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data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目錄</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">收埋</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">文頭</div> </a> </li> <li id="toc-影響" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#影響"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>影響</span> </div> </a> <ul id="toc-影響-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-生平" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#生平"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>生平</span> </div> </a> <button aria-controls="toc-生平-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去生平細章節</span> </button> <ul id="toc-生平-sublist" class="vector-toc-list"> <li id="toc-細個" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#細個"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>細個</span> </div> </a> <ul id="toc-細個-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-中期" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#中期"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>中期</span> </div> </a> <ul id="toc-中期-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-後期" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#後期"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>後期</span> </div> </a> <ul id="toc-後期-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-歐幾里德幾何同黎曼幾何" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歐幾里德幾何同黎曼幾何"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>歐幾里德幾何同黎曼幾何</span> </div> </a> <ul id="toc-歐幾里德幾何同黎曼幾何-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-高維" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#高維"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>高維</span> </div> </a> <ul id="toc-高維-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-睇埋" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#睇埋"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>睇埋</span> </div> </a> <ul id="toc-睇埋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參攷" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參攷"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>參攷</span> </div> </a> <ul id="toc-參攷-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-出面網頁" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#出面網頁"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>出面網頁</span> </div> </a> <ul id="toc-出面網頁-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="目錄" 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="開/收內容一覽" > <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">開/收內容一覽</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">伯恩哈德·黎曼</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="去睇另一種語文嘅文章。有100種語言版本。" > <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-100" 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">100種語言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 南非荷蘭文" lang="af" hreflang="af" data-title="Bernhard Riemann" data-language-autonym="Afrikaans" data-language-local-name="南非荷蘭文" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 阿拉貢文" lang="an" hreflang="an" data-title="Bernhard Riemann" data-language-autonym="Aragonés" data-language-local-name="阿拉貢文" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D8%A7%D8%B1%D8%AF_%D8%B1%D9%8A%D9%85%D8%A7%D9%86" title="برنارد ريمان – 阿拉伯文" lang="ar" hreflang="ar" data-title="برنارد ريمان" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D8%A7%D8%B1%D8%AF_%D8%B1%D9%8A%D9%85%D8%A7%D9%86" title="برنارد ريمان – 埃及阿拉伯文" lang="arz" hreflang="arz" data-title="برنارد ريمان" data-language-autonym="مصرى" data-language-local-name="埃及阿拉伯文" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BE%E0%A7%B0%E0%A7%8D%E0%A6%A8%E0%A6%B9%E0%A6%BE%E0%A7%B0%E0%A7%8D%E0%A6%A1_%E0%A7%B0%E0%A6%BF%E0%A6%AE%E0%A6%BE%E0%A6%A8" title="বাৰ্নহাৰ্ড ৰিমান – 阿薩姆文" lang="as" hreflang="as" data-title="বাৰ্নহাৰ্ড ৰিমান" data-language-autonym="অসমীয়া" data-language-local-name="阿薩姆文" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 阿斯圖里亞文" lang="ast" hreflang="ast" data-title="Bernhard Riemann" data-language-autonym="Asturianu" data-language-local-name="阿斯圖里亞文" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Bernhard_Riman" title="Bernhard Riman – 亞塞拜然文" lang="az" hreflang="az" data-title="Bernhard Riman" data-language-autonym="Azərbaycanca" data-language-local-name="亞塞拜然文" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D9%87%D8%A7%D8%B1%D8%AA_%D8%B1%DB%8C%D9%85%D8%A7%D9%86" title="برنهارت ریمان – South Azerbaijani" lang="azb" hreflang="azb" data-title="برنهارت ریمان" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D1%80%D0%B3_%D0%A4%D1%80%D1%8B%D0%B4%D1%80%D1%8B%D1%85_%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D1%8B%D0%BC%D0%B0%D0%BD" title="Георг Фрыдрых Бернхард Рыман – 白俄羅斯文" lang="be" hreflang="be" data-title="Георг Фрыдрых Бернхард Рыман" data-language-autonym="Беларуская" data-language-local-name="白俄羅斯文" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%91%D1%8D%D1%80%D0%BD%D0%B3%D0%B0%D1%80%D0%B4_%D0%A0%D1%8B%D0%BC%D0%B0%D0%BD" title="Бэрнгард Рыман – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Бэрнгард Рыман" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Бернхард Риман – 保加利亞文" lang="bg" hreflang="bg" data-title="Бернхард