{"id":40474,"date":"2020-02-29T00:00:27","date_gmt":"2020-02-28T21:00:27","guid":{"rendered":"https:\/\/bilimvegelecek.com.tr\/?p=40474"},"modified":"2020-03-21T17:25:28","modified_gmt":"2020-03-21T14:25:28","slug":"matematigin-buyuk-teoremleri","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2020\/02\/29\/matematigin-buyuk-teoremleri","title":{"rendered":"Matemati\u011fin b\u00fcy\u00fck teoremleri"},"content":{"rendered":"

Matematikte do\u011frulu\u011fu kan\u0131tlanabilen \u00f6nermelere teorem deniliyor. Tarih boyunca matemati\u011fin in\u015fas\u0131 s\u00fcresince binlerce \u00f6nerme kan\u0131tland\u0131, kan\u0131tlan\u0131yor. En \u00f6nemli, en iz b\u0131rakan ve bir kilometre ta\u015f\u0131 olarak g\u00f6r\u00fclebilecek teoremler hangileridir? Bu soruyu matematikle u\u011fra\u015fan hemen herkes farkl\u0131 listeler yaparak yan\u0131tlayabilir.
\nEn iyi 100 film, en iyi 100 roman gibi matemati\u011fin en b\u00fcy\u00fck 100 teoreminin listesi matematik\u00e7iler Jack ve Paul Abad taraf\u0131ndan olu\u015fturulup, 1999\u2019daki bir matematik konferans\u0131na sunuldu.(1) Abad\u2019lar listeyi haz\u0131rlarken \u015fu \u00fc\u00e7 kriteri kulland\u0131klar\u0131n\u0131 a\u00e7\u0131klad\u0131lar: Teoremin literat\u00fcrdeki \u00f6nem ve yeri, kan\u0131t\u0131n kalitesi ve do\u011furdu\u011fu sonu\u00e7lar.
\nYukar\u0131daki kriterlere ek olarak, teoremi ortaya atan veya kan\u0131tlayan matematik\u00e7inin tan\u0131n\u0131rl\u0131\u011f\u0131n\u0131, b\u00fcy\u00fck matematik\u00e7i olmas\u0131n\u0131 da dikkate alarak daha dar ve pop\u00fcler bir liste Amerikal\u0131 matematik tarih\u00e7isi William Dunham taraf\u0131ndan olu\u015fturulmu\u015f.(3)
\nB\u00fcy\u00fck matematik\u00e7ilere ait teoremleri \u00f6nemsemek gerekti\u011fini d\u00fc\u015f\u00fcn\u00fcyorum, \u00e7\u00fcnk\u00fc nas\u0131l ki edebiyat tarihinin en \u00f6nemli eserlerinden s\u00f6z edilirken Dostoyevski, Balzac gibi dev yazarlar\u0131n isimlerinin ge\u00e7memesi m\u00fcmk\u00fcn de\u011filse, teoremlerle ilgili bir listede de Newton, Euler, Gauss gibi b\u00fcy\u00fck matematik\u00e7ilerin yer almas\u0131 son derece do\u011fal.
\nKu\u015fkusuz ki, matemati\u011fin b\u00fcy\u00fck teoremlerinin listesi her matematik\u00e7i i\u00e7in keyfi bir se\u00e7imle farkl\u0131 teoremleri kapsayacakt\u0131r. A\u015fa\u011f\u0131daki liste de yukar\u0131da sayd\u0131\u011f\u0131m\u0131z \u00f6zellikleri ta\u015f\u0131makla birlikte eksiktir. \u00d6te yandan okuru matematik tarihinde k\u00fc\u00e7\u00fck bir geziye \u00e7\u0131karmay\u0131 ama\u00e7layarak kronolojik bir liste yapmaya \u00e7al\u0131\u015ft\u0131m.
\nTeoremlerin kan\u0131tlar\u0131n\u0131 bu yaz\u0131n\u0131n kapsam\u0131 i\u00e7inde vermem m\u00fcmk\u00fcn olmad\u0131\u011f\u0131ndan merakl\u0131 okur i\u00e7in her teoremin kan\u0131t\u0131n\u0131n yer ald\u0131\u011f\u0131 kaynaklar\u0131 yaz\u0131n\u0131n sonunda belirttim.<\/p>\n

