Niels Henrik Abel | Biography & Facts

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mathematician</div> </div> </div> <div class="d-none d-sm-flex flex-row"> <div class="mr-10 mb-15"> <button class="ai-ask-button btn border-2 btn-sm js-inline-ai-ask-button btn-outline-red-400 border-red-400"> Ask the Chatbot a Question </button> </div> <div class="d-none d-sm-block md-topic-tools qa-action-buttons mb-15" data-topic-id="1025"> <button class="js-tooltip btn btn-sm btn-outline-blue border pr-10 border-2" > <em class="material-icons md-icon ml-n10 my-n5 mr-5" data-icon="more_vert"></em> More Actions </button> <div class="md-more-popover popover popover-sm p-0 font-14 z-1"> <div> <a class="js-modal btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" href="/print/article/1025" target="_blank" > <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="print"></em> Print </a> </div> <div> <button class="js-modal qa-cite-modal-button btn btn-sm btn-link gtm-topic-tool font-weight-bold btn-link" data-modal="[data-topic-id=1025] .md-cite-modal"> <em 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In 1815 Niels entered the <a href="https://www.britannica.com/topic/cathedral-school" class="md-crosslink autoxref " data-show-preview="true">cathedral school</a> in <a href="https://www.britannica.com/place/Oslo" class="md-crosslink autoxref " data-show-preview="true">Oslo</a>, where his mathematical talent was recognized in 1817 with the arrival of a new mathematics teacher, Bernt Michael Holmboe, who introduced him to the classics in mathematical literature and proposed original problems for him to solve. Abel studied the mathematical works of the 17th-century Englishman <a href="https://www.britannica.com/biography/Isaac-Newton" class="md-crosslink " data-show-preview="true">Sir Isaac Newton</a>, the 18th-century Swiss <a href="https://www.britannica.com/biography/Leonhard-Euler" class="md-crosslink " data-show-preview="true">Leonhard Euler</a>, and his <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="contemporaries" href="https://www.britannica.com/dictionary/contemporaries" data-type="EB">contemporaries</a> the Frenchman <a href="https://www.britannica.com/biography/Joseph-Louis-Lagrange-comte-de-lEmpire" class="md-crosslink " data-show-preview="true">Joseph-Louis Lagrange</a> and the German <a href="https://www.britannica.com/biography/Carl-Friedrich-Gauss" class="md-crosslink " data-show-preview="true">Carl Friedrich Gauss</a> in preparation for his own research.</p><span class="marker MOD2 mod-inline"></span><span class="marker PREMOD3 mod-inline"></span><div class="assemblies"><div class="w-100"><figure class="md-assembly m-0 mb-md-0 card card-borderless print-false" data-assembly-id="21320" data-asm-type="image"><div class="md-assembly-wrapper card-media " data-type="image"><a href="https://cdn.britannica.com/42/28742-050-E596D301/lithograph-drawing-Niels-Henrik-Abel-Johan-Gorbitz-1826.jpg" class="gtm-assembly-link position-relative d-flex align-items-center justify-content-center media-overlay-link card-media" data-href="/media/1/1025/21320"><picture><source media="(min-width: 680px)" srcset="https://cdn.britannica.com/42/28742-050-E596D301/lithograph-drawing-Niels-Henrik-Abel-Johan-Gorbitz-1826.jpg?w=300"><img src="https://cdn.britannica.com/42/28742-050-E596D301/lithograph-drawing-Niels-Henrik-Abel-Johan-Gorbitz-1826.jpg?w=300" alt="Niels Henrik Abel" data-width="1216" data-height="1600" loading="eager"></picture><button class="magnifying-glass btn btn-circle position-absolute shadow btn-white top-10 right-10" aria-label="Zoom in"><em class="material-icons link-blue" data-icon="zoom_in"></em></button></a></div><figcaption class="card-body"><div class="md-assembly-caption text-muted font-14 font-serif line-clamp"><span><a class="gtm-assembly-link md-assembly-title font-weight-bold d-inline font-sans-serif mr-5 media-overlay-link" href="https://cdn.britannica.com/42/28742-050-E596D301/lithograph-drawing-Niels-Henrik-Abel-Johan-Gorbitz-1826.jpg" data-href="/media/1/1025/21320">Niels Henrik Abel</a><span>Niels Henrik Abel, lithograph after a drawing by Johan Gorbitz, 1826.