló Általános Iskola és Gimnázium in <a href="/wiki/Szombathely" title="Szombathely">Szombathely</a>, and the Bolyai János Általános Iskola in <a href="/wiki/Debrecen" title="Debrecen">Debrecen</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2013)">citation needed</span></a></i>]</sup> Streets in Budapest, Cluj-Napoca,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Timi%C8%99oara" title="Timișoara">Timișoara</a><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> are named after Bolyai. </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&section=5" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>"Appendix scientiam spatii absolute veram exhibens; a veritate aut falsitate axiomatis XI Euclidei, a priori haud unquam", appendix to <a href="/wiki/Farkas_Bolyai" title="Farkas Bolyai">Farkas Bolyai</a>, <i>Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi (An Attempt to Introduce Studious Youths to the Elements of Pure Mathematics)</i>, 1832. <ul><li>English translation: <a rel="nofollow" class="external text" href="http://real-eod.mtak.hu/2790/">"The Science Absolute of Space: Independent of the Truth or Falsity of Euclid's Axiom XI (Which Can Never Be Decided A Priori)"</a>, The Neomon, Austin, 1896.</li></ul></li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bolyai-1.jpg" class="mw-file-description" title="1896 copy of Bolyai's "The science absolute of space, independent of the truth or falsity of Euclid's axiom XI (which can never be decided a priori)""><img alt="1896 copy of Bolyai's "The science absolute of space, independent of the truth or falsity of Euclid's axiom XI (which can never be decided a priori)"" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Bolyai-1.jpg/80px-Bolyai-1.jpg" decoding="async" width="80" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Bolyai-1.jpg/120px-Bolyai-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Bolyai-1.jpg/160px-Bolyai-1.jpg 2x" data-file-width="2972" data-file-height="4462" /></a></span></div> <div class="gallerytext">1896 copy of Bolyai's "<i>The science absolute of space, independent of the truth or falsity of Euclid's axiom XI (which can never be decided a priori)</i>"</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bolyai-2.jpg" class="mw-file-description" title="Appendix to "The science absolute of space""><img alt="Appendix to "The science absolute of space"" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bolyai-2.jpg/77px-Bolyai-2.jpg" decoding="async" width="77" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bolyai-2.jpg/116px-Bolyai-2.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bolyai-2.jpg/155px-Bolyai-2.jpg 2x" data-file-width="2662" data-file-height="4123" /></a></span></div> <div class="gallerytext">Appendix to "<i>The science absolute of space</i>"</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bolyai-3.jpg" class="mw-file-description" title="First page to "The science absolute of space""><img alt="First page to "The science absolute of space"" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bolyai-3.jpg/79px-Bolyai-3.jpg" decoding="async" width="79" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bolyai-3.jpg/118px-Bolyai-3.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bolyai-3.jpg/158px-Bolyai-3.jpg 2x" data-file-width="2845" data-file-height="4318" /></a></span></div> <div class="gallerytext">First page to "<i>The science absolute of space</i>"</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&section=6" title="Edit section: Gallery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1248256098">@media all and (max-width:720px){.mw-parser-output .mod-gallery{width:100%!important}}.mw-parser-output .mod-gallery{display:table}.mw-parser-output .mod-gallery-default{background:transparent;margin-top:4px}.mw-parser-output .mod-gallery-center{margin-left:auto;margin-right:auto}.mw-parser-output .mod-gallery-left{float:left}.mw-parser-output .mod-gallery-right{float:right}.mw-parser-output .mod-gallery-none{float:none}.mw-parser-output .mod-gallery-collapsible{width:100%}.mw-parser-output .mod-gallery .title,.mw-parser-output .mod-gallery .main,.mw-parser-output .mod-gallery .footer{display:table-row}.mw-parser-output .mod-gallery .title>div{display:table-cell;padding:0 4px 4px;text-align:center;font-weight:bold}.mw-parser-output .mod-gallery .main>div{display:table-cell}.mw-parser-output .mod-gallery .gallery{line-height:1.35em}.mw-parser-output .mod-gallery .footer>div{display:table-cell;padding:4px;text-align:right;font-size:85%;line-height:1em}.mw-parser-output .mod-gallery .title>div *,.mw-parser-output .mod-gallery .footer>div *{overflow:visible}.mw-parser-output .mod-gallery .gallerybox img{background:none!important}.mw-parser-output .mod-gallery .bordered-images .thumb img{border:solid var(--background-color-neutral,#eaecf0)1px}.mw-parser-output .mod-gallery .whitebg .thumb{background:var(--background-color-base,#fff)!important}</style><div class="mod-gallery mod-gallery-default"><div class="main"><div><ul class="gallery mw-gallery-traditional nochecker bordered-images whitebg"> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Pseudosphaera2.JPG" class="mw-file-description" title="The Pseudosphere monument in Târgu Mureș"><img alt="The Pseudosphere monument in Târgu Mureș" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Pseudosphaera2.JPG/180px-Pseudosphaera2.JPG" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Pseudosphaera2.JPG/270px-Pseudosphaera2.