Say\u0131lar teorisi \u00fczerine yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalarla tan\u0131nan Christian Goldbach\u2019\u0131n, \u00fcnl\u00fc \u0130svi\u00e7re\u2019li matematik\u00e7i Leonhard Euler\u2019le d\u00fczenli olarak mektupla\u015ft\u0131\u011f\u0131 bilinmektedir. Goldbach, 1742\u2019de g\u00f6nderdi\u011fi mektuplar\u0131n birinde \u015f\u00f6yle bir \u00f6nermeden s\u00f6z eder: 2\u2019den b\u00fcy\u00fck her tamsay\u0131 3 asal say\u0131n\u0131n toplam\u0131 olarak yaz\u0131labilir. Goldbcah, (1 say\u0131s\u0131n\u0131 asal say\u0131 kabul ederek!), 3=1+1+1, 4=2+1+1 gibi pek \u00e7ok tamsay\u0131y\u0131 inceledi\u011fini, hepsinde de b\u00f6ylesi e\u015fitliklerin yaz\u0131labildi\u011fini ifade ederek Euler\u2019e bu varsay\u0131m\u0131n\u0131n kan\u0131tlan\u0131p kan\u0131tlanmayaca\u011f\u0131n\u0131 sorar. \u201cCanl\u0131 analiz\u201d olarak bilinen b\u00fcy\u00fck matematik\u00e7i Euler, cevaben g\u00f6nderdi\u011fi mektupta bu \u00f6nermenin do\u011frulu\u011funu kan\u0131tlayamad\u0131\u011f\u0131n\u0131 belirtir, ama ona e\u015fde\u011fer daha g\u00fc\u00e7l\u00fc bir varsay\u0131mda bulunur: 2\u2019den b\u00fcy\u00fck her \u00e7ift tamsay\u0131, iki asal say\u0131n\u0131n toplam\u0131 olarak yaz\u0131labilir. \u00d6rne\u011fin 4=2+2, 6=3+3, 8=5+3, 10=3+7=5+5 gibi. Euler mektuba ayr\u0131ca, ifade etti\u011fi \u00f6nermenin do\u011fru oldu\u011funa inand\u0131\u011f\u0131n\u0131 ama kan\u0131tlayamad\u0131\u011f\u0131n\u0131 da yazar.<\/p>\n
Matematik tarihine Goldbach Hipotezi olarak ge\u00e7en, asl\u0131nda Euler\u2019in ifade etti\u011fi bu \u00f6nerme 300 y\u0131l\u0131 a\u015fk\u0131n bir s\u00fcredir kan\u0131tlanmay\u0131 bekliyor. Her say\u0131 i\u00e7in do\u011fru oldu\u011fu bilinmiyor, ama do\u011fru oldu\u011fu san\u0131l\u0131yor. \u00d6te yandan bilgisayarla yap\u0131lan testlerle, hipotezin\u00a01018<\/sup> say\u0131s\u0131na kadar b\u00fct\u00fcn \u00e7ift tamsay\u0131lar i\u00e7in do\u011frulu\u011fu g\u00f6sterilmi\u015f, ama bu sonucun matematiksel kan\u0131t i\u00e7in hi\u00e7bir de\u011feri yok tabii ki.<\/p>\n Hipotezi kan\u0131tlaman\u0131z halinde ad\u0131n\u0131z\u0131n matematik tarihine alt\u0131n harflerle yaz\u0131laca\u011f\u0131ndan, \u00f6l\u00fcms\u00fczler aras\u0131nda yer alaca\u011f\u0131n\u0131zdan emin olabilirsiniz. Belki de \u201cKan\u0131tlansa ne olur, kan\u0131tlanmasa ne olur, \u00f6l\u00fcms\u00fczl\u00fck m\u00fcmk\u00fcn de\u011fil ki.\u201d diyenlerimiz olabilir. Bak\u0131n, \u00fcnl\u00fc \u0130ngiliz matematik\u00e7i Hardy bu g\u00f6r\u00fc\u015fe nas\u0131l itiraz ediyor: \u201c\u00d6l\u00fcms\u00fczl\u00fck\u201d aptalca bir s\u00f6zc\u00fck belki, ama ne anlam gelirse gelsin, herhalde \u00f6l\u00fcms\u00fcz olma \u015fans\u0131na en \u00e7ok bir matematik\u00e7i sahiptir.<\/p>\n Bir matematik\u00e7i i\u00e7in a\u00e7\u0131klanabilir bir d\u00fcnyada a\u00e7\u0131klanmayandan daha de\u011ferli bir \u015fey yoktur san\u0131r\u0131m. Ger\u00e7e\u011fi ke\u015ffetme tutkusu! Ve elbette \u015fan ve en son maddi kazan\u00e7\u2026 Ayr\u0131ca \u015funu da belirtmek gerekir ki; matematik tarihi, matematiksel kan\u0131tlar\u0131n, matemati\u011fin di\u011fer alanlar\u0131na ve bilime derin etkilerinin oldu\u011fu \u00f6rneklerle doludur.