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subbagian Sejarah</span> </button> <ul id="toc-Sejarah-sublist" class="vector-toc-list"> <li id="toc-Yunani_Kuno" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Yunani_Kuno"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Yunani Kuno</span> </div> </a> <ul id="toc-Yunani_Kuno-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abad_ke-19" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abad_ke-19"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Abad ke-19</span> </div> </a> <ul id="toc-Abad_ke-19-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abad_ke-20" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abad_ke-20"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Abad ke-20</span> </div> </a> <ul id="toc-Abad_ke-20-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Umum_dan_abstraksi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Umum_dan_abstraksi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Umum dan abstraksi</span> </div> </a> <ul id="toc-Umum_dan_abstraksi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lihat_pula" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lihat_pula"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lihat pula</span> </div> </a> <ul id="toc-Lihat_pula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referensi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referensi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referensi</span> </div> </a> <ul id="toc-Referensi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pranala_luar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pranala_luar"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Pranala luar</span> </div> </a> <ul id="toc-Pranala_luar-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="Daftar isi" 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="Gulingkan daftar isi" > <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">Gulingkan daftar isi</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">Matematika murni</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="Pergi ke artikel dalam bahasa lain. Terdapat 53 bahasa" > <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-53" 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">53 bahasa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA_%D8%A8%D8%AD%D8%AA%D8%A9" title="رياضيات بحتة – Arab" lang="ar" hreflang="ar" data-title="رياضيات بحتة" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Matem%C3%A1tiques_pures" title="Matemátiques pures – Asturia" lang="ast" hreflang="ast" data-title="Matemátiques pures" data-language-autonym="Asturianu" data-language-local-name="Asturia" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="نظری ریاضیات – South Azerbaijani" lang="azb" hreflang="azb" data-title="نظری ریاضیات" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D0%B0%D1%84_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Саф математика – Bashkir" lang="ba" hreflang="ba" data-title="Саф математика" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%81%E0%A6%A6%E0%A7%8D%E0%A6%A7_%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বিশুদ্ধ গণিত – Bengali" lang="bn" hreflang="bn" data-title="বিশুদ্ধ গণিত" data-language-autonym="বাংলা" data-language-local-name="Bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tica_pura" title="Matemàtica pura – Katalan" lang="ca" hreflang="ca" data-title="Matemàtica pura" data-language-autonym="Català" data-language-local-name="Katalan" 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/%C4%8Cist%C3%A1_matematika" title="Čistá matematika – Cheska" lang="cs" hreflang="cs" data-title="Čistá matematika" data-language-autonym="Čeština" data-language-local-name="Cheska" 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%A2%D0%B0%D1%81%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Таса математика – Chuvash" lang="cv" hreflang="cv" data-title="Таса математика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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/Mathemateg_bur" title="Mathemateg bur – Welsh" lang="cy" hreflang="cy" data-title="Mathemateg bur" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%B1%CE%B8%CE%B1%CF%81%CE%AC_%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Καθαρά μαθηματικά – Yunani" lang="el" hreflang="el" data-title="Καθαρά μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="Yunani" 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/Pure_mathematics" title="Pure mathematics – Inggris" lang="en" hreflang="en" data-title="Pure mathematics" data-language-autonym="English" data-language-local-name="Inggris" 