Hilalin karele\u015ftirmesi<\/strong>
\nAntik \u00c7a\u011f Yunan matemati\u011finin \u00f6nemli problemlerden biri \u201cdairenin karele\u015ftirilmesi\u201d, yani bir dairenin alan\u0131na e\u015fit olan bir karenin pergel ve cetvel kullan\u0131larak \u00e7izimidir. Sak\u0131zl\u0131 Hipokrat (M\u00d6 440) (Hekim olan Koslu Hipokrat\u2019la kar\u0131\u015ft\u0131r\u0131lmamal\u0131.) bu problemle u\u011fra\u015f\u0131rken hilallerin (ayc\u0131klar) karele\u015ftirilmesini ba\u015farm\u0131\u015f, yani hilalle e\u015fit alanl\u0131 bir kare in\u015fa etmi\u015ftir.<\/p>\n

A\u015fa\u011f\u0131daki \u015fekilde O merkezli AC \u00e7apl\u0131 ve D merkezli AB \u00e7apl\u0131 yar\u0131m dairelerle olu\u015fan AFBE hilalinin alan\u0131n\u0131n AOB ikizkenar dik \u00fc\u00e7genin alan\u0131na e\u015fit oldu\u011funu kan\u0131tlayan Hipokrat, bu \u00fc\u00e7genin alan\u0131n\u0131n iki kat\u0131na kar\u015f\u0131l\u0131k gelen bir kareyi olu\u015fturarak hilali karele\u015ftirmi\u015ftir.(2)
\n\"\"<\/p>\n

Hipokrat, hilallerin alanlar\u0131yla ilgili yukar\u0131dakine benzer \u00e7ok say\u0131da \u00f6rnek vererek matematik\u00e7iler aras\u0131nda dairenin karele\u015ftirilmesi probleminin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in iyimser bir hava yaratm\u0131\u015ft\u0131r. Binlerce y\u0131l bir\u00e7ok matematik\u00e7inin bu y\u00f6nde \u00e7al\u0131\u015fm\u0131\u015f olmas\u0131na kar\u015f\u0131n sonu\u00e7 al\u0131namam\u0131\u015ft\u0131r. Bu problemin \u00e7\u00f6z\u00fcms\u00fcz oldu\u011fu yakla\u015f\u0131k 2000 y\u0131l sonra, 1882\u2019de Alman matematik\u00e7i Ferdinand von Lindemann (1852-1939) taraf\u0131ndan g\u00f6sterilmi\u015ftir.Lindemann, Pi say\u0131s\u0131n\u0131n \u201ca\u015fk\u0131n\u201d bir say\u0131 (katsay\u0131lar\u0131 rasyonel say\u0131 olan bir polinomun k\u00f6k\u00fc olmayan reel say\u0131) oldu\u011funu kan\u0131tlad\u0131\u011f\u0131ndan, pergel ve cetvelle bir kenar\u0131 Pi\u2019nin karek\u00f6k\u00fc olan bir karenin in\u015fa edilemeyece\u011fi sonucuna ula\u015f\u0131lm\u0131\u015ft\u0131r.<\/p>\n

\u00d6klid\u2019in Elemanlar\u0131\u2019nda yer alan Pisagor Teoremi\u2019nin ispat\u0131
\n<\/strong><\/em>\u00d6klid\u2019in (M.\u00d6 330-270) kendinden \u00f6nceki matematik\u00e7ilerin eserlerini ve \u00f6z \u00e7al\u0131\u015fmalar\u0131n\u0131 derleyerek olu\u015fturdu\u011fu Elemanlar <\/em>isimli kitab\u0131 matemati\u011fi, hatta bilim ve felsefeyi ola\u011fan\u00fcst\u00fc etkilemi\u015ftir. 13 kitapta 465 \u00f6nermenin yer ald\u0131\u011f\u0131 bu yap\u0131t, tan\u0131m, \u00f6nerme ve ispatlardan olu\u015fanaksiyomatik sistemin temellerini atarak teorik matemati\u011finba\u015flang\u0131\u00e7 metni olarak kabul edilir.
\nElemanlar<\/em>\u2019\u0131n 1\u2019inci kitab\u0131n\u0131n 47\u2019inci \u00f6nermesi Pisagor Teoremi\u2019dir: Dik a\u00e7\u0131l\u0131 \u00fc\u00e7genlerde dik a\u00e7\u0131y\u0131 g\u00f6ren kenar \u00fczerindeki kare, dik a\u00e7\u0131y\u0131 i\u00e7eren kenarlar \u00fczerindeki karelere e\u015fittir.<\/p>\n