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Pseudosphaera2.JPG/360px-Pseudosphaera2.JPG 2x" data-file-width="2272" data-file-height="1704" /></a></span></div> <div class="gallerytext">The <a href="/wiki/Pseudosphere" title="Pseudosphere">Pseudosphere</a> monument in <a href="/wiki/T%C3%A2rgu_Mure%C8%99" title="Târgu Mureș">Târgu Mureș</a></div> </li> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Bolyai_J%C3%A1nos-szobor.jpg" class="mw-file-description" title="Bust of János Bolyai in Cluj-Napoca"><img alt="Bust of János Bolyai in Cluj-Napoca" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Bolyai_J%C3%A1nos-szobor.jpg/135px-Bolyai_J%C3%A1nos-szobor.jpg" decoding="async" width="135" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Bolyai_J%C3%A1nos-szobor.jpg/202px-Bolyai_J%C3%A1nos-szobor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Bolyai_J%C3%A1nos-szobor.jpg/270px-Bolyai_J%C3%A1nos-szobor.jpg 2x" data-file-width="768" data-file-height="1024" /></a></span></div> <div class="gallerytext">Bust of János Bolyai in <a href="/wiki/Cluj-Napoca" title="Cluj-Napoca">Cluj-Napoca</a></div> </li> <li class="gallerybox" style="width: 215px"> <div class="thumb" style="width: 210px; height: 210px;"><span typeof="mw:File"><a href="/wiki/File:Nuseni_(6).JPG" class="mw-file-description" title="Bust of János Bolyai in Nușeni"><img alt="Bust of János Bolyai in Nușeni" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuseni_%286%29.JPG/180px-Nuseni_%286%29.JPG" decoding="async" width="180" height="135" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuseni_%286%29.JPG/270px-Nuseni_%286%29.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuseni_%286%29.JPG/360px-Nuseni_%286%29.JPG 2x" data-file-width="3264" data-file-height="2448" /></a></span></div> <div class="gallerytext">Bust of János Bolyai in <a href="/wiki/Nu%C8%99eni" title="Nușeni">Nușeni</a></div> </li> </ul></div></div></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=J%C3%A1nos_Bolyai&action=edit&section=7" 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-amsNotices-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-amsNotices_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-amsNotices_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-amsNotices_1-2"><sup><i><b>c</b></i></sup></a></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="CITEREFDénes2011" class="citation journal cs1">Dénes, Tamás (January 2011). <a rel="nofollow" class="external text" href="https://www.ams.org/notices/201101/rtx110100041p.pdf">"Real Face of János Bolyai"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Notices_of_the_American_Mathematical_Society" title="Notices of the American Mathematical Society">Notices of the American Mathematical Society</a></i>. <b>58</b> (1): 41–51<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-06-18</span></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+American+Mathematical+Society&rft.atitle=Real+Face+of+J%C3%A1nos+Bolyai&rft.volume=58&rft.issue=1&rft.pages=41-51&rft.date=2011-01&rft.aulast=D%C3%A9nes&rft.aufirst=Tam%C3%A1s&rft_id=https%3A%2F%2Fwww.ams.org%2Fnotices%2F201101%2Frtx110100041p.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Tucker McElroy. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MiZIWtX9AJUC&pg=PA40"><i>A to Z of Mathematicians</i></a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/72441/Janos-Bolyai">Encyclopædia Britannica: János Bolyai</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://kollegium.uni-miskolc.hu/aboutbolyai">"About Bolyai"</a>. Miskolci Egyetem Bolyai Kollégium<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=About+Bolyai&rft.pub=Miskolci+Egyetem+Bolyai+Koll%C3%A9gium&rft_id=https%3A%2F%2Fkollegium.uni-miskolc.hu%2Faboutbolyai&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> <li id="cite_note-Ellenberg-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Ellenberg_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Ellenberg_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Ellenberg_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEllenberg2014" class="citation book cs1"><a href="/wiki/Jordan_Ellenberg" title="Jordan Ellenberg">Ellenberg, Jordan</a> (May 2014). <i><a href="/wiki/How_Not_to_Be_Wrong" title="How Not to Be Wrong">How Not to Be Wrong</a></i>. <a href="/wiki/New_York_City" title="New York City">New York, NY</a>: <a href="/wiki/Penguin_Group" title="Penguin Group">Penguin Group</a>. p. 365. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-14-312-753-6" title="Special:BookSources/978-0-14-312-753-6"><bdi>978-0-14-312-753-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Not+to+Be+Wrong&rft.place=New+York%2C+NY&rft.pages=365&rft.pub=Penguin+Group&rft.date=2014-05&rft.isbn=978-0-14-312-753-6&rft.aulast=Ellenberg&rft.aufirst=Jordan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> <li id="cite_note-Tóth_1965-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-Tóth_1965_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Tóth_1965_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTóth1965" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="/wiki/L%C3%A1szl%C3%B3_Fejes_T%C3%B3th" title="László Fejes Tóth">Tóth, László Fejes</a> (1965). "1.3.4. Anmerkungen". <i>Reguläre Figuren</i> (in German) (1 ed.). <a href="/wiki/B._G._Teubner_Verlagsgesellschaft" class="mw-redirect" title="B. G. Teubner Verlagsgesellschaft">B. G. Teubner Verlagsgesellschaft</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/B._G._Teubner_Verlag" class="extiw" title="de:B. G. Teubner Verlag">de</a>]</span>, Leipzig, East-Germany / <a href="/wiki/Akad%C3%A9miai_Kiad%C3%B3" title="Akadémiai Kiadó">Akadémiai Kiadó</a>, Budapest, Hungary. pp. 97–98. ES-No. 19 83. Kenn-No. 375. Lizenz-No. 294.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=1.3.4.+Anmerkungen&rft.btitle=Regul%C3%A4re+Figuren&rft.pages=97-98&rft.edition=1&rft.pub=B.+G.+Teubner+Verlagsgesellschaft%3Cspan+class%3D%22noprint%22+style%3D%22font-size%3A85%25%3B+font-style%3A+normal%3B+%22%3E+%26%2391%3Bde%26%2393%3B%3C%2Fspan%3E%2C+Leipzig%2C+East-Germany+%2F+Akad%C3%A9miai+Kiad%C3%B3%2C+Budapest%2C+Hungary&rft.date=1965&rft.aulast=T%C3%B3th&rft.aufirst=L%C3%A1szl%C3%B3+Fejes&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span> (2+316+6 pages, 12 <a href="/wiki/Anaglyph_3D" title="Anaglyph 3D">anaglyph</a> cards, 1 red-green glasses)</span> </li> <li id="cite_note-St_Andrews-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-St_Andrews_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-St_Andrews_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="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Bolyai.html">"János Bolyai"</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=J%C3%A1nos+Bolyai&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%2FBolyai.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" 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"><a rel="nofollow" class="external text" href="https://archive.org/details/briefwechselzwi00gausgoog/page/n146/mode/2up">Letter from Gauss to Farkas Bolyai from 6 March 1832</a></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">Greenberg 2008, p. 243-244</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOsserman2005" class="citation journal cs1">Osserman, Robert (2005). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/notices/200509/rev-osserman.pdf">"Book Review: Non-Euclidean Geometry, and the Nature of Space"</a> <span class="cs1-format">(PDF)</span>. <i>Notices of the AMS</i>. <b>52</b> (9).</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=Book+Review%3A+Non-Euclidean+Geometry%2C+and+the+Nature+of+Space.&rft.volume=52&rft.issue=9&rft.date=2005&rft.aulast=Osserman&rft.aufirst=Robert&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fnotices%2F200509%2Frev-osserman.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Greenberg 2008, p. 242</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 id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Extras/Bolyai_house_grave.html">"Janos Bolyai's birth house and original grave"</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=Janos+Bolyai%27s+birth+house+and+original+grave&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%2FExtras%2FBolyai_house_grave.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" 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">Elemér, Kiss, <a rel="nofollow" class="external text" href="http://mek.oszk.hu/05300/05321/05321.pdf">"Matematikai kincsek Bolyai János kéziratos hagyatékából"</a></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 id="CITEREFHinton1912" class="citation book cs1"><a href="/wiki/Charles_Howard_Hinton" title="Charles Howard Hinton">Hinton, Charles Howard</a> (1912) [1904]. <a rel="nofollow" class="external text" href="https://archive.org/stream/fourthdimension00hintarch#page/46/"><i>The Fourth Dimension</i></a>. London: <a href="/wiki/Allen_%26_Unwin" title="Allen & Unwin">G. Allen & Unwin Ltd.</a> p. 46.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fourth+Dimension&rft.place=London&rft.pages=46&rft.pub=G.+Allen+%26+Unwin+Ltd.&rft.date=1912&rft.aulast=Hinton&rft.aufirst=Charles+Howard&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Ffourthdimension00hintarch%23page%2F46%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span> Sources cited, p. 41. Entire chapter V, "The Second Chapter in the History of Four Space", pp. 41–60, provides accessible, illustrated introduction to his life and work.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://lunar.arc.nasa.gov/printerready/science/geography_items/carters/craters_b.html">NASA website</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20051023083235/http://lunar.arc.nasa.gov/printerready/science/geography_items/carters/craters_b.html">Archived</a> 23 October 2005 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://www.clujeni.com/despre/strada_bolyai_janos/">"Strada Bolyai Janos"</a>. <i>www.clujeni.com</i> (in Romanian)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-01-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.clujeni.com&rft.atitle=Strada+Bolyai+Janos&rft_id=https%3A%2F%2Fwww.clujeni.com%2Fdespre%2Fstrada_bolyai_janos%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://www.harti-orase.ro/timisoara/strazi/strada-bolyai-janos-timisoara.html">"Strada Bolyai János, Timișoara"</a>. <i>www.harti-orase.ro</i> (in Romanian)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-01-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.harti-orase.ro&rft.atitle=Strada+Bolyai+J%C3%A1nos%2C+Timi%C8%99oara&rft_id=http%3A%2F%2Fwww.harti-orase.ro%2Ftimisoara%2Fstrazi%2Fstrada-bolyai-janos-timisoara.