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/Pura_matematiko" title="Pura matematiko – Esperanto" lang="eo" hreflang="eo" data-title="Pura matematiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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/Matem%C3%A1tica_pura" title="Matemática pura – Spanyol" lang="es" hreflang="es" data-title="Matemática pura" data-language-autonym="Español" data-language-local-name="Spanyol" 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/Puhas_matemaatika" title="Puhas matemaatika – Esti" lang="et" hreflang="et" data-title="Puhas matemaatika" data-language-autonym="Eesti" data-language-local-name="Esti" 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/Matematika_huts" title="Matematika huts – Basque" lang="eu" hreflang="eu" data-title="Matematika huts" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA_%D9%85%D8%AD%D8%B6" title="ریاضیات محض – Persia" lang="fa" hreflang="fa" data-title="ریاضیات محض" data-language-autonym="فارسی" data-language-local-name="Persia" 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/Puhdas_matematiikka" title="Puhdas matematiikka – Suomi" lang="fi" hreflang="fi" data-title="Puhdas matematiikka" data-language-autonym="Suomi" data-language-local-name="Suomi" 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/Math%C3%A9matiques_pures" title="Mathématiques pures – Prancis" lang="fr" hreflang="fr" data-title="Mathématiques pures" data-language-autonym="Français" data-language-local-name="Prancis" 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/Matem%C3%A1tica_pura" title="Matemática pura – Galisia" lang="gl" hreflang="gl" data-title="Matemática pura" data-language-autonym="Galego" data-language-local-name="Galisia" 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%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94_%D7%A2%D7%99%D7%95%D7%A0%D7%99%D7%AA" title="מתמטיקה עיונית – Ibrani" lang="he" hreflang="he" data-title="מתמטיקה עיונית" data-language-autonym="עברית" data-language-local-name="Ibrani" 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%B6%E0%A5%81%E0%A4%A6%E0%A5%8D%E0%A4%A7_%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="शुद्ध गणित – Hindi" lang="hi" hreflang="hi" data-title="शुद्ध गणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D6%84%D5%B8%D6%82%D6%80_%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1" title="Մաքուր մաթեմատիկա – Armenia" lang="hy" hreflang="hy" data-title="Մաքուր մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="Armenia" 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/Mathematica_pur" title="Mathematica pur – Interlingua" lang="ia" hreflang="ia" data-title="Mathematica pur" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Pura_matematiko" title="Pura matematiko – Ido" lang="io" hreflang="io" data-title="Pura matematiko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica_pura" title="Matematica pura – Italia" lang="it" hreflang="it" data-title="Matematica pura" data-language-autonym="Italiano" data-language-local-name="Italia" 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/%E7%B4%94%E7%B2%8B%E6%95%B0%E5%AD%A6" title="純粋数学 – Jepang" lang="ja" hreflang="ja" data-title="純粋数学" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%9B%E1%83%98%E1%83%9C%E1%83%93%E1%83%90_%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="წმინდა მათემატიკა – Georgia" lang="ka" hreflang="ka" data-title="წმინდა მათემატიკა" data-language-autonym="ქართული" data-language-local-name="Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%9C%EC%88%98%EC%88%98%ED%95%99" title="순수수학 – Korea" lang="ko" hreflang="ko" data-title="순수수학" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Matematica_pur" title="Matematica pur – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Matematica pur" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Matematik_tulen" title="Matematik tulen – Melayu" lang="ms" hreflang="ms" data-title="Matematik tulen" data-language-autonym="Bahasa Melayu" data-language-local-name="Melayu" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC%E1%80%9E%E1%80%94%E1%80%B7%E1%80%BA%E1%80%9E%E1%80%94%E1%80%B7%E1%80%BA" title="သင်္ချာသန့်သန့် – Burma" lang="my" hreflang="my" data-title="သင်္ချာသန့်သန့်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zuivere_wiskunde" title="Zuivere wiskunde – Belanda" lang="nl" hreflang="nl" data-title="Zuivere wiskunde" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Ren_matematikk" title="Ren matematikk – Bokmål Norwegia" lang="nb" hreflang="nb" data-title="Ren matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmål Norwegia" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Puri_matematike" title="Puri matematike – Novial" lang="nov" hreflang="nov" data-title="Puri matematike" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyka_czysta" title="Matematyka czysta – Polski" lang="pl" hreflang="pl" data-title="Matematyka czysta" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AE%D8%A7%D9%84%D8%B5_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="خالص ریاضی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="خالص ریاضی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica_pura" title="Matemática pura – Portugis" lang="pt" hreflang="pt" data-title="Matemática pura" data-language-autonym="Português" data-language-local-name="Portugis" 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/Matematic%C4%83_pur%C4%83" title="Matematică pură – Rumania" lang="ro" hreflang="ro" data-title="Matematică pură" data-language-autonym="Română" data-language-local-name="Rumania" 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%A4%D1%83%D0%BD%D0%B4%D0%B0%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Фундаментальная математика – Rusia" lang="ru" hreflang="ru" data-title="Фундаментальная математика" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tusnakt_ta%E1%B8%A5u%E1%B9%9B%E1%B9%9Bit" title="Tusnakt taḥuṛṛit – Tachelhit" lang="shi" hreflang="shi" data-title="Tusnakt taḥuṛṛit" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Pure_mathematics" title="Pure mathematics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pure mathematics" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/%C4%8Cista_matematika" title="Čista matematika – Sloven" lang="sl" hreflang="sl" data-title="Čista matematika" data-language-autonym="Slovenščina" data-language-local-name="Sloven" 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/%C4%8Cista_matematika" title="Čista matematika – Serbia" lang="sr" hreflang="sr" data-title="Čista matematika" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%9A%E0%B8%A3%E0%B8%B4%E0%B8%AA%E0%B8%B8%E0%B8%97%E0%B8%98%E0%B8%B4%E0%B9%8C" title="คณิตศาสตร์บริสุทธิ์ – Thai" lang="th" hreflang="th" data-title="คณิตศาสตร์บริสุทธิ์" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Purong_matematika" title="Purong matematika – Tagalog" lang="tl" hreflang="tl" data-title="Purong matematika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" 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/Soyut_matematik" title="Soyut matematik – Turki" lang="tr" hreflang="tr" data-title="Soyut matematik" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D1%82%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Чиста математика – Ukraina" lang="uk" hreflang="uk" data-title="Чиста математика" data-language-autonym="Українська" data-language-local-name="Ukraina" 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data-language-autonym="Volapük" data-language-local-name="Volapuk" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BA%AF%E7%B2%B9%E6%95%B0%E5%AD%A6" title="纯粹数学 – Wu Tionghoa" lang="wuu" hreflang="wuu" data-title="纯粹数学" data-language-autonym="吴语" data-language-local-name="Wu Tionghoa" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%B4%94%E7%B2%B9%E6%95%B8%E5%AD%B8" title="純粹數學 – Tionghoa" lang="zh" hreflang="zh" data-title="純粹數學" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B4%94%E7%B2%B9%E6%95%B8%E5%AD%B8" title="純粹數學 – Kanton" lang="yue" hreflang="yue" data-title="純粹數學" 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#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 #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Periksaterjemahan plainlinks metadata ambox ambox-content ambox-rough_translation" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/Berkas:Translation_to_english_arrow.svg" class="mw-file-description" title="Translation arrow icon"><img alt="Translation arrow icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Translation_to_english_arrow.svg/50px-Translation_to_english_arrow.svg.png" decoding="async" width="50" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Translation_to_english_arrow.svg/75px-Translation_to_english_arrow.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Translation_to_english_arrow.svg/100px-Translation_to_english_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">Artikel atau sebagian dari artikel ini mungkin diterjemahkan dari <i><a href="https://en.wikipedia.org/wiki/Pure_mathematics" class="extiw" title="en:Pure mathematics">Pure mathematics</a></i> di en.wikipedia.org. <b>Isinya masih belum akurat</b>, karena bagian yang diterjemahkan masih perlu diperhalus dan disempurnakan. Jika Anda menguasai bahasa aslinya, harap pertimbangkan untuk menelusuri referensinya dan menyempurnakan terjemahan ini. Anda juga dapat ikut bergotong royong pada <a href="/wiki/Wikipedia:ProyekWiki_Perbaikan_Terjemahan" title="Wikipedia:ProyekWiki Perbaikan Terjemahan">ProyekWiki Perbaikan Terjemahan</a>.