Риман" data-language-autonym="Български" data-language-local-name="保加利亞文" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%87%E0%A6%B0%E0%A7%8D%E0%A6%A8%E0%A6%B9%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%9F_%E0%A6%B0%E0%A6%BF%E0%A6%AE%E0%A6%BE%E0%A6%A8" title="বের্নহার্ট রিমান – 孟加拉文" lang="bn" hreflang="bn" data-title="বের্নহার্ট রিমান" data-language-autonym="বাংলা" data-language-local-name="孟加拉文" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 波士尼亞文" lang="bs" hreflang="bs" data-title="Bernhard Riemann" data-language-autonym="Bosanski" data-language-local-name="波士尼亞文" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 加泰羅尼亞文" lang="ca" hreflang="ca" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Català" data-language-local-name="加泰羅尼亞文" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%8E%D8%B1%D9%86%D8%A7%D8%B1%D8%AF_%DA%95%DB%8C%D9%85%D8%A7%D9%86" title="بێرنارد ڕیمان – 索拉尼庫爾德文" lang="ckb" hreflang="ckb" data-title="بێرنارد ڕیمان" data-language-autonym="کوردی" data-language-local-name="索拉尼庫爾德文" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 捷克文" lang="cs" hreflang="cs" data-title="Bernhard Riemann" data-language-autonym="Čeština" data-language-local-name="捷克文" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Бернхард Риман – 楚瓦什文" lang="cv" hreflang="cv" data-title="Бернхард Риман" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 威爾斯文" lang="cy" hreflang="cy" data-title="Bernhard Riemann" data-language-autonym="Cymraeg" data-language-local-name="威爾斯文" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 丹麥文" lang="da" hreflang="da" data-title="Bernhard Riemann" data-language-autonym="Dansk" data-language-local-name="丹麥文" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 德文" lang="de" hreflang="de" data-title="Bernhard Riemann" data-language-autonym="Deutsch" data-language-local-name="德文" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – Zazaki" lang="diq" hreflang="diq" data-title="Bernhard Riemann" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CF%80%CE%AD%CF%81%CE%BD%CE%B1%CF%81%CE%BD%CF%84_%CE%A1%CE%AF%CE%BC%CE%B1%CE%BD" title="Μπέρναρντ Ρίμαν – 希臘文" lang="el" hreflang="el" data-title="Μπέρναρντ Ρίμαν" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 英文" lang="en" hreflang="en" data-title="Bernhard Riemann" data-language-autonym="English" data-language-local-name="英文" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 世界文" lang="eo" hreflang="eo" data-title="Bernhard Riemann" data-language-autonym="Esperanto" data-language-local-name="世界文" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 西班牙文" lang="es" hreflang="es" data-title="Bernhard Riemann" data-language-autonym="Español" data-language-local-name="西班牙文" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 愛沙尼亞文" lang="et" hreflang="et" data-title="Bernhard Riemann" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 巴斯克文" lang="eu" hreflang="eu" data-title="Bernhard Riemann" data-language-autonym="Euskara" data-language-local-name="巴斯克文" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%D9%87%D8%A7%D8%B1%D8%AA_%D8%B1%DB%8C%D9%85%D8%A7%D9%86" title="برنهارت ریمان – 波斯文" lang="fa" hreflang="fa" data-title="برنهارت ریمان" data-language-autonym="فارسی" data-language-local-name="波斯文" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 芬蘭文" lang="fi" hreflang="fi" data-title="Bernhard Riemann" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 法文" lang="fr" hreflang="fr" data-title="Bernhard Riemann" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 西弗里西亞文" lang="fy" hreflang="fy" data-title="Bernhard Riemann" data-language-autonym="Frysk" data-language-local-name="西弗里西亞文" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Georg_Friedrich_Bernhardt_Riemann" title="Georg Friedrich Bernhardt Riemann – 愛爾蘭文" lang="ga" hreflang="ga" data-title="Georg Friedrich Bernhardt Riemann" data-language-autonym="Gaeilge" data-language-local-name="愛爾蘭文" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 蘇格蘭蓋爾文" lang="gd" hreflang="gd" data-title="Bernhard Riemann" data-language-autonym="Gàidhlig" data-language-local-name="蘇格蘭蓋爾文" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 加里西亞文" lang="gl" hreflang="gl" data-title="Bernhard Riemann" data-language-autonym="Galego" data-language-local-name="加里西亞文" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%A8%D7%A0%D7%94%D7%A8%D7%93_%D7%A8%D7%99%D7%9E%D7%9F" title="ברנהרד רימן – 希伯來文" lang="he" hreflang="he" data-title="ברנהרד רימן" data-language-autonym="עברית" data-language-local-name="希伯來文" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A4%B0%E0%A5%8D%E0%A4%A8%E0%A4%B9%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="बर्नहार्ड रीमान – 北印度文" lang="hi" hreflang="hi" data-title="बर्नहार्ड रीमान" data-language-autonym="हिन्दी" data-language-local-name="北印度文" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Bernhard Riemann" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 海地文" lang="ht" hreflang="ht" data-title="Bernhard Riemann" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地文" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 匈牙利文" lang="hu" hreflang="hu" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Magyar" data-language-local-name="匈牙利文" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B2%D5%A5%D5%BC%D5%B6%D5%A1%D6%80%D5%A4_%D5%8C%D5%AB%D5%B4%D5%A1%D5%B6" title="Բեռնարդ Ռիման – 亞美尼亞文" lang="hy" hreflang="hy" data-title="Բեռնարդ Ռիման" data-language-autonym="Հայերեն" data-language-local-name="亞美尼亞文" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 國際文" lang="ia" hreflang="ia" data-title="Bernhard Riemann" data-language-autonym="Interlingua" data-language-local-name="國際文" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 印尼文" lang="id" hreflang="id" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 伊多文" lang="io" hreflang="io" data-title="Bernhard Riemann" data-language-autonym="Ido" data-language-local-name="伊多文" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 冰島文" lang="is" hreflang="is" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Íslenska" data-language-local-name="冰島文" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 義大利文" lang="it" hreflang="it" data-title="Bernhard Riemann" data-language-autonym="Italiano" data-language-local-name="義大利文" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%99%E3%83%AB%E3%83%B3%E3%83%8F%E3%83%AB%E3%83%88%E3%83%BB%E3%83%AA%E3%83%BC%E3%83%9E%E3%83%B3" title="ベルンハルト・リーマン – 日文" lang="ja" hreflang="ja" data-title="ベルンハルト・リーマン" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 爪哇文" lang="jv" hreflang="jv" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Jawa" data-language-local-name="爪哇文" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%91%E1%83%94%E1%83%A0%E1%83%9C%E1%83%B0%E1%83%90%E1%83%A0%E1%83%93_%E1%83%A0%E1%83%98%E1%83%9B%E1%83%90%E1%83%9C%E1%83%98" title="ბერნჰარდ რიმანი – 喬治亞文" lang="ka" hreflang="ka" data-title="ბერნჰარდ რიმანი" data-language-autonym="ქართული" data-language-local-name="喬治亞文" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – Kabiye" lang="kbp" hreflang="kbp" data-title="Bernhard Riemann" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D1%80%D0%B3_%D0%A4%D1%80%D0%B8%D0%B4%D1%80%D0%B8%D1%85_%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Георг Фридрих Бернхард Риман – 哈薩克文" lang="kk" hreflang="kk" data-title="Георг Фридрих Бернхард Риман" data-language-autonym="Қазақша" data-language-local-name="哈薩克文" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%94%E1%9F%8A%E1%9F%82%E1%9E%93%E1%9E%A0%E1%9E%B6%E1%9E%8A_%E1%9E%9A%E1%9E%B8%E1%9E%98%E1%9F%89%E1%9E%B6%E1%9E%93" title="ប៊ែនហាដ រីម៉ាន – 高棉文" lang="km" hreflang="km" data-title="ប៊ែនហាដ រីម៉ាន" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="高棉文" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B2%B0%E0%B3%8D%E0%B2%A8%E0%B3%8D%E2%80%8C%E0%B2%B9%E0%B2%BE%E0%B2%B0%E0%B3%8D%E0%B2%A1%E0%B3%8D_%E0%B2%B0%E0%B3%80%E0%B2%AE%E0%B2%A8%E0%B3%8D" title="ಬರ್ನ್‌ಹಾರ್ಡ್ ರೀಮನ್ – 坎那達文" lang="kn" hreflang="kn" data-title="ಬರ್ನ್‌ಹಾರ್ಡ್ ರೀಮನ್" data-language-autonym="ಕನ್ನಡ" data-language-local-name="坎那達文" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B2%A0%EB%A5%B8%ED%95%98%EB%A5%B4%ED%8A%B8_%EB%A6%AC%EB%A7%8C" title="베른하르트 리만 – 韓文" lang="ko" hreflang="ko" data-title="베른하르트 리만" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 康瓦耳文" lang="kw" hreflang="kw" data-title="Bernhard Riemann" data-language-autonym="Kernowek" data-language-local-name="康瓦耳文" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Бернхард Риман – 吉爾吉斯文" lang="ky" hreflang="ky" data-title="Бернхард Риман" data-language-autonym="Кыргызча" data-language-local-name="吉爾吉斯文" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Bernardus_Riemann" title="Bernardus Riemann – 拉丁文" lang="la" hreflang="la" data-title="Bernardus Riemann" data-language-autonym="Latina" data-language-local-name="拉丁文" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 利古里亞文" lang="lij" hreflang="lij" data-title="Bernhard Riemann" data-language-autonym="Ligure" data-language-local-name="利古里亞文" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 立陶宛文" lang="lt" hreflang="lt" data-title="Bernhard Riemann" data-language-autonym="Lietuvių" data-language-local-name="立陶宛文" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bernhards_R%C4%ABmanis" title="Bernhards Rīmanis – 拉脫維亞文" lang="lv" hreflang="lv" data-title="Bernhards Rīmanis" data-language-autonym="Latviešu" data-language-local-name="拉脫維亞文" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 馬拉加什文" lang="mg" hreflang="mg" data-title="Bernhard Riemann" data-language-autonym="Malagasy" data-language-local-name="馬拉加什文" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Бернхард Риман – 馬其頓文" lang="mk" hreflang="mk" data-title="Бернхард Риман" data-language-autonym="Македонски" data-language-local-name="馬其頓文" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%95%EA%AF%94%EA%AF%9F%EA%AF%8D%EA%AF%A5%EA%AF%94%EA%AF%97_%EA%AF%94%EA%AF%A5%EA%AF%8F%EA%AF%83%EA%AF%A6%EA%AF%9F" title="ꯕꯔꯟꯍꯥꯔꯗ ꯔꯥꯏꯃꯦꯟ – 曼尼普裡文" lang="mni" hreflang="mni" data-title="ꯕꯔꯟꯍꯥꯔꯗ ꯔꯥꯏꯃꯦꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="曼尼普裡文" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%87%E0%A4%B0%E0%A5%8D%E0%A4%A8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%BE%E0%A4%A8" title="बेर्नार्ड रीमान – 馬拉地文" lang="mr" hreflang="mr" data-title="बेर्नार्ड रीमान" data-language-autonym="मराठी" data-language-local-name="馬拉地文" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 米蘭德斯文" lang="mwl" hreflang="mwl" data-title="Bernhard Riemann" data-language-autonym="Mirandés" data-language-local-name="米蘭德斯文" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%98%E1%80%94%E1%80%BA%E1%80%B8%E1%80%9F%E1%80%90%E1%80%BA_%E1%80%9B%E1%80%AE%E1%80%B8%E1%80%99%E1%80%94%E1%80%BA" title="ဘန်းဟတ် ရီးမန် – 