\"\"<\/p>\n

\u00d6klid, Pisagor Teoremi\u2019ni bu \u00f6nermeden \u00f6nce ifade etti\u011fi tan\u0131m, \u00f6nerme ve teoremlere dayanarak m\u00fcthi\u015f bir titizlikle kan\u0131tlam\u0131\u015ft\u0131r.[3]Yukar\u0131daki \u015fekil yard\u0131m\u0131yla yap\u0131lan bu kan\u0131t Pisagor Teoremi\u2019nin bilinen ilk yaz\u0131l\u0131 kan\u0131t\u0131 olmakla birlikte, aksiyomatik y\u00f6ntemin en \u00e7arp\u0131c\u0131 \u00f6rne\u011fidir.<\/p>\n

Asal say\u0131lar sonsuz say\u0131dad\u0131r<\/em>
\n<\/strong>Bu teorem say\u0131lar teorisinin temel bir \u00f6nermesidir ve sonsuz say\u0131da asal say\u0131n\u0131n oldu\u011funu ifade eder. \u00d6klid bu teoremi Elemanlar<\/em>\u2019\u0131n 9. kitab\u0131n\u0131n 20. \u00f6nermesi olarak ifade etmi\u015f, \u00a0her sonlu asal say\u0131 listesi i\u00e7in bu listede bulunmayan ba\u015fka bir asal say\u0131n\u0131n olaca\u011f\u0131n\u0131, bu y\u00fczden de asal say\u0131lar\u0131n sonsuz say\u0131da oldu\u011funu g\u00f6stererek kan\u0131tlam\u0131\u015ft\u0131r.[,(3)<\/p>\n

\u00d6klid\u2019in \u00e7eli\u015fki yaratma yoluyla (olmayana ergi) yapt\u0131\u011f\u0131 bu kan\u0131t bir\u00e7ok matematik\u00e7i taraf\u0131ndan en g\u00fczel kan\u0131tlardan biri olarak g\u00f6sterilmi\u015f ve bu teorem daha sonra bir\u00e7ok farkl\u0131 yolla kan\u0131tlanm\u0131\u015ft\u0131r.<\/p>\n

\u221a2 irrasyonel say\u0131d\u0131r<\/strong><\/em><\/p>\n

D\u00fcnyan\u0131n ilk matematik\u00e7ilerinden biri olan Pisagor (Pythagoras) (M\u00d6 572-497) \u201cTanr\u0131 say\u0131d\u0131r\u201d diyordu ve say\u0131 olarak sadece do\u011fal say\u0131lar\u0131 kabul ediyordu; kurdu\u011fu okulda evrenin, do\u011fal say\u0131lar ve onlar\u0131n oranlar\u0131 kullan\u0131larak olu\u015ftu\u011fu \u00f6\u011fretiliyordu.<\/p>\n

\u221a2 irrasyonel bir say\u0131d\u0131r teoremi Pisagorcular\u0131n k\u00e2busu olmu\u015ftur. Bu olay\u0131n ilgin\u00e7 hik\u00e2yesini daha \u00f6nce bu k\u00f6\u015fede anlatm\u0131\u015ft\u0131k.(8)<\/p>\n

\u221a2\u2019nin rasyonel olmad\u0131\u011f\u0131n\u0131n ilk yaz\u0131l\u0131 kan\u0131t\u0131 yine \u00d6klid\u2019in Elemanlar\u2019\u0131nda (2) (10\u2019uncu kitap \u00f6nerme 117) verilmi\u015ftir. Bu teoremin kan\u0131t\u0131nda da olmayana ergi y\u00f6ntemi kullan\u0131lm\u0131\u015f, \u221a2\u2019nin rasyonel oldu\u011fu, iki tamsay\u0131n\u0131n oran\u0131 olarak yaz\u0131labilece\u011fi kabul edilmi\u015f, \u00e7eli\u015fkili bir sonu\u00e7la teoremin do\u011frulu\u011fu g\u00f6sterilmi\u015ftir.<\/p>\n