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&section=8" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Martin_Gardner" title="Martin Gardner">Martin Gardner</a> (2001) <i>Non-Euclidean Geometry</i>, Chapter 4 of <i>The Colossal Book of Mathematics</i>, <a href="/wiki/W._W._Norton_%26_Company" title="W. W. Norton & Company">W. W. Norton & Company</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-02023-1" title="Special:BookSources/0-393-02023-1">0-393-02023-1</a></li> <li><a href="/wiki/Jeremy_Gray" title="Jeremy Gray">Jeremy Gray</a> (2004) <i>Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space,</i> MIT Press <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0262571749" title="Special:BookSources/0262571749">0262571749</a></li> <li><a href="/wiki/Marvin_Greenberg" title="Marvin Greenberg">Marvin Greenberg</a> (2008) <i>Euclidean and Non-Euclidean Geometries: Development and History</i>, 4th edition, <a href="/wiki/W._H._Freeman_and_Company" title="W. H. Freeman and Company">W. H. Freeman</a></li> <li>Elemér Kiss (1999) <i>Mathematical Gems from the Bolyai Chests. János Bolyai's discoveries in number theory and algebra as recently deciphered from his manuscripts</i>. Translated by Anikó Csirmaz and Gábor Oláh. <a href="/wiki/Akad%C3%A9miai_Kiad%C3%B3" title="Akadémiai Kiadó">Akadémiai Kiadó</a>, Budapest; TypoTeX, Budapest, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/963-05-7563-9" title="Special:BookSources/963-05-7563-9">963-05-7563-9</a>;</li> <li>Tibor Weszely (2013) <i>János Bolyai. Die ersten 200 Jahre</i>, <a href="/wiki/Birkh%C3%A4user" title="Birkhäuser">Birkhäuser</a>, (translated from Hungarian by Manfred Stern), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-0346-0046-0" title="Special:BookSources/978-3-0346-0046-0">978-3-0346-0046-0</a></li> <li>Ana Todea, Maria Fűllop, Monica Avram (2004) <i>Oameni de știință mureșeni - Dicționar biobibliografic</i>, CJ Mureș Biblioteca Județeană Mureș, tipografia Mediaprint SRL <span class="languageicon">(in Romanian)</span></li> <li>Silva Oliva (2018) <i>Janos Bolyai. Uno sguardo psicoanalitico su genio matematico e follia</i>, ed Mimesis.</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=J%C3%A1nos_Bolyai&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/J%C3%A1nos_Bolyai" class="extiw" title="commons:János Bolyai">János Bolyai</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=101411">János Bolyai</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://telekiteka.ro/index.php?lang=en">"The Bolyai Memorial Museum"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Bolyai+Memorial+Museum&rft_id=http%3A%2F%2Ftelekiteka.ro%2Findex.php%3Flang%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJ%C3%A1nos+Bolyai" class="Z3988"></span></li></ul> <div class="navbox-styles"><style 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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/Q16924#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/Q16924#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/Q16924#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000108651826">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/5062952">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/58917/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJw937WtmGpFvVW4GqgtKd">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/119372886">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n80102026">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb129506836">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb129506836">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Bolyai, János"><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/PUVV136642">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35274155">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=jn20010525264&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX4854813">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p073433705">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90144934">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000131795&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/khwzzr335fvljtz">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810607167405606">Poland</a></span></li><li><span class="uid"><a class="external text" href="https://wikidata-externalid-url.toolforge.org/?p=8034&url_prefix=https://opac.vatlib.it/auth/detail/&id=495/174972">Vatican</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007258847105171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA01180644?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=101411">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:bolyai.janos">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/39020">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/892631">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd119372886.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/119372886">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/027359697">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6z32psw">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img 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