緬甸文" lang="my" hreflang="my" data-title="ဘန်းဟတ် ရီးမန်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="緬甸文" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A4%B0%E0%A5%8D%E0%A4%A8%E0%A5%8D%E0%A4%B9%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%A8" title="बर्न्हार्ड रीम्यान – 尼瓦爾文" lang="new" hreflang="new" data-title="बर्न्हार्ड रीम्यान" data-language-autonym="नेपाल भाषा" data-language-local-name="尼瓦爾文" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 荷蘭文" lang="nl" hreflang="nl" data-title="Bernhard Riemann" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Bernhard Riemann" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Bernhard Riemann" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 奧克西坦文" lang="oc" hreflang="oc" data-title="Bernhard Riemann" data-language-autonym="Occitan" data-language-local-name="奧克西坦文" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 波蘭文" lang="pl" hreflang="pl" data-title="Bernhard Riemann" data-language-autonym="Polski" data-language-local-name="波蘭文" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Bernhard Riemann" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 葡萄牙文" lang="pt" hreflang="pt" data-title="Bernhard Riemann" data-language-autonym="Português" data-language-local-name="葡萄牙文" 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/Bernhard_Riemann" title="Bernhard Riemann – 羅馬尼亞文" lang="ro" hreflang="ro" data-title="Bernhard Riemann" data-language-autonym="Română" data-language-local-name="羅馬尼亞文" 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%A0%D0%B8%D0%BC%D0%B0%D0%BD,_%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4" title="Риман, Бернхард – 俄文" lang="ru" hreflang="ru" data-title="Риман, Бернхард" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%AC%E0%A4%B0%E0%A5%8D%E0%A4%A8%E0%A5%8D%E0%A4%B9%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A1_%E0%A4%B0%E0%A5%80%E0%A4%AE%E0%A4%A8" title="बर्न्हार्ड रीमन – 梵文" lang="sa" hreflang="sa" data-title="बर्न्हार्ड रीमन" data-language-autonym="संस्कृतम्" data-language-local-name="梵文" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 西西里文" lang="scn" hreflang="scn" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Sicilianu" data-language-local-name="西西里文" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 蘇格蘭文" lang="sco" hreflang="sco" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Scots" data-language-local-name="蘇格蘭文" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 塞爾維亞克羅埃西亞文" lang="sh" hreflang="sh" data-title="Bernhard Riemann" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞爾維亞克羅埃西亞文" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – Simple English" lang="en-simple" hreflang="en-simple" data-title="Bernhard Riemann" 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/Georg_Friedrich_Bernhard_Riemann" title="Georg Friedrich Bernhard Riemann – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Georg Friedrich Bernhard Riemann" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" 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/Bernhard_Riemann" title="Bernhard Riemann – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Bernhard Riemann" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Bernhard Riemann" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Bernhard_Riman" title="Bernhard Riman – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Bernhard Riman" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 瑞典文" lang="sv" hreflang="sv" data-title="Bernhard Riemann" data-language-autonym="Svenska" data-language-local-name="瑞典文" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%87%E0%AE%B0%E0%AF%8D%E0%AE%A9%E0%AE%BE%E0%AE%9F%E0%AF%8D_%E0%AE%B0%E0%AF%80%E0%AE%AE%E0%AE%A9%E0%AF%8D" title="பேர்னாட் ரீமன் – 坦米爾文" lang="ta" hreflang="ta" data-title="பேர்னாட் ரீமன்" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%9A%E0%B8%A3%E0%B9%8C%E0%B8%99%E0%B8%AE%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%97_%E0%B8%A3%E0%B8%B5%E0%B8%A1%E0%B8%B1%E0%B8%99" title="แบร์นฮาร์ท รีมัน – 泰文" lang="th" hreflang="th" data-title="แบร์นฮาร์ท รีมัน" data-language-autonym="ไทย" data-language-local-name="泰文" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 塔加路族文" lang="tl" hreflang="tl" data-title="Bernhard Riemann" data-language-autonym="Tagalog" data-language-local-name="塔加路族文" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 土耳其文" lang="tr" hreflang="tr" data-title="Bernhard Riemann" data-language-autonym="Türkçe" data-language-local-name="土耳其文" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%B1%D9%89%D9%85%D8%A7%D9%86" title="رىمان – 維吾爾文" lang="ug" hreflang="ug" data-title="رىمان" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="維吾爾文" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B5%D1%80%D0%BD%D0%B3%D0%B0%D1%80%D0%B4_%D0%A0%D1%96%D0%BC%D0%B0%D0%BD" title="Бернгард Ріман – 烏克蘭文" lang="uk" hreflang="uk" data-title="Бернгард Ріман" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A8%D8%B1%D9%86%DB%81%D8%A7%D8%B1%DA%88_%D8%B1%DB%8C%D9%85%D8%A7%D9%86" title="برنہارڈ ریمان – 烏都文" lang="ur" hreflang="ur" data-title="برنہارڈ ریمان" data-language-autonym="اردو" data-language-local-name="烏都文" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Riman_Georg_Fridrix_Bernhard" title="Riman Georg Fridrix Bernhard – 烏茲別克文" lang="uz" hreflang="uz" data-title="Riman Georg Fridrix