</span><button class="js-more-btn d-none btn btn-unstyled font-12 bg-white js-content" aria-label="Toggle more/less fact data"><span class="link-blue">(more)</span></button></span></div></figcaption></figure></div></div><p class="topic-paragraph">Abel’s father died in 1820, leaving the family in straitened circumstances, but Holmboe contributed and raised funds that enabled Abel to enter the University of Christiania (Oslo) in 1821. Abel obtained a preliminary degree from the university in 1822 and continued his studies independently with further subsidies obtained by Holmboe.</p><a class="link-module shadow-sm d-block qa-quiz-module" href="/quiz/Numbers-and-mathematics" data-link-module-iframe-link=""> <img loading="lazy" src="https://cdn.britannica.com/86/94086-131-0BAE374D/Equations-blackboard.jpg" alt="Equations written on blackboard" class="rounded-sm mr-15" width="70" /> <div class="line-clamp clamp-5"> <div class="module-title bg-green">Britannica Quiz</div> <div class="font-weight-semi-bold mt-5">Numbers and Mathematics</div> </div> </a><span class="marker MOD3 mod-inline"></span><span class="marker PREMOD4 mod-inline"></span><p class="topic-paragraph">Abel’s first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an <span id="ref1030850"></span><a href="https://www.britannica.com/science/integral-equation" class="md-crosslink " data-show-preview="true">integral equation</a>. His friends <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="urged" href="https://www.britannica.com/dictionary/urged" data-type="EB">urged</a> the Norwegian government to grant him a fellowship for study in Germany and France. In 1824, while waiting for a royal decree to be issued, he published at his own expense his proof of the impossibility of solving algebraically the general <a href="https://www.britannica.com/science/equation" class="md-crosslink autoxref " data-show-preview="true">equation</a> of the fifth degree, which he hoped would bring him recognition. He sent the pamphlet to <span id="ref1030851"></span><a href="https://www.britannica.com/biography/Carl-Friedrich-Gauss" class="md-crosslink " data-show-preview="true">Gauss</a>, who dismissed it, failing to recognize that the famous problem had indeed been settled.</p><span class="marker MOD4 mod-inline"></span><span class="marker PREMOD5 mod-inline"></span><p class="topic-paragraph">Abel spent the winter of 1825–26 with Norwegian friends in Berlin, where he met <span id="ref210588"></span><a href="https://www.britannica.com/biography/August-Leopold-Crelle" class="md-crosslink " data-show-preview="true">August Leopold Crelle</a>, civil engineer and self-taught enthusiast of mathematics, who became his close friend and mentor. With Abel’s warm encouragement, Crelle founded the <em>Journal für die reine und angewandte Mathematik</em> (“Journal for Pure and Applied Mathematics”), commonly known as <em><span id="ref756071"></span><a href="https://www.britannica.com/topic/Crelles-Journal" class="md-crosslink ">Crelle’s Journal</a></em>. The first volume (1826) contains papers by Abel, including a more elaborate version of his work on the quintic equation. Other papers dealt with equation theory, <a href="https://www.britannica.com/science/calculus-mathematics" class="md-crosslink " data-show-preview="true">calculus</a>, and theoretical <a href="https://www.britannica.com/science/mechanics" class="md-crosslink " data-show-preview="true">mechanics</a>. Later volumes presented Abel’s theory of <a href="https://www.britannica.com/science/elliptic-equation" class="md-crosslink " data-show-preview="true">elliptic functions</a>, which are complex functions (<em>see</em> <a href="https://www.britannica.com/science/complex-number" class="md-crosslink " data-show-preview="true">complex number</a>) that generalize the usual <a href="https://www.britannica.com/science/trigonometric-function" class="md-crosslink " data-show-preview="true">trigonometric functions</a>.</p><span class="marker MOD5 mod-inline"></span><span class="marker PREMOD6 mod-inline"></span><p class="topic-paragraph">In 1826 Abel went to Paris, then the world centre for mathematics, where he called on the foremost mathematicians and completed a major paper on the theory of <a class="md-dictionary-link md-dictionary-tt-off mw" data-term="integrals" href="https://www.merriam-webster.com/dictionary/integrals" data-type="MW">integrals</a> of algebraic functions. His central result, known as <span id="ref210589"></span>Abel’s theorem, is the basis for the later theory of Abelian integrals and Abelian functions, a generalization of elliptic <a href="https://www.britannica.com/science/function-mathematics" class="md-crosslink autoxref " data-show-preview="true">function</a> theory to functions of several variables. However, Abel’s visit to Paris was unsuccessful in securing him an appointment, and the memoir he submitted to the French <a href="https://www.britannica.com/topic/Academy-of-Sciences-French-organization" class="md-crosslink " data-show-preview="true">Academy of Sciences</a> was lost.