<br /> <small>(Pesan ini dapat dihapus jika terjemahan dirasa sudah cukup tepat. Lihat pula: <a href="/wiki/Wikipedia:Panduan_dalam_menerjemahkan_artikel" title="Wikipedia:Panduan dalam menerjemahkan artikel">panduan penerjemahan artikel</a>)</small></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/Berkas:E8Petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/250px-E8Petrie.svg.png" decoding="async" width="250" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/376px-E8Petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/500px-E8Petrie.svg.png 2x" data-file-width="512" data-file-height="514" /></a><figcaption>Matematika murni mempelajari properti dan struktur objek abstrak, seperti <a href="/w/index.php?title=E8_(matematika)&action=edit&redlink=1" class="new" title="E8 (matematika) (halaman belum tersedia)">grup E8</a> dalam <a href="/wiki/Teori_grup" title="Teori grup">teori grup</a>. Dapat dilakukan tanpa berfokus pada aplikasi konkret dari konsep di dunia fisik</figcaption></figure> <p>Secara umum, <b>matematika murni</b> adalah <a href="/wiki/Matematika" title="Matematika">matematika</a> yang sepenuhnya termotivasi lebih pada sebab dan akibat, alasan, berbandingkan sebagai sebuah aplikasi. Hal ini dibedakan dengan oleh adanya ketelitian, abstraksi dan keindahan. Dari abad kedelapan belas dan seterusnya merupakan kategori yang diakui bagi kegiatan matematika, kadang-kadang dicirikan sebagai matematika spekulatif,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> dan terdapat perbedaan adanya kecenderungan lain untuk memenuhi kebutuhan <a href="/wiki/Navigasi" title="Navigasi">navigasi</a>, <a href="/wiki/Astronomi" title="Astronomi">astronomi</a>, <a href="/wiki/Fisika" title="Fisika">fisika</a>, <a href="/wiki/Teknik" class="mw-redirect" title="Teknik">teknik</a>, dan seterusnya. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Sejarah">Sejarah</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=1" title="Sunting bagian: Sejarah" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=1" title="Sunting kode sumber bagian: Sejarah"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Yunani_Kuno">Yunani Kuno</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=2" title="Sunting bagian: Yunani Kuno" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=2" title="Sunting kode sumber bagian: Yunani Kuno"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Matematikawan Yunani Kuno termasuk di antara yang paling awal untuk membuat perbedaan antara matematika murni dengan <a href="/wiki/Matematika_terapan" title="Matematika terapan">matematika terapan</a>. Plato membantu menciptakan kesenjangan antara <i><a href="/wiki/Aritmetika" title="Aritmetika">aritmetika</a></i> yang sekarang disebut <a href="/wiki/Teori_bilangan" title="Teori bilangan">teori bilangan</a> dengan <i><a href="/wiki/Logistik" title="Logistik">logistik</a></i> yang saat sekarang disebut <i>aritmetika</i>. </p><p>Plato beranggapan bahwa logistik (aritmetika) sesuai dengan kebutuhan pengusaha dan peperangan yang dikatakannya <i>dengan belajar </i>seni bilangan<i> atau para pengusaha dan peperangan tidak akan pernah bisa mengetahui bagaimana dengan keadaan susunan kekuatan yang sebenarnya</i> dibandingkan dngan aritmetika (teori bilangan) yang lebih sesuai bagi kebutuhan para filsuf <i>karena telah mempunyai untuk muncul dari lautan perubahan dan berusaha untuk menangkap kebenaran</i>.<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> </p><p><a href="/wiki/Euklides" title="Euklides">Euclid</a> dari Alexandria, ketika ditanya oleh salah seorang siswaya tentang apa kegunaan untuk belajar mengenai <a href="/wiki/Geometri" title="Geometri">geometri</a> lalu Euclid meminta kepada pelayannya untuk memberikan <i>threepence</i> kepada siswa tersebut sambil mengatakan bahwa karena siswa tersebut mempunyai kebutuhan yang dapat membuat keuntungan dari apa yang siswa tersebut pelajari<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> sedangkan seorang matematikawan <a href="/wiki/Yunani" title="Yunani">Yunani</a> yang bernama <a href="/wiki/Apollonius_dari_Perga" title="Apollonius dari Perga">Apollonius dari Perga</a> ketika ditanya tentang manfaat atas bagian dari kaidahnya di dalam Buku IV Conics dengan bangga ia menegaskan sebagai berikut <sup id="cite_ref-Apollonius_4-0" class="reference"><a href="#cite_note-Apollonius-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <blockquote><p>They are worthy of acceptance for the sake of the demonstrations themselves, in the same way as we accept many other things in mathematics for this and for no other reason.