Bu kan\u0131t irrasyonel say\u0131lar k\u00fcmesinin varl\u0131\u011f\u0131n\u0131n habercisi oldu\u011fu i\u00e7in say\u0131lar teorisi i\u00e7in ayr\u0131 bir \u00f6neme sahiptir.<\/p>\n

Ar\u015fimet\u2019in dairenin alan\u0131n\u0131 hesaplama y\u00f6ntemi
\n<\/strong><\/em>Ar\u015fimet\u2019in (M\u00d6 287-212) gelmi\u015f ge\u00e7mi\u015f en b\u00fcy\u00fck matematik\u00e7ilerden biri olarak g\u00f6r\u00fclmesi bo\u015funa de\u011fildir. Ona bu payenin verilmesi bir\u00e7ok kavram\u0131 ilk kez bilimsel incelemeye tabi tutmu\u015f olmas\u0131ndan kaynaklan\u0131r. Alan ve hacim hesaplar\u0131nda kulland\u0131\u011f\u0131 y\u00f6ntemler y\u00fczy\u0131llar sonra Newton ve Leibniz\u2019indiferansiyel ve integral hesab\u0131 ke\u015ffetmesine ilham kayna\u011f\u0131 olmu\u015ftur.<\/p>\n

Ar\u015fimet\u2019in bir dairenin d\u00fczg\u00fcn d\u0131\u015f te\u011fet \u00e7okgeniyle dairenin i\u00e7ine \u00e7izilen d\u00fczg\u00fcn kiri\u015f \u00e7okgeninin alanlar\u0131n\u0131 hesaplayarak dairenin alan\u0131n\u0131 bulma \u00e7abas\u0131 \u03c0 say\u0131s\u0131n\u0131n de\u011ferinin 3 10\/71 say\u0131s\u0131yla 3 1\/7 say\u0131s\u0131 aras\u0131nda oldu\u011funu g\u00f6stermi\u015ftir.<\/p>\n

A\u015fa\u011f\u0131daki \u015fekilde dairenin i\u00e7ine ve d\u0131\u015f\u0131na \u00e7izilmi\u015f iki alt\u0131gen g\u00f6r\u00fcl\u00fcyor. D\u0131\u015ftaki alt\u0131genin alan\u0131 dairenin alan\u0131ndan b\u00fcy\u00fck i\u00e7tekininse k\u00fc\u00e7\u00fckt\u00fcr. Ar\u015fimet, bu \u00e7okgenlerin kenar say\u0131s\u0131n\u0131 12, 24, 48 ve son olarak 96 alarak \u00a0say\u0131s\u0131n\u0131n de\u011fer aral\u0131\u011f\u0131n\u0131 saf bir zihin g\u00fcc\u00fcyle bulmay\u0131 ba\u015farm\u0131\u015ft\u0131r.(2)<\/p>\n

\"\"<\/p>\n

\u00dc\u00e7genin alan\u0131 i\u00e7in Heron form\u00fcl\u00fc<\/strong><\/p>\n

\u00dc\u00e7 kenar uzunlu\u011fu bilinen bir \u00fc\u00e7genin alan\u0131 veren bu form\u00fcl \u0130skenderiye\u2019li geometrici, mekanik\u00e7i Heron\u2019un (M.S 75) Metrica isimli kitab\u0131nda yer alm\u0131\u015ft\u0131r. Kenar uzunluklar\u0131 \u00a0olan bir \u00fc\u00e7genin alan\u0131 u= (a+b+c)\/2 olmak \u00fczere \u221a(u(u-a)(u-b)(u-c)) olarak hesaplanm\u0131\u015ft\u0131r.<\/p>\n

Bu form\u00fcl\u00fc listeye \u201cb\u00fcy\u00fck teorem\u201d\u00a0 olarak almam\u0131z\u0131n nedeni, form\u00fcl sayesinde \u00fc\u00e7genin alan\u0131n\u0131npratik yoldan bulunuyor olmas\u0131n\u0131n yan\u0131 s\u0131ra, kan\u0131t\u0131ndaki ad\u0131mlar\u0131n m\u00fckemmel bir soyutlamayla geometrik ak\u0131l y\u00fcr\u00fctmeye sahip olmas\u0131d\u0131r.<\/p>\n