</p><span class="marker MOD6 mod-inline"></span><span class="marker PREMOD7 mod-inline"></span><div class="assemblies"><div class="w-100"><figure class="md-assembly m-0 mb-md-0 card card-borderless print-false" data-assembly-id="155220" data-asm-type="image"><div class="md-assembly-wrapper card-media " data-type="image"><a href="https://cdn.britannica.com/46/149046-050-FA92E2CE/bust-Niels-Henrik-Abel-Gjerstad.jpg" class="gtm-assembly-link position-relative d-flex align-items-center justify-content-center media-overlay-link card-media" data-href="/media/1/1025/155220"><picture><source media="(min-width: 680px)" srcset="https://cdn.britannica.com/46/149046-050-FA92E2CE/bust-Niels-Henrik-Abel-Gjerstad.jpg?w=300"><img src="https://cdn.britannica.com/46/149046-050-FA92E2CE/bust-Niels-Henrik-Abel-Gjerstad.jpg?w=300" alt="Niels Henrik Abel" data-width="906" data-height="1585" loading="eager"></picture><button class="magnifying-glass btn btn-circle position-absolute shadow btn-white top-10 right-10" aria-label="Zoom in"><em class="material-icons link-blue" data-icon="zoom_in"></em></button></a></div><figcaption class="card-body"><div class="md-assembly-caption text-muted font-14 font-serif line-clamp"><span><a class="gtm-assembly-link md-assembly-title font-weight-bold d-inline font-sans-serif mr-5 media-overlay-link" href="https://cdn.britannica.com/46/149046-050-FA92E2CE/bust-Niels-Henrik-Abel-Gjerstad.jpg" data-href="/media/1/1025/155220">Niels Henrik Abel</a><span>Niels Henrik Abel, bust in Gjerstad, Norway.</span><button class="js-more-btn d-none btn btn-unstyled font-12 bg-white js-content" aria-label="Toggle more/less fact data"><span class="link-blue">(more)</span></button></span></div></figcaption></figure></div></div><p class="topic-paragraph">Abel returned to Norway heavily in debt and suffering from <a href="https://www.britannica.com/science/tuberculosis" class="md-crosslink autoxref " data-show-preview="true">tuberculosis</a>. He subsisted by tutoring, supplemented by a small grant from the University of Christiania and, beginning in 1828, by a temporary teaching position. His poverty and ill health did not decrease his production; he wrote a great number of papers during this period, principally on equation theory and elliptic functions. Among them are the theory of polynomial equations with Abelian groups. He rapidly developed the theory of elliptic functions in competition with the German <a href="https://www.britannica.com/biography/Carl-Jacobi" class="md-crosslink " data-show-preview="true">Carl Gustav Jacobi</a>. By this time Abel’s fame had spread to all mathematical centres, and strong efforts were made to secure a suitable position for him by a group from the <a href="https://www.britannica.com/topic/French-Academy" class="md-crosslink autoxref " data-show-preview="true">French Academy</a>, who addressed King <a href="https://www.britannica.com/topic/House-of-Bernadotte" class="md-crosslink " data-show-preview="true">Bernadotte</a> of Norway-Sweden; Crelle also worked to secure a professorship for him in Berlin.</p><div class="module-spacing"> <DIV class="marketing-INLINE_SUBSCRIPTION marketing-content" data-marketing-id="INLINE_SUBSCRIPTION"><style> .student-promo-banner-wrapper { container-type: inline-size; margin-bottom: 15px; } @container (min-width: 475px) { .student-promo-banner { flex-direction: row; } .student-promo-banner-img-wrapper { margin-bottom: 0; margin-right: 10px; justify-content: flex-start; } .student-promo-banner-text-wrapper { text-align: left; margin-bottom: 0px; margin-left: 10px; } .student-promo-banner-button-wrapper { margin-right: 0; } }</style> <div class="student-promo-banner-wrapper"> <div class="student-promo-banner d-flex flex-column align-items-center bg-blue rounded p-20"> <div class="student-promo-banner-img-wrapper mb-20 mr-0 d-flex justify-content-center"> <img class="rounded" style="max-width: 100px; min-width: 80px" src="https://cdn.britannica.com/marketing/BlueThistle.webp" /> </div> <div class="student-promo-banner-text-wrapper ml-0 mb-10 text-center text-white"> <div class="h2 mb-10">Get Unlimited Access</div> <div class="h4 font-weight-semi-bold">Try Britannica Premium for free and discover more.