Bernhard" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="烏茲別克文" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 越南文" lang="vi" hreflang="vi" data-title="Bernhard Riemann" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 瓦瑞文" lang="war" hreflang="war" data-title="Bernhard Riemann" data-language-autonym="Winaray" data-language-local-name="瓦瑞文" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" title="伯恩哈德·黎曼 – 吳語" lang="wuu" hreflang="wuu" data-title="伯恩哈德·黎曼" data-language-autonym="吴语" data-language-local-name="吳語" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D1%80%D0%B3_%D0%A4%D1%80%D0%B8%D0%B4%D1%80%D0%B8%D1%85_%D0%91%D0%B5%D1%80%D0%BD%D1%85%D0%B0%D1%80%D0%B4_%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD" title="Георг Фридрих Бернхард Риман – 卡爾梅克文" lang="xal" hreflang="xal" data-title="Георг Фридрих Бернхард Риман" data-language-autonym="Хальмг" data-language-local-name="卡爾梅克文" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%91%E1%83%94%E1%83%A0%E1%83%9C%E1%83%B0%E1%83%90%E1%83%A0%E1%83%93_%E1%83%A0%E1%83%98%E1%83%9B%E1%83%90%E1%83%9C%E1%83%98" title="ბერნჰარდ რიმანი – 明格列爾文" lang="xmf" hreflang="xmf" data-title="ბერნჰარდ რიმანი" data-language-autonym="მარგალური" data-language-local-name="明格列爾文" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" title="伯恩哈德·黎曼 – 中文" lang="zh" hreflang="zh" data-title="伯恩哈德·黎曼" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Bernhard_Riemann" title="Bernhard Riemann – 閩南語" lang="nan" hreflang="nan" data-title="Bernhard Riemann" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="閩南語" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q42299#sitelinks-wikipedia" title="改跨語言拎" class="wbc-editpage">改拎</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="空間名"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" title="睇吓內容頁[c]" accesskey="c"><span>文章</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" rel="discussion" title="關於內容頁嘅討論[t]" accesskey="t"><span>討論</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="改語言變體" > <label id="vector-variants-dropdown-label" 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mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="多啲選項" > <div class="vector-menu-heading"> 動作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC"><span>閱</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit" title="改呢版嘅代碼[e]" accesskey="e"><span>改</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=history"><span>睇返紀錄</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 基本 </div> <div class="vector-menu-content"> <ul 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dir="ltr"><style data-mw-deduplicate="TemplateStyles:r2009783">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid 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src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/50px-Translation_to_zh_arrow.svg.png" decoding="async" width="50" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/75px-Translation_to_zh_arrow.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/100px-Translation_to_zh_arrow.svg.png 2x" data-file-width="60" data-file-height="20" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">呢篇文或者呢段要 <a href="/wiki/Wikipedia:%E7%BF%BB%E8%AD%AF%E8%AB%8B%E6%B1%82" title="Wikipedia:翻譯請求">翻譯</a>（或者由 <a href="https://en.wikipedia.org/wiki/Bernhard_Riemann" class="extiw" title="en:Bernhard Riemann">en:Bernhard Riemann</a>加料）。<span class="hide-when-compact"> 請<span class="plainlinks"><a class="external text" href="https://zh-yue.wikipedia.org/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit">譯</a></span>佢。<br /> 上次編輯：2022年10月20號 13:04。<small>(<a href="/wiki/Wikipedia:%E7%BF%BB%E8%AD%AF" title="Wikipedia:翻譯">翻譯指引</a>)</small></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Georg_Friedrich_Bernhard_Riemann.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Georg_Friedrich_Bernhard_Riemann.jpeg/220px-Georg_Friedrich_Bernhard_Riemann.jpeg" decoding="async" width="220" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Georg_Friedrich_Bernhard_Riemann.jpeg/330px-Georg_Friedrich_Bernhard_Riemann.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Georg_Friedrich_Bernhard_Riemann.jpeg/440px-Georg_Friedrich_Bernhard_Riemann.jpeg 2x" data-file-width="903" data-file-height="986" /></a><figcaption>伯恩哈德·黎曼</figcaption></figure> <p><b>伯恩哈德·黎曼</b>（<a href="/wiki/%E5%BE%B7%E6%96%87" title="德文">德文</a>：<span lang="de" title="德文文字"><b>Georg Friedrich Bernhard Riemann</b></span>，<a href="/wiki/1826%E5%B9%B4" title="1826年">1826年</a><a href="/wiki/9%E6%9C%8817%E8%99%9F" title="9月17號">9月17號</a>—<a href="/wiki/1866%E5%B9%B4" title="1866年">1866年</a><a href="/wiki/7%E6%9C%8820%E8%99%9F" title="7月20號">7月20號</a>），<a href="/wiki/%E5%BE%B7%E5%9C%8B" title="德國">德國</a><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%AE%B6" title="數學家">數學家</a>，喺<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a>同<a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a>做咗重要嘅基本嘅工夫；佢有啲諗頭後來做咗<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>嘅基礎。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="影響"><span id=".E5.BD.B1.E9.9F.BF"></span>影響</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=1" title="編輯小節: 影響"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>伯恩哈德·黎曼嘅著作打開咗分析夾埋幾何研究嘅路。