</p></blockquote> <p>And since many of his results were not applicable to the science or engineering of his day, Apollonius further argued in the preface of the fifth book of <i>Conics</i> that the subject is one of those that "...seem worthy of study for their own <a href="/wiki/Sake" title="Sake">sake</a>."<sup id="cite_ref-Apollonius_4-1" class="reference"><a href="#cite_note-Apollonius-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Abad_ke-19">Abad ke-19</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=3" title="Sunting bagian: Abad ke-19" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=3" title="Sunting kode sumber bagian: Abad ke-19"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Istilah itu sendiri diabadikan dalam judul lengkap <a href="/w/index.php?title=Sadleirian_Profesor_Matematika_Murni&action=edit&redlink=1" class="new" title="Sadleirian Profesor Matematika Murni (halaman belum tersedia)">Sadleirian Profesor Matematika Murni</a> kadang-kadang disebut pula sebagai <a href="/w/index.php?title=Sadleirian,_Profesor_Matematika_Murni&action=edit&redlink=1" class="new" title="Sadleirian, Profesor Matematika Murni (halaman belum tersedia)">Sadlerian Chair</a>,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> sebagai pencetus (sebagai <a href="/wiki/Profesor" title="Profesor">profesor</a>) pada pertengahan abad kesembilan belas. Gagasannya tentang disiplin terpisah <i>matematika murni</i> mungkin telah muncul pada saat itu. </p><p>Generasi dari <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a> tidak dapat menyentuh perbedaan antara <i>murni</i> dengan <i>terapan</i>. Kemudian pada tahun-tahun berikutnya, spesialisasi dan profesionalisasi (terutama di <a href="/wiki/Weierstrass" class="mw-redirect" title="Weierstrass">Weierstrass</a> pendekatan untuk melakukan <a href="/wiki/Analisis" title="Analisis">analisis</a> <a href="/wiki/Matematis" class="mw-redirect" title="Matematis">matematis</a>) telah membuka celah yang menjadikannya menjadi lebih jelas. </p> <div class="mw-heading mw-heading3"><h3 id="Abad_ke-20">Abad ke-20</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=4" title="Sunting bagian: Abad ke-20" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=4" title="Sunting kode sumber bagian: Abad ke-20"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pada awal abad keduapuluh para matematikawan yang mengambil metode <a href="/wiki/Aksioma" title="Aksioma">aksioma</a> lebih dipengaruhi oleh pemeikiran dari <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Perumusan logis matematika murni yang diusulkan oleh <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> dalam bentuk struktur pembilang proposisi akan tampak lebih dan masuk akal karena sebagian besar matematika telah menjadi axiomatik dan dengan demikian semua harus tunduk pada kriteria sederhana dari pembuktian yang setepat-tepatnya. </p><p>Bahkan dalam pengaturan aksiomatik setepat-tepatnya menambahkan tidak ada ide pembuktian. Matematika murni, menurut pandangan yang dapat dinisbahkan kepada kelompok <a href="/w/index.php?title=Bourbaki&action=edit&redlink=1" class="new" title="Bourbaki (halaman belum tersedia)">Bourbaki</a> adalah apa yang telah dibuktikan. Matematikawan murni akan menjadi kemungkinan bila dicapai dengan melalui pelatihan. </p> <div class="mw-heading mw-heading2"><h2 id="Umum_dan_abstraksi">Umum dan abstraksi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=5" title="Sunting bagian: Umum dan abstraksi" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=5" title="Sunting kode sumber bagian: Umum dan abstraksi"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Banach-Tarski_Paradox.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/350px-Banach-Tarski_Paradox.svg.png" decoding="async" width="350" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/525px-Banach-Tarski_Paradox.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/74/Banach-Tarski_Paradox.svg/700px-Banach-Tarski_Paradox.svg.png 2x" data-file-width="445" data-file-height="100" /></a><figcaption>Ilustrasi dari <a href="/wiki/Paradoks_Banach%E2%80%93Tarski" title="Paradoks Banach–Tarski">paradoks Banach–Tarski</a>, hasil terkenal dalam matematika murni. Meskipun terbukti bahwa dapat mengubah satu bola menjadi dua hanya dengan menggunakan pemotongan dan rotasi, transformasi melibatkan objek yang tidak dapat ada di dunia fisik.