Bundan sonraki ba\u015fl\u0131kta yer alan teoremin ortaya \u00e7\u0131k\u0131\u015f\u0131yla yukar\u0131daki aras\u0131nda yakla\u015f\u0131k 1500 y\u0131l ge\u00e7mi\u015ftir. Bilindi\u011fi gibi bu d\u00f6nemde Hint ve \u0130slam matematik\u00e7ilerinin \u00e7al\u0131\u015fmalar\u0131 \u00f6n plandad\u0131r. Musa al-Harezmi (780-850), Sabit bin Kurra (826-901), \u00d6mer Hayyam (1048-1131), \u015earafeddin Al-Tusi(1135-1213), Nasireddin Al-Tusi (1201-1274) Cem\u015fit Al-Ka\u015fi (1380-1429) \u00a0gibi bir\u00e7ok bilgin ve matematik\u00e7ilerin k\u00fcresel geometriye, cebire, say\u0131lar teorisine, trigonometri ve astronomiye \u00f6zg\u00fcn ve \u00f6nemli katk\u0131lar\u0131 olmu\u015ftur.[3] Ama bu \u00e7al\u0131\u015fmalar bir\u00e7ok nedenden dolay\u0131 matematik literat\u00fcr\u00fcnde \u00a0\u201cteorem\u201d olarak yer alamam\u0131\u015ft\u0131r. \u00d6rne\u011fin \u015eerafeddin Al-Tusi \u00fc\u00e7\u00fcnc\u00fc dereceden denklemlerin \u00e7\u00f6z\u00fcm\u00fcn\u00fc ara\u015ft\u0131r\u0131rken \u201ct\u00fcrevi\u201d tan\u0131mlam\u0131\u015f, ama t\u00fcrev, sonras\u0131nda Frans\u0131z matematik\u00e7i Fermat ve daha sonra da Newton ve Leibniz taraf\u0131ndan ke\u015ffedilerek literat\u00fcre girmi\u015ftir.<\/p>\n

\u00dc\u00e7\u00fcnc\u00fc dereceden denklemlerin \u00e7\u00f6z\u00fcm\u00fc<\/em>
\n<\/strong>\u0130kinci dereceden denklemlerin k\u0131smi \u00e7\u00f6z\u00fcm\u00fc (pozitif k\u00f6klerin bulunmas\u0131) M\u00d6 2000-1000\u2019lerde Babilliler taraf\u0131ndan biliniyordu; fakat \u00fc\u00e7\u00fcnc\u00fc dereceden denklemlerin genel \u00e7\u00f6z\u00fcm\u00fcn\u00fcn ke\u015ffi, o tarihten sonra insanl\u0131\u011f\u0131n en az 2500 y\u0131l\u0131n\u0131 alm\u0131\u015ft\u0131r.<\/p>\n

\u00dc\u00e7\u00fcnc\u00fc dereceden denklemlere Antik Yunan\u2019da baz\u0131 \u00f6zel \u00e7\u00f6z\u00fcmler yap\u0131lm\u0131\u015f, sonras\u0131nda \u00d6mer Hayyam, \u015eerafeddin Al-Tusi gibi matematik\u00e7iler k\u0131smi \u00e7\u00f6z\u00fcmlere ula\u015fm\u0131\u015ft\u0131r. \u00d6zellikle \u0130ran\u2019l\u0131 \u015fair ve matematik\u00e7i Hayyam, 1075 y\u0131ll\u0131nda yay\u0131mlad\u0131\u011f\u0131 Cebir Problemleri ve Kar\u015f\u0131tl\u0131k Kan\u0131tlar\u0131 \u00dczerine <\/em>adl\u0131 eserinde geometrik yap\u0131lar\u0131 (konik kesitlerinin kesi\u015fim noktalar\u0131n\u0131) kullanarak bu yolda \u00f6nemli ad\u0131mlar atm\u0131\u015f; ama k\u00f6kleri katsay\u0131lara ba\u011fl\u0131 olarak ifade edemeyip, bunu gelece\u011fin matematik\u00e7ilerinin ba\u015farmas\u0131 temennisinde bulunmu\u015ftur.<\/p>\n