呢啲研究發展成<a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%B9%BE%E4%BD%95" title="黎曼幾何">黎曼幾何</a>、<a href="/wiki/%E4%BB%A3%E6%95%B8%E5%B9%BE%E4%BD%95" title="代數幾何">代數幾何</a>同埋<a href="/w/index.php?title=%E8%A4%87%E6%B5%81%E5%BD%A2&action=edit&redlink=1" class="new" title="複流形 (無呢版)">複流形</a>理論嘅重心。<a href="/wiki/%E9%BB%8E%E6%9B%BC%E6%9B%B2%E9%9D%A2" title="黎曼曲面">黎曼曲面</a>嘅理論由後來嘅<a href="/w/index.php?title=%E5%85%8B%E4%BE%86%E6%81%A9&action=edit&redlink=1" class="new" title="克來恩 (無呢版)">克來恩</a>同<a href="/w/index.php?title=Adolf_Hurwitz&action=edit&redlink=1" class="new" title="Adolf Hurwitz (無呢版)">Adolf Hurwitz</a>加深推廣。黎曼曲面理論係複幾何嘅重要部分，影響咗拓樸學同代數幾何嘅發展，亦喺<a href="/w/index.php?title=%E6%95%B8%E7%90%86%E7%89%A9%E7%90%86&action=edit&redlink=1" class="new" title="數理物理 (無呢版)">數理物理</a>同<a href="/wiki/%E5%BC%A6%E8%AB%96" title="弦論">弦論</a>上有用。 </p><p>黎曼喺<a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>有重要貢獻。佢用<a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%92%8C" title="黎曼和">黎曼和</a>來定義<a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%A9%8D%E5%88%86" title="黎曼積分">黎曼積分</a>，發展咗套唔係<a href="/w/index.php?title=Fourier_%E7%B4%9A%E6%95%B8&action=edit&redlink=1" class="new" title="Fourier 級數 (無呢版)">Fourier 級數</a>嘅<a href="/w/index.php?title=%E4%B8%89%E8%A7%92%E7%B4%9A%E6%95%B8&action=edit&redlink=1" class="new" title="三角級數 (無呢版)">三角級數</a>理論 — 係<a href="/w/index.php?title=%E5%BB%A3%E7%BE%A9%E5%87%BD%E6%95%B8&action=edit&redlink=1" class="new" title="廣義函數 (無呢版)">廣義函數</a>論嘅第一步—，又研究過<a href="/w/index.php?title=Riemann-Liouville_differintegral&action=edit&redlink=1" class="new" title="Riemann-Liouville differintegral (無呢版)">Riemann-Liouville differintegral</a>。 </p><p>黎曼嚮現代<a href="/wiki/%E8%A7%A3%E6%9E%90%E6%95%B8%E8%AB%96" title="解析數論">解析數論</a>做咗啲重要嘢。渠喺數論發表嘅單丁一篇短文中提出<a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC_zeta_%E5%87%BD%E6%95%B8&action=edit&redlink=1" class="new" title="黎曼 zeta 函數 (無呢版)">黎曼 zeta 函數</a>，同時建立咗 zeta 函數喺<a href="/wiki/%E8%B3%AA%E6%95%B8" title="質數">質數</a>分布研究嘅重要性。關於 zeta 函數嘅性質，渠提出一連串猜想，包括出名嘅<a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E5%81%87%E8%A8%AD&action=edit&redlink=1" class="new" title="黎曼假設 (無呢版)">黎曼假設</a>。 </p><p>黎曼有力咁用<a href="/wiki/%E8%AE%8A%E5%88%86%E6%B3%95" title="變分法">變分法</a>上嘅<a href="/w/index.php?title=Dirichlet_%E5%8E%9F%E7%90%86&action=edit&redlink=1" class="new" title="Dirichlet 原理 (無呢版)">Dirichlet 原理</a>；後來嘅人睇呢啲用法做好勁嘅<a href="/w/index.php?title=Heuristic&action=edit&redlink=1" class="new" title="Heuristic (無呢版)">heuristic</a>（輔助推理？），而唔係嚴謹嘅方法；呢啲做法要等再過一代人之後至得證。黎曼喺<a href="/w/index.php?title=Monodromy&action=edit&redlink=1" class="new" title="Monodromy (無呢版)">monodromy</a>同複<a href="/w/index.php?title=%E8%B6%85%E5%B9%BE%E4%BD%95%E5%87%BD%E6%95%B8&action=edit&redlink=1" class="new" title="超幾何函數 (無呢版)">超幾何函數</a>嘅工夫影響好大，帶頭「淨用函數嘅<a href="/w/index.php?title=%E5%A5%87%E9%BB%9E&action=edit&redlink=1" class="new" title="奇點 (無呢版)">奇點</a>（<a href="https://en.wikipedia.org/wiki/mathematical_singularities" class="extiw" title="en:mathematical singularities">en:mathematical singularities</a>）」來玩啲函數。 </p> <div class="mw-heading mw-heading2"><h2 id="生平"><span id=".E7.94.9F.E5.B9.B3"></span>生平</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=2" title="編輯小節: 生平"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="細個"><span id=".E7.B4.B0.E5.80.8B"></span>細個</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=3" title="編輯小節: 細個"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>黎曼喺<a href="/w/index.php?title=Breselenz&action=edit&redlink=1" class="new" title="Breselenz (無呢版)">Breselenz</a>出世；Breselenz 係 <a href="/w/index.php?title=Hanover_(state)&action=edit&redlink=1" class="new" title="Hanover (state) (無呢版)">Hanover 王國</a>近 <a href="/w/index.php?title=Dannenberg&action=edit&redlink=1" class="new" title="Dannenberg (無呢版)">Dannenberg</a> 嘅一條村。渠阿爸 <i>Friedrich Bernhard Riemann</i> 係 Breselenz 嘅一個窮<a href="/wiki/%E8%B7%AF%E5%BE%B7%E6%9C%83" title="路德會">路德會</a> pastor，打過<a href="/w/index.php?title=%E6%8B%BF%E7%A0%B4%E4%BE%96%E4%BB%97&action=edit&redlink=1" class="new" title="拿破侖仗 (無呢版)">拿破侖仗</a>（<a href="https://en.wikipedia.org/wiki/Napoleonic_Wars" class="extiw" title="en:Napoleonic Wars">en:Napoleonic Wars</a>）。黎曼阿媽喺啲<a href="/wiki/%E7%B4%B0%E8%B7%AF" title="細路">細路</a>未大個就死咗。黎曼喺六個細路入面排第二。黎曼細細個就顯出特出嘅數學能力，好似好勁嘅計算力，但<a href="/wiki/%E6%80%95%E9%86%9C" title="怕醜">怕醜</a>，驚喺公衆面前講嘢；又試過好多次精神崩潰（<a href="https://en.wikipedia.org/wiki/nervous_breakdowns" class="extiw" title="en:nervous breakdowns">en:nervous breakdowns</a>）。 </p> <div class="mw-heading mw-heading3"><h3 id="中期"><span id=".E4.B8.AD.E6.9C.9F"></span>中期</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=4" title="編輯小節: 中期"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>中學<sup class="noprint Template-Fact"><a href="/wiki/Wikipedia:%E6%A0%B9%E6%93%9A" title="Wikipedia:根據">[未記出處或冇根據]</a></sup>時，黎曼深究本<a href="/wiki/%E8%81%96%E7%B6%93" title="聖經">聖經</a>，但佢成日諗諗下諗返去數學嗰邊。He even tried to <a href="/wiki/Mathematical_proof" class="mw-redirect" title="Mathematical proof">prove</a> mathematically the correctness of the book of <a href="/wiki/Genesis" class="mw-redirect mw-disambig" title="Genesis">Genesis</a>. <a href="/wiki/1840%E5%B9%B4" title="1840年">1840年</a>，黎曼去咗<a href="/wiki/Hanover" class="mw-redirect" title="Hanover">Hanover</a>，同佢 grandmother 一齊住，同埋去 <a href="/w/index.php?title=Lyceum&action=edit&redlink=1" class="new" title="Lyceum (無呢版)">Lyceum</a>。