</figcaption></figure> <p>Salah satu konsep sentral dalam matematika murni adalah pada ide umum, matematika murni sering tampak menampilkan kecenderungan secara umum. Secara umum memiliki banyak manifestasi yang berbeda, seperti membuktikan kaidah di bawah asumsi yang lebih lemah atau mendefinisikan struktur matematis dengan menggunakan asumsi yang lebih sedikit. Meskipun kadang-kadang ditempuh umum atau dinilai demi kepentingannya akan tetapi dapat memiliki kelebihan tertentu, seperti termasuk: </p> <ul><li>Generalisasi kaidah atau struktur matematika dapat menyebabkan pemahaman yang lebih mendalam pada kaidah asli atau struktur dengan melakukan eksplorasi implikasi yang dapat melemahkan asumsi, salah-satu keuntungan dalam pemahaman yang lebih baik dari asumsi-asumsi yang memainkan peran dalam kaidah asli atau struktur.</li> <li>Secara umum lebih dapat menyederhanakan materi presentasi, sehingga bukti-bukti atau argumen lebih pendek yang lebih mudah diikuti.</li> <li>Secara umum lebih dapat menghindari duplikasi upaya dengan membuktikan hasil umum darpada harus membuktikan kasus-kasus yang terpisah secara independen atau menggunakan wilayah lain dari matematika.</li> <li>Secara umum dapat sebagai fasilitas hubungan antara berbagai cabang matematika dengan menekankan kesamaan struktur yang mungkin tidak akan terlihat pada tingkat yang kurang umum. <a href="/wiki/Teori_kategori" title="Teori kategori">Teori kategori</a> merupakan bidang matematika yang didedikasikan untuk menjelajahi kesamaan struktur ini seperti dibeberapa bidang matematika.</li></ul> <p>Dampak umum pada intuisi terdapat ketergantungan antara subjek dan masalah preferensi pribadi atau gaya belajar, pada umumnya sering dipandang sebagai penghalang bagi intuisi, meskipun sebenarnya dapat berfunsi berlaku sebagai bantuan terhadap hal tersebut, terutama bila dapat memberikan ketersediaan bahan <a href="/wiki/Analogi" title="Analogi">analogi</a> untuk yang sudah memiliki intuisi yang baik. </p><p>Sebagai contoh umum yang utama yakni dalam <a href="/w/index.php?title=Program_Erlangen&action=edit&redlink=1" class="new" title="Program Erlangen (halaman belum tersedia)">Program Erlangen</a> ikut melibatkan perluasan <a href="/wiki/Geometri" title="Geometri">geometri</a> guna mengakomodasi <a href="/w/index.php?title=Geometri_non-Euclidean&action=edit&redlink=1" class="new" title="Geometri non-Euclidean (halaman belum tersedia)">geometri non-Euclidean</a> yang termasuk di dalamnya bidang <a href="/wiki/Topologi" title="Topologi">topologi</a> dan bentuk lain dari geometri, bila dilihat dari geometri sebagai ruang studi bersama dengan <a href="/wiki/Himpunan_(matematika)" title="Himpunan (matematika)">himpunan</a> dari transformasi. </p><p>Studi tentang <a href="/wiki/Bilangan" title="Bilangan">bilangan</a> yang disebut sebagai <a href="/wiki/Aljabar" title="Aljabar">aljabar</a> pada awal pendidikan tingkat sarjana kemudian meluas menuju pada <a href="/wiki/Aljabar_abstrak" title="Aljabar abstrak">aljabar abstrak</a> lalu pada tingkat selanjutnya dalam studi tentang <a href="/wiki/Fungsi_(matematika)" title="Fungsi (matematika)">fungsi</a> yang disebut pula sebagai <a href="/wiki/Kalkulus" title="Kalkulus">kalkulus</a> dan bila diteruskan pada tingkatan selanjutnya akan mendapatkan <a href="/wiki/Analisis_matematis" title="Analisis matematis">analisis matematis</a> dan <a href="/wiki/Analisis_fungsional" title="Analisis fungsional">analisis fungsional</a>. Masing-masing cabang ini tampak lebih kepada matematika abstrak yang akan memiliki banyak bidang sub-spesialisasi dan pada hakekatnya terdapat banyak hubungan antara matematika murni dengan disiplin keilmuan matematika terapan. </p><p>Dalam praktik perkembangan ini menyebabkan terjadinya penyimpangan yang sangat tajam dari fisika, khususnya terjadi antara tahun 1950-1980 yang kemudian mendapatkan kritikan, antara lain oleh <a href="/wiki/Vladimir_Arnold" title="Vladimir Arnold">Vladimir Arnold</a> atau <a href="/w/index.php?title=Hilbert&action=edit&redlink=1" class="new" title="Hilbert (halaman belum tersedia)">Hilbert</a> yang banyak sekali melakukan kirikannya yang lalu disusul kemudian oleh <a href="/w/index.php?title=Poincar%C3%A9&action=edit&redlink=1" class="new" title="Poincaré (halaman belum tersedia)">Poincaré</a>. Inti perdebatan ini tampaknya belum tampak dapat diselesaikan (dasar kontroversi tidak terlihat pada segi padangan kumpulan teori) bila dalam untaian teori dapat saling menarik sedangkan dalam matematika mempunyai ciri-ciri tersendiri yang dapat menarik kembali kepada bukti sebagai pusat. </p> <div class="mw-heading mw-heading2"><h2 