1535\u2019te her \u015fey de\u011fi\u015fmi\u015f, Hayyam\u2019\u0131n temennisi ger\u00e7ekle\u015fmi\u015ftir. \u0130talyan matematik\u00e7i Niccol\u00f2Tartaglia(1499-1557) a\u22600 olmak \u00fczere<\/p>\n

ax^3+bx^2+cx+d=0<\/p>\n

denklemini \u00a0katsay\u0131lar\u0131na ba\u011fl\u0131 olarak \u00e7\u00f6zm\u00fc\u015ft\u00fcr.(3)<\/p>\n

Tartaglia\u2019n\u0131n \u00e7\u00f6z\u00fcm\u00fc matematik literat\u00fcr\u00fcne Cardano form\u00fclleri<\/strong> ismiyle ge\u00e7mi\u015ftir; \u00e7\u00fcnk\u00fc Milano\u2019lu bilgin Gerolamo Cardano (1501-1576) Tartaglia\u2019n\u0131n bir s\u0131r gibi saklad\u0131\u011f\u0131 \u00e7\u00f6z\u00fcm\u00fc Tartaglia\u2019dan \u00f6\u011frenip, a\u00e7\u0131klamayaca\u011f\u0131na dair s\u00f6z vermi\u015f olmas\u0131na kar\u015f\u0131n Ars Magna isimli eserinde yay\u0131mlam\u0131\u015ft\u0131r.(4)<\/p>\n

Cardano, Ars Magna\u2019da \u00fc\u00e7\u00fcnc\u00fc dereceden denklemlerin k\u00f6kleri aras\u0131nda karesi negatif say\u0131 olan say\u0131lar\u0131n da varl\u0131\u011f\u0131na dikkat \u00e7ekerek karma\u015f\u0131k say\u0131lar kuram\u0131n\u0131n i\u015faret fi\u015fe\u011fini ate\u015flemi\u015ftir.<\/p>\n

Newton\u2019un alan hesaplama y\u00f6ntemi ve \u03c0<\/strong> say\u0131s\u0131
\n<\/strong><\/em>Isaac Newton ( 1643\u2013 1727) \u00f6nce Newton\u2019un Binom Teoremi ad\u0131yla bilinen teoremi form\u00fcle etmi\u015f ve sonras\u0131nda da m\u00fckemmel bir y\u00f6ntemle e\u011fri alt\u0131nda kalan alan hesab\u0131n\u0131 ke\u015ffetmi\u015ftir.<\/p>\n

Newton, merkezi 1\/2,0) ve yar\u0131\u00e7ap\u0131 1 birim olan \u00e7ember x=1\/4 do\u011frusunu ve x ekseni aras\u0131nda kalan b\u00f6lgenin alan\u0131n\u0131 \u221a(1-x)’i seriye a\u00e7arak hesaplam\u0131\u015f ve \u03c0 say\u0131s\u0131n\u0131n 16 basama\u011f\u0131n\u0131 bulmu\u015ftur.(3)<\/p>\n

Ters karelerin toplam\u0131<\/strong><\/em>
\nBasel problemi ad\u0131yla bilinen bu teorem Pietro Mengoli taraf\u0131ndan 1644\u2019te ortaya at\u0131lm\u0131\u015f ve yakla\u015f\u0131k y\u00fczy\u0131l sonra 1735 y\u0131l\u0131nda Leonhard Euler (1707-1783) taraf\u0131ndan \u00e7\u00f6z\u00fclm\u00fc\u015f \u00fcnl\u00fc bir say\u0131 kuram\u0131 problemidir. Bu problem sayma say\u0131lar\u0131n\u0131n karelerinin \u00e7arpmaya g\u00f6re terslerinin toplam\u0131ndan olu\u015fan a\u015fa\u011f\u0131daki serinin hangi say\u0131ya yak\u0131nsad\u0131\u011f\u0131n\u0131 sormaktad\u0131r.<\/p>\n