</div> </div> <div class="student-promo-banner-button-wrapper d-flex justify-content-center align-items-center ml-auto mr-auto"> <a class="btn btn-m btn-orange" href="https://premium.britannica.com/premium-membership/?utm_source=premium&utm_medium=inline-cta&utm_campaign=black-friday-2024">Subscribe</a> </div> </div> </div> </DIV></div><div class="one-good-fact-module"> </div><span class="marker MOD7 mod-inline"></span><span class="marker PREMOD8 mod-inline"></span><p class="topic-paragraph">In the fall of 1828 Abel became seriously ill, and his condition <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="deteriorated" href="https://www.britannica.com/dictionary/deteriorated" data-type="EB">deteriorated</a> on a sled trip at Christmastime to visit his fiancée at Froland, where he died. The French Academy published his memoir in 1841.</p><span class="marker MOD8 mod-inline"></span></section> <span class="md-signature">This article was most recently revised and updated by <a href="/contributor/encyclopaedia-britannica/12989892">Encyclopaedia Britannica</a>.</span><span class="marker end-of-content"></span><span class="marker after-article"></span></div> <div id="chatbot-root"></div> </div> </div> </div> <div class="ai-dialog-placeholder"></div> </div> </div> <aside class="col-md-da-320"></aside> </div> </div> </div> </div> </article></div> </div></div> </div> </main> <div id="md-footer"></div> <noscript><iframe src="//www.googletagmanager.com/ns.html?id=GTM-5W6NC8" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <script type="text/javascript" id="_informizely_script_tag"> var IzWidget = IzWidget || {}; (function (d) { var scriptElement = d.createElement('script'); scriptElement.type = 'text/javascript'; scriptElement.async = true; scriptElement.src = "https://insitez.blob.core.windows.net/site/f780f33e-a610-4ac2-af81-3eb184037547.js"; var node = d.getElementById('_informizely_script_tag'); node.parentNode.insertBefore(scriptElement, node); } )(document); </script>  <script> window.ap3c = window.ap3c || {}; var ap3c = window.ap3c; ap3c.cmd = ap3c.cmd || []; ap3c.cmd.push(function() { ap3c.init('ZO4siT4cLwnykPnzZWJtd3Byb2Q', 'https://engage.email.britannica.com/'); ap3c.track({v: 0}); }); ap3c.activity = function(act) { ap3c.act = (ap3c.act || []); ap3c.act.push(act); }; var s, t; s = document.createElement('script'); s.type = 'text/javascript'; s.src = "https://engage.email.britannica.com/app.js"; t = document.getElementsByTagName('script')[0]; t.parentNode.insertBefore(s, t); </script> <script class="marketing-page-info" type="application/json"> {"pageType":"Topic","templateName":"DESKTOP","pageNumber":1,"pagesTotal":1,"pageId":1025,"pageLength":645,"initialLoad":true,"lastPageOfScroll":false} </script> <script class="marketing-content-info" type="application/json"> [] </script> <script src="https://cdn.britannica.com/mendel-resources/3-130/js/libs/jquery-3.5.0.min.js?v=3.130.14"></script> <script type="text/javascript" data-type="Init Mendel Code Splitting"> (function() { $.ajax({ dataType: 'script', cache: true, url: 'https://cdn.britannica.com/mendel-resources/3-130/dist/topic-page.js?v=3.130.14' }); })(); </script> <script class="analytics-metadata" type="application/json"> {"leg":"A","adLeg":"A","userType":"ANONYMOUS","pageType":"Topic","pageSubtype":null,"articleTemplateType":"BIO_MEDIUM","gisted":false,"pageNumber":1,"hasSummarizeButton":false,"hasAskButton":false} </script> <script type="text/javascript"> EBStat={accountId:-1,hostnameOverride:'webstats.eb.com',domain:'www.britannica.com', json:''}; </script> <script type="text/javascript"> ( function() { $.ajax( { dataType: 'script', cache: true, url: '//www.britannica.com/webstats/mendelstats.js?v=1' } ) .done( function() { try {writeStat(null,EBStat);} catch(err){} } ); })(); </script> <div id="bc-fixed-dialogue"></div> </body> </html>

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Niels Henrik Abel | Biography & Facts | Britannica