id="Lihat_pula">Lihat pula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=6" title="Sunting bagian: Lihat pula" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=6" title="Sunting kode sumber bagian: Lihat pula"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Matematika_terapan" title="Matematika terapan">Matematika terapan</a></li> <li><a href="/wiki/Logika" title="Logika">Logika</a></li> <li><a href="/wiki/Metalogika" title="Metalogika">Metalogika</a></li> <li><a href="/wiki/Metamatematika" title="Metamatematika">Metamatematika</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referensi">Referensi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=7" title="Sunting bagian: Referensi" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=7" title="Sunting kode sumber bagian: Referensi"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r18833634">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2" style=""> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Lihat misalnya beberapa karya dari <a href="/w/index.php?title=Thomas_Simpson&action=edit&redlink=1" class="new" title="Thomas Simpson (halaman belum tersedia)">Thomas Simpson</a> dari abad pertengahan ke-18 antara lain: <i>Essays on Several Curious and Useful Subjects in Speculative and Mixed Mathematicks</i>, <i>Miscellaneous Tracts on Some Curious and Very Interesting Subjects in Mechanics, Physical Astronomy and Speculative Mathematics</i><a rel="nofollow" class="external autonumber" href="http://www.1911encyclopedia.org/Thomas_Simpson">[1]</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation book"><a href="/w/index.php?title=Carl_Benjamin_Boyer&action=edit&redlink=1" class="new" title="Carl Benjamin Boyer (halaman belum tersedia)">Boyer, Carl B.</a> (1991). "The age of Plato and Aristotle". <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328"><i>A History of Mathematics</i></a> (edisi ke-Second Edition). John Wiley & Sons, Inc. hlm. <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328/page/n105">86</a>. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Istimewa:Sumber_buku/0471543977" title="Istimewa:Sumber buku/0471543977">0471543977</a>. <q>Plato is important in the history of mathematics largely for his role as inspirer and director of others, and perhaps to him is due the sharp distinction in ancient Greece between arithmetic (in the sense of the theory of numbers) and logistic (the technique of computation). Plato regarded logistic as appropriate for the businessman and for the man of war, who "must learn the art of numbers or he will not know how to array his troops." The philosopher, on the other hand, must be an arithmetician "because he has to arise out of the sea of change and lay hold of true being."</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+age+of+Plato+and+Aristotle&rft.btitle=A+History+of+Mathematics&rft.pages=86&rft.edition=Second+Edition&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=1991&rft.isbn=0471543977&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistorymathemati00boye_328&rfr_id=info%3Asid%2Fid.wikipedia.org%3AMatematika+murni" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">Pemeliharaan CS1: Teks tambahan (<a href="/wiki/Kategori:Pemeliharaan_CS1:_Teks_tambahan" title="Kategori:Pemeliharaan CS1: Teks tambahan">link</a>) </span></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"><cite class="citation book"><a href="/w/index.php?title=Carl_Benjamin_Boyer&action=edit&redlink=1" class="new" title="Carl Benjamin Boyer (halaman belum tersedia)">Boyer, Carl B.</a> (1991). "Euclid of Alexandria". <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328"><i>A History of Mathematics</i></a> (edisi ke-Second Edition). John Wiley & Sons, Inc. hlm. <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328/page/n120">101</a>. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Istimewa:Sumber_buku/0471543977" title="Istimewa:Sumber buku/0471543977">0471543977</a>. <q>Evidently Euclid did not stress the practical aspects of his subject, for there is a tale told of him that when one of his students asked of what use was the study of geometry, Euclid asked his slave to hive the student threepence, "since he must make gain of what he learns."