1\/1^2 +1\/2^2<\/p>\n

Jacob, Johann ve Daniel Bernoulli gibi matematik\u00e7ileri yakla\u015f\u0131k bir as\u0131r boyunca u\u011fra\u015ft\u0131ran bu serinin Euler \u03c0^2\/6\u2019ya yak\u0131nsad\u0131\u011f\u0131n\u0131 g\u00f6stererek 28 ya\u015f\u0131nda b\u00fcy\u00fck \u00fcn sahibi olmu\u015ftur.(3) Euler\u2019in seri \u00fczerinde yapt\u0131\u011f\u0131 baz\u0131 oynamalar zaman\u0131n matematik\u00e7ilerince kabul g\u00f6rmemi\u015f ve Euler daha kesin sonu\u00e7lar veren kan\u0131t\u0131n\u0131 6 y\u0131l sonra 1741\u2019de tamamlayarak problemi genelle\u015ftirmi\u015ftir. Onun d\u00fc\u015f\u00fcnceleri Bernhard Riemann\u2019\u0131n 1859\u2019da yazd\u0131\u011f\u0131 \u201cBelirli Bir B\u00fcy\u00fckl\u00fckten K\u00fc\u00e7\u00fck Asal Say\u0131lar \u00dczerine\u201d isimli makaleye esin kayna\u011f\u0131 olmu\u015ftur.<\/p>\n

Cebirin Temel Teoremi<\/strong><\/em>
\nBu teorem karma\u015f\u0131k de\u011fi\u015fkenli polinomlar\u0131n varl\u0131\u011f\u0131yla ilgili temel bir sonu\u00e7tur. Teoremin a\u00e7\u0131k ifadesi \u015f\u00f6yledir: Katsay\u0131lar\u0131 karma\u015f\u0131k say\u0131 olan ve sabit olmayan tek de\u011fi\u015fkenli her polinomun en az bir (karma\u015f\u0131k) k\u00f6k\u00fc vard\u0131r.<\/p>\n

Teoremi \u00f6nce d\u2019Alembert (1717-1783), Euler ve Daniel Bernoulli kan\u0131tlad\u0131klar\u0131n\u0131 a\u00e7\u0131klam\u0131\u015flar ama bu kan\u0131tlar\u0131n yanl\u0131\u015f oldu\u011fu anla\u015f\u0131lm\u0131\u015ft\u0131r. 1799\u2019da Carl Friedrich Gauss (1777-1855) geometrik bir kan\u0131t vermi\u015ftir, ama bu kan\u0131tta da topolojik bir hata ortaya \u00e7\u0131km\u0131\u015ft\u0131r. \u0130lk do\u011fru kan\u0131t\u0131 1806\u2019da kitap\u00e7\u0131 ve matematik\u00e7i Jean Robert Argand (1768-1822) taraf\u0131ndan bulunmu\u015ftur. Gauss
\n1816\u2019da teoremin iki de\u011fi\u015fik kan\u0131t\u0131n\u0131 vermi\u015f ve daha sonra 1849\u2019da ilk kan\u0131t\u0131 d\u00fczeltmi\u015ftir. O g\u00fcn bug\u00fcn teoremin bir\u00e7ok de\u011fi\u015fik kan\u0131t\u0131 yap\u0131lm\u0131\u015ft\u0131r.(5)
\nCebirin Temel Teoremi g\u00fcn\u00fcm\u00fczde cisimler teorisinden spektral analize kadar bir\u00e7ok teorinin temelinde yer alan bir teoremdir.<\/p>\n

Cantor Teoremi<\/strong><\/em>
\nAlman matematik\u00e7i Georg Cantor (1845-1918) sonsuz k\u00fcmeler kuram\u0131n\u0131 in\u015fa ederek matematikte devrim niteli\u011finde ad\u0131mlar atm\u0131\u015ft\u0131r. Matematik literat\u00fcr\u00fcne Cantor Teoremi ad\u0131yla ge\u00e7en \u00f6nerme, bo\u015f olmayan herhangi bir A k\u00fcmesinin kuvvet k\u00fcmesinin g\u00fcc\u00fcn\u00fcn (kardinalitesinin), A k\u00fcmesinin g\u00fcc\u00fcnden b\u00fcy\u00fck oldu\u011funu s\u00f6yler. Kuvvet k\u00fcmesi P(A) g\u00f6sterilirse, teoreme g\u00f6re A k\u00fcmesi ile P(A) aras\u0131nda birebir e\u015fleme yap\u0131lamaz.
\nCantor\u2019un 1891\u2019de kan\u0131tlad\u0131\u011f\u0131 bu \u00f6nerme sonlu k\u00fcmeler i\u00e7in bariz bir sonu\u00e7 olsa da sonsuz k\u00fcmeler i\u00e7in \u00e7\u0131\u011f\u0131r a\u00e7\u0131c\u0131 sonu\u00e7lar do\u011furmu\u015ftur.<\/p>\n