佢 grandmother 喺<a href="/wiki/1842%E5%B9%B4" title="1842年">1842年</a>死後，佢去咗<a href="/w/index.php?title=L%C3%BCneburg&action=edit&redlink=1" class="new" title="Lüneburg (無呢版)">Lüneburg</a>嘅 Johanneum。<a href="/wiki/1846%E5%B9%B4" title="1846年">1846年</a>，黎曼 19歲，佢開始<a href="/wiki/%E6%96%87%E5%AD%97%E5%AD%B8" title="文字學">文字學</a>（<a href="https://en.wikipedia.org/wiki/philology" class="extiw" title="en:philology">en:philology</a>）同埋<a href="/wiki/%E7%A5%9E%E5%AD%B8" title="神學">神學</a>（<a href="https://en.wikipedia.org/wiki/theology" class="extiw" title="en:theology">en:theology</a>），希望做個牧師（<a href="https://en.wikipedia.org/wiki/priest" class="extiw" title="en:priest">en:priest</a>）來幫補屋企嘅開支。 </p><p><a href="/wiki/1847%E5%B9%B4" title="1847年">1847年</a>，黎曼阿爸儲夠錢畀佢去大學，佢停咗神學而開始學數。佢被送去<a href="/wiki/%E5%93%A5%E5%BB%B7%E6%A0%B9%E5%A4%A7%E5%AD%B8" title="哥廷根大學">哥廷根大學</a>，第一次見到<a href="/wiki/%E9%AB%98%E6%96%AF" class="mw-redirect" title="高斯">高斯</a>（<a href="https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss" class="extiw" title="en:Carl Friedrich Gauss">en:Carl Friedrich Gauss</a>），上過佢講<a href="/w/index.php?title=%E6%9C%80%E7%B4%B0%E5%B9%B3%E6%96%B9%E6%B3%95&action=edit&redlink=1" class="new" title="最細平方法 (無呢版)">最細平方法</a>嘅堂。 </p><p><a href="/wiki/1847%E5%B9%B4" title="1847年">1847年</a>，黎曼搬去<a href="/wiki/%E6%9F%8F%E6%9E%97" title="柏林">柏林</a>；嗰度有<a href="/w/index.php?title=Carl_Gustav_Jakob_Jacobi&action=edit&redlink=1" class="new" title="Carl Gustav Jakob Jacobi (無呢版)">雅可比</a>、<a href="/w/index.php?title=Johann_Peter_Gustav_Lejeune_Dirichlet&action=edit&redlink=1" class="new" title="Johann Peter Gustav Lejeune Dirichlet (無呢版)">狄利克雷</a>同<a href="/w/index.php?title=Jakob_Steiner&action=edit&redlink=1" class="new" title="Jakob Steiner (無呢版)">Steiner</a>教。佢喺柏林住咗兩年，喺<a href="/wiki/1849%E5%B9%B4" title="1849年">1849年</a>返<a href="/wiki/%E5%93%A5%E5%BB%B7%E6%A0%B9" title="哥廷根">哥廷根</a>（<a href="https://de.wikipedia.org/wiki/G%C3%B6ttingen" class="extiw" title="de:Göttingen">de:Göttingen</a>）。 </p> <div class="mw-heading mw-heading3"><h3 id="後期"><span id=".E5.BE.8C.E6.9C.9F"></span>後期</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=5" title="編輯小節: 後期"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/1854%E5%B9%B4" title="1854年">1854年</a>，黎曼開講，建立咗<a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%B9%BE%E4%BD%95" title="黎曼幾何">黎曼幾何</a>，日後成為<a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%9B%B8%E5%B0%8D%E8%AB%96" title="廣義相對論">廣義相對論</a>嘅基礎。 <a href="/wiki/1857%E5%B9%B4" title="1857年">1857年</a>，有人想幫黎曼升做<a href="/wiki/%E5%93%A5%E5%BB%B7%E6%A0%B9%E5%A4%A7%E5%AD%B8" title="哥廷根大學">哥廷根大學</a>副教授（？）<a href="https://en.wikipedia.org/wiki/extraordinary_professor" class="extiw" title="en:extraordinary professor">en:extraordinary professor</a>；雖然唔成功，但黎曼終於攞得到正式<a href="/wiki/%E4%BA%BA%E5%B7%A5" title="人工">人工</a>。<a href="/wiki/1859%E5%B9%B4" title="1859年">1859年</a>，<a href="/w/index.php?title=Johann_Peter_Gustav_Lejeune_Dirichlet&action=edit&redlink=1" class="new" title="Johann Peter Gustav Lejeune Dirichlet (無呢版)">狄利克雷</a>死後，黎曼升做<a href="/w/index.php?title=%E5%93%A5%E5%BB%B7%E6%A0%B9%E6%95%B8%E5%AD%B8%E7%B3%BB&action=edit&redlink=1" class="new" title="哥廷根數學系 (無呢版)">哥廷根數學系</a><a href="/wiki/%E9%98%BF%E9%A0%AD" title="阿頭">阿頭</a>。 <a href="/wiki/1862%E5%B9%B4" title="1862年">1862年</a>黎曼同 Elise Koch 結婚，佢哋有個女。佢第三次去<a href="/wiki/%E6%84%8F%E5%A4%A7%E5%88%A9" title="意大利">意大利</a>時，死喺 Selasca，即係而家<a href="/w/index.php?title=Maggiore_%E6%B9%96&action=edit&redlink=1" class="new" title="Maggiore 湖 (無呢版)">Maggiore 湖</a>邊嘅<a href="/w/index.php?title=Ghiffa&action=edit&redlink=1" class="new" title="Ghiffa (無呢版)">Ghiffa</a><a href="/w/index.php?title=Hamlet&action=edit&redlink=1" class="new" title="Hamlet (無呢版)">村</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="歐幾里德幾何同黎曼幾何"><span id=".E6.AD.90.E5.B9.BE.E9.87.8C.E5.BE.B7.E5.B9.BE.E4.BD.95.E5.90.8C.E9.BB.8E.E6.9B.BC.E5.B9.BE.E4.BD.95"></span>歐幾里德幾何同黎曼幾何</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=6" title="編輯小節: 歐幾里德幾何同黎曼幾何"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Hypercube.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/150px-Hypercube.svg.png" decoding="async" width="150" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/225px-Hypercube.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hypercube.svg/300px-Hypercube.svg.png 2x" data-file-width="417" data-file-height="453" /></a><figcaption>四維嘅<a href="/w/index.php?title=%E8%B6%85%E6%96%B9%E5%BD%A2&action=edit&redlink=1" class="new" title="超方形 (無呢版)">超方形</a>（<a href="https://en.wikipedia.org/wiki/hypercube" class="extiw" title="en:hypercube">en:hypercube</a>）嘅兩維投影</figcaption></figure> <p><a href="/wiki/1853%E5%B9%B4" title="1853年">1853年</a>，<a href="/wiki/%E9%AB%98%E6%96%AF" class="mw-redirect" title="高斯">高斯</a>叫佢學生黎曼用幾何基礎做題目，來預備佢份<i><a href="/w/index.php?title=Habilitationsschrift&action=edit&redlink=1" class="new" title="Habilitationsschrift (無呢版)">Habilitationsschrift</a></i>。黎曼用咗幾個月來發展佢套高維嘅理論。 </p><p>結果黎曼發展出<a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%B9%BE%E4%BD%95" title="黎曼幾何">黎曼幾何</a>呢科。佢揾到法子將微分幾何由曲面推到 <i>n</i> 維，定義咗<a href="/w/index.php?title=%E6%9B%B2%E7%8E%87%E5%BC%B5%E9%87%8F&action=edit&redlink=1" class="new" title="曲率張量 (無呢版)">曲率張量</a>來推廣高斯嘅<i><a href="/w/index.php?title=Theorema_egregium&action=edit&redlink=1" class="new" title="Theorema egregium (無呢版)">theorema egregium</a></i>。