</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Euclid+of+Alexandria&rft.btitle=A+History+of+Mathematics&rft.pages=101&rft.edition=Second+Edition&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=1991&rft.isbn=0471543977&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistorymathemati00boye_328&rfr_id=info%3Asid%2Fid.wikipedia.org%3AMatematika+murni" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">Pemeliharaan CS1: Teks tambahan (<a href="/wiki/Kategori:Pemeliharaan_CS1:_Teks_tambahan" title="Kategori:Pemeliharaan CS1: Teks tambahan">link</a>) </span></span> </li> <li id="cite_note-Apollonius-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Apollonius_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Apollonius_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite class="citation book"><a href="/w/index.php?title=Carl_Benjamin_Boyer&action=edit&redlink=1" class="new" title="Carl Benjamin Boyer (halaman belum tersedia)">Boyer, Carl B.</a> (1991). "Apollonius of Perga". <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328"><i>A History of Mathematics</i></a> (edisi ke-Second Edition). John Wiley & Sons, Inc. hlm. <a rel="nofollow" class="external text" href="https://archive.org/details/historymathemati00boye_328/page/n171">152</a>. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Istimewa:Sumber_buku/0471543977" title="Istimewa:Sumber buku/0471543977">0471543977</a>. <q>It is in connection with the theorems in this book that Apollonius makes a statement implying that in his day, as in ours, there were narrow-minded opponents of pure mathematics who pejoratively inquired about the usefulness of such results. The author proudly asserted: "They are worthy of acceptance for the sake of the demonstrations themselves, in the same way as we accept many other things in mathematics for this and for no other reason." (Heath 1961, p.lxxiv).<br />The preface to Book V, relating to maximum and minimum straight lines drawn to a conic, again argues that the subject is one of those that seem "worthy of study for their own sake." While one must admire the author for his lofty intellectual attitude, it may be pertinently pointed out that s day was beautiful theory, with no prospect of applicability to the science or engineering of his time, has since become fundamental in such fields as terrestrial dynamics and celestial mechanics.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Apollonius+of+Perga&rft.btitle=A+History+of+Mathematics&rft.pages=152&rft.edition=Second+Edition&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=1991&rft.isbn=0471543977&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistorymathemati00boye_328&rfr_id=info%3Asid%2Fid.wikipedia.org%3AMatematika+murni" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33; margin-left:0.3em">Pemeliharaan CS1: Teks tambahan (<a href="/wiki/Kategori:Pemeliharaan_CS1:_Teks_tambahan" title="Kategori:Pemeliharaan CS1: Teks tambahan">link</a>) </span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">For example, <a href="/wiki/Encyclopaedia_Britannica" class="mw-redirect" title="Encyclopaedia Britannica">Encyclopaedia Britannica</a>, 15th edition</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.britannica.com/eb/article-9040439/David-Hilbert">"David Hilbert"</a>. Encyclopædia Britannica. 2007<span class="reference-accessdate">. Diakses tanggal <span class="nowrap">2009-12-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=David+Hilbert&rft.pub=Encyclop%C3%A6dia+Britannica&rft.date=2007&rft_id=http%3A%2F%2Fwww.britannica.com%2Feb%2Farticle-9040439%2FDavid-Hilbert&rfr_id=info%3Asid%2Fid.wikipedia.org%3AMatematika+murni" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Pranala_luar">Pranala luar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_murni&veaction=edit&section=8" title="Sunting bagian: Pranala luar" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_murni&action=edit&section=8" title="Sunting kode sumber bagian: Pranala luar"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.math.uwaterloo.ca/PM_Dept/What_Is/what_is.shtml"><i>What is Pure Mathematics?</i> Department of Pure Mathematics, University of Waterloo</a></li> <li><a rel="nofollow" class="external text" href="http://www.liv.ac.uk/maths/PURE/wipm.html"><i> What is Pure Mathematics?</i> by Professor P.J. Giblin The University of Liverpool</a></li> <li><a rel="nofollow" class="external text" href="http://fair-use.org/bertrand-russell/the-principles-of-mathematics"><i> The Principles of Mathematics </i> by Bertrand Russell</a></li> <li><a rel="nofollow" class="external text" href="http://hk.mathphy.googlepages.com/puremath.htm">How to Become a Pure Mathematician (or Statistician)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090823064312/http://hk.mathphy.googlepages.com/puremath.htm">Diarsipkan</a> 2009-08-23 di <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r23782733">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline 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