G\u00f6del\u2019in Eksiklik Teoremleri<\/strong><\/em>
\nAvusturyal\u0131 mant\u0131k\u00e7\u0131 ve matematik\u00e7i Kurt G\u00f6del (1906-1978) matemati\u011fin mant\u0131ksal olarak tutarl\u0131 oldu\u011funu kan\u0131tlaman\u0131n m\u00fcmk\u00fcn olmad\u0131\u011f\u0131n\u0131 kan\u0131tlayarak matemati\u011fin temellerine olan bak\u0131\u015f\u0131 k\u00f6kten de\u011fi\u015ftirmi\u015ftir. G\u00f6del, aksiyomatik bir sistemin tutarl\u0131 ise eksiksiz olamayaca\u011f\u0131n\u0131 g\u00f6stermi\u015f ve ayr\u0131ca aksiyomatik bir sistemin tutarl\u0131l\u0131\u011f\u0131n\u0131 sistemin kendi i\u00e7indeki ad\u0131mlarla kan\u0131tlaman\u0131n olanaks\u0131z oldu\u011funu ispatlam\u0131\u015ft\u0131r.(7)
\nG\u00f6del\u2019in eksiklik teoremleri matematikten felsefeye ve yapay zek\u00e2ya kadar bir\u00e7ok alanda \u00f6nemli sonu\u00e7lar do\u011furmu\u015ftur.<\/p>\n

KAYNAKLAR<\/strong>
\n1) http:\/\/pirate.shu.edu\/~kahlnath\/Top100.html
\n2) \u00d6klid\u2019in Elemanlar\u0131, \u00c7ev. Ali Sinan Sert\u00f6z, T\u00fcbitak Yay\u0131nlar\u0131,
\n3) 2019.http:\/\/jwilson.coe.uga.edu\/emt725\/References\/Dunham.pdf
\n4) https:\/\/bilimvegelecek.com.tr\/index.php\/2018\/1\/31\/matematiksel-duello\/
\n5) Carl Friedrich Gauss, Cebirin Temel Teoremi \u0130\u00e7in D\u00f6rt \u0130spat, Bo\u011fazi\u00e7i \u00dcniversitesi Yay\u0131nevi,\u00c7ev. G\u00fclnihal Y\u00fccel, 2015.
\n6) http:\/\/mat.msgsu.edu.tr\/~dpierce\/Dersler\/Kumeler-kurami\/2015\/kumeler-kurami-2016-02.pdf (S.107)
\n7) James R. Newman, Ernest Nagel, G\u00f6del Kan\u0131tlamas\u0131, Bo\u011fazi\u00e7i \u00dcniversitesi Yay\u0131nevi, 2008.
\n8) https:\/\/bilimvegelecek.com.tr\/index.php\/2018\/01\/01\/%e2%88%9a2-krizi\/<\/p>\n","protected":false},"excerpt":{"rendered":"

Matematikte do\u011frulu\u011fu kan\u0131tlanabilen \u00f6nermelere teorem deniliyor. Tarih boyunca matemati\u011fin in\u015fas\u0131 s\u00fcresince binlerce \u00f6nerme kan\u0131tland\u0131, kan\u0131tlan\u0131yor. En \u00f6nemli, en iz b\u0131rakan ve bir kilometre ta\u015f\u0131 olarak g\u00f6r\u00fclebilecek teoremler hangileridir? Bu soruyu matematikle u\u011fra\u015fan hemen herkes farkl\u0131 listeler yaparak yan\u0131tlayabilir. En iyi 100 film, en iyi 100 roman gibi matemati\u011fin en b\u00fcy\u00fck 100 teoreminin listesi matematik\u00e7iler Jack […]<\/p>\n","protected":false},"author":375,"featured_media":40479,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[5844,38,1,514,510],"tags":[4095,2279,5874],"class_list":["post-40474","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-193-sayi","category-dergi-sayilari","category-genel","category-matematik-sohbetleri","category-surekli-bolumler","tag-gauss","tag-godel","tag-matematigin-buyuk-teoremleri"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t