喺維度 2 嘅曲面上，曲率張量係個純量，當呢個純量係非零常數，塊曲面就係已知嘅<a href="/w/index.php?title=%E9%9D%9E%E6%AD%90%E5%B9%BE%E4%BD%95%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="非歐幾何模型 (無呢版)">非歐幾何模型</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="高維"><span id=".E9.AB.98.E7.B6.AD"></span>高維</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=7" title="編輯小節: 高維"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>黎曼有個諗頭：空間每一點畀佢一套數值，來描述個空間點扭點屈。咁樣，黎曼發現，喺四維流形，每點總共要十個數，唔理佢點扭法。呢套數就係所謂嘅<a href="/w/index.php?title=%E5%BA%A6%E8%A6%8F%E5%BC%B5%E9%87%8F&action=edit&redlink=1" class="new" title="度規張量 (無呢版)">度規張量</a>（<a href="https://en.wikipedia.org/wiki/metric_tensor" class="extiw" title="en:metric tensor">en:metric tensor</a>）。 </p> <div class="mw-heading mw-heading2"><h2 id="睇埋"><span id=".E7.9D.87.E5.9F.8B"></span>睇埋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%BC%AF%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC&action=edit&section=8" title="編輯小節: 睇埋"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="style="-moz-column-count:3;"> <ul><li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%8C%9C%E6%83%B3" title="黎曼猜想">黎曼猜想</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC_zeta_%E5%87%BD%E6%95%B8&action=edit&redlink=1" class="new" title="黎曼 zeta 函數 (無呢版)">黎曼 zeta 函數</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%A9%8D%E5%88%86" title="黎曼積分">黎曼積分</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%92%8C" title="黎曼和">黎曼和</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E5%BC%95%E7%90%86&action=edit&redlink=1" class="new" title="黎曼引理 (無呢版)">黎曼引理</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E6%B5%81%E5%BD%A2" title="黎曼流形">黎曼流形</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E6%98%A0%E5%B0%84%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="黎曼映射定理 (無呢版)">黎曼映射定理</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E5%B8%8C%E7%88%BE%E4%BC%AF%E7%89%B9%E5%95%8F%E9%A1%8C&action=edit&redlink=1" class="new" title="黎曼希爾伯特問題 (無呢版)">黎曼希爾伯特問題</a></li> <li><a href="/w/index.php?title=Riemann-Hurwitz_formula&action=edit&redlink=1" class="new" title="Riemann-Hurwitz formula (無呢版)">Riemann-Hurwitz formula</a></li> <li><a href="/w/index.php?title=Riemann-von_Mangoldt_formula&action=edit&redlink=1" class="new" title="Riemann-von Mangoldt formula (無呢版)">Riemann-von Mangoldt formula</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E6%9B%B2%E9%9D%A2" title="黎曼曲面">黎曼曲面</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E9%A7%B1%E5%85%8B%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="黎曼駱克定理 (無呢版)">黎曼駱克定理</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC_theta_%E5%87%BD%E6%95%B8&action=edit&redlink=1" class="new" title="黎曼 theta 函數 (無呢版)">黎曼 theta 函數</a></li> <li><a href="/w/index.php?title=Riemann-Siegel_theta_function&action=edit&redlink=1" class="new" title="Riemann-Siegel theta function (無呢版)">Riemann-Siegel theta function</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&action=edit&redlink=1" class="new" title="黎曼微分方程 (無呢版)">黎曼微分方程</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E7%9F%A9%E9%99%A3&action=edit&redlink=1" class="new" title="黎曼矩陣 (無呢版)">黎曼矩陣</a></li> <li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%90%83%E9%9D%A2" title="黎曼球面">黎曼球面</a></li> <li><a href="/w/index.php?title=Metric_tensor&action=edit&redlink=1" class="new" title="Metric tensor (無呢版)">黎曼度規張量</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E6%9B%B2%E7%8E%87%E5%BC%B5%E9%87%8F&action=edit&redlink=1" class="new" title="黎曼曲率張量 (無呢版)">黎曼曲率張量</a></li> <li><a href="/w/index.php?title=%E6%9F%AF%E8%A5%BF%E9%BB%8E%E6%9B%BC%E6%96%B9%E7%A8%8B&action=edit&redlink=1" class="new" title="柯西黎曼方程 (無呢版)">柯西黎曼方程</a></li> <li><a href="/w/index.php?title=Hirzebruch-Riemann-Roch_theorem&action=edit&redlink=1" class="new" title="Hirzebruch-Riemann-Roch theorem (無呢版)">Hirzebruch-Riemann-Roch theorem</a></li> <li><a href="/w/index.php?title=%E9%BB%8E%E6%9B%BC%E5%8B%92%E8%B2%9D%E6%A0%BC%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="黎曼勒貝格定理 (無呢版)">黎曼勒貝格定理</a></li> <li><a href="/w/index.php?title=Riemann-Stieltjes_integral&action=edit&redlink=1" class="new" title="Riemann-Stieltjes integral (無呢版)">Riemann-Stieltjes integral</a></li> <li><a href="/w/index.php?title=Riemann-Liouville_differintegral&action=edit&redlink=1" class="new" title="Riemann-Liouville differintegral (無呢版)">Riemann-Liouville differintegral</a></li> <li><a href="/w/index.php?title=Riemann_series_theorem&action=edit&redlink=1" class="new" title="Riemann series theorem (無呢版)">Riemann series theorem</a></li> <li><a href="/w/index.php?title=On_the_Number_of_Primes_Less_Than_a_Given_Magnitude&action=edit&redlink=1" class="new" title="On the Number of Primes Less Than a Given Magnitude (無呢版)">黎曼喺 1859年篇文，提出 zeta 函數</a></li> <li><i><a href="/w/index.php?title=Prime_Obsession&action=edit&redlink=1" class="new" title="Prime Obsession (無呢版)">Prime Obsession</a></i></li> <li><i><a href="/w/index.php?title=The_Music_of_the_Primes&action=edit&redlink=1" class="new" title="The Music of the Primes (無呢版)">The Music of the Primes</a></i></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="參攷"><span id=".E5.8F.83.E6.94.B7"></span>參攷</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a 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