<\/p>\n Matematiksel evrenin yap\u0131 ta\u015flar\u0131 olan, y\u00fczy\u0131llard\u0131r matematik\u00e7ilere k\u00f6k s\u00f6kt\u00fcren asallar esrarengiz say\u0131lard\u0131r. \u00c7ok kolay tan\u0131mlan\u0131rlar ama \u00e7ok s\u0131ra d\u0131\u015f\u0131 davran\u0131rlar. Goldbach Hipotezi de ilk bak\u0131\u015fta kolay g\u00f6r\u00fcnen ama Say\u0131lar Kuram\u0131\u2019n\u0131n en zor problemlerinden biridir. Hardy, Goldbach Hipotezi\u2019ndeki zor olan\u0131n kolay g\u00f6r\u00fcn\u00fcyor olmas\u0131n\u0131 \u015f\u00f6yle anlat\u0131r: \u201cKan\u0131tlanamayan ve herhangi bir aptal\u0131n tahmin edebilece\u011fi Goldbach Hipotezi gibi ak\u0131ll\u0131 tahminler yapmak olduk\u00e7a kolayd\u0131r\u201d.<\/p>\n \u00dcnl\u00fc yay\u0131nevi Faber&Faber, Goldbach Hipotezi\u2019ni 20 Mart 2000 ile 20 Mart 2002 tarihleri aras\u0131nda kan\u0131tlayan ki\u015fiye 1 milyon dolar \u00f6d\u00fcl verece\u011fini a\u00e7\u0131klar, ama \u00f6d\u00fcl\u00fc hak eden \u00e7\u0131kmaz.<\/p>\n Euler sonras\u0131 hipotezin kan\u0131t\u0131 i\u00e7in u\u011fra\u015f verenler aras\u0131nda Hardy, Littlewood, Ramanujan gibi bir\u00e7ok \u00fcnl\u00fc matematik\u00e7inin oldu\u011fu bilinmektedir. \u00d6te yandan \u00e7o\u011fu matematik\u00e7i asal say\u0131larla ilgili as\u0131l \u00f6nemli problemin Riemann Hipotezi (Ge\u00e7en say\u0131daki yaz\u0131m\u0131zda ele alm\u0131\u015ft\u0131k.) oldu\u011fu kan\u0131s\u0131ndad\u0131r, \u00e7\u00fcnk\u00fc Riemann Hipotezinin Goldbach Hipotezine g\u00f6re sonu\u00e7lar\u0131 bak\u0131m\u0131ndan \u00e7ok daha etkili olaca\u011f\u0131 d\u00fc\u015f\u00fcn\u00fclmektedir.<\/p>\n 1941\u2019de Rus matematik\u00e7i Vingradov, Goldbach Hipotezinin kan\u0131t\u0131 y\u00f6n\u00fcnde baz\u0131 k\u0131smi ad\u0131mlar atm\u0131\u015f oldu\u011fu i\u00e7in Stalin taraf\u0131ndan 100.000 Rubleyle \u00f6d\u00fcllendirilir.<\/p>\n Hipoteze y\u00f6nelik en yak\u0131n sonu\u00e7 1973\u2019te \u00c7inli matematik\u00e7i Chen Jingrun taraf\u0131ndan ke\u015ffedilir. Chen, yeterince b\u00fcy\u00fck her \u00e7ift say\u0131n\u0131n bir asal ve bir de en \u00e7ok iki asal \u00e7arpan\u0131 olan bir say\u0131n\u0131n toplam\u0131 olarak ifade edilebilece\u011fini kan\u0131tlar. 1951\u2019de Rus matematik\u00e7i Linnik, her yeterince \u00e7ift say\u0131n\u0131n, iki asl\u0131n ve 2\u2019nin K\u2019inci kuvvetinin toplam\u0131 olacak \u015fekilde bir K say\u0131s\u0131n\u0131n var oldu\u011funu kan\u0131tlan\u0131r. 2002\u2019de bu sonucun ?=13, 2003\u2019te de ?=8 i\u00e7in ge\u00e7erli oldu\u011fu g\u00f6sterilir.<\/p>\n Matematikte pek \u00e7ok \u00fcnl\u00fc problemde oldu\u011fu gibi Goldbach Hipotezi i\u00e7in de bir tak\u0131m kan\u0131tlar ortaya at\u0131lm\u0131\u015f, ama g\u00fcn\u00fcm\u00fcze dek bunlardan hi\u00e7biri matematik toplulu\u011fu taraf\u0131ndan onaylanmam\u0131\u015ft\u0131r.<\/p>\n 1931\u2019de G\u00f6del, matemati\u011fin temellerini sarsan \u201ceksiklik teoremleriyle\u201d hangi \u00f6nermenin kan\u0131tlanabilir, hangilerinin kan\u0131tlanamaz oldu\u011funu \u00f6nsel olarak belirlemenin m\u00fcmk\u00fcn olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir. Bu karar verilemezlik ilkesi Goldbach Hipotezi i\u00e7in de ge\u00e7erli olabilir, yani belki bu \u00f6nerme hi\u00e7bir zaman kan\u0131tlanamayacakt\u0131r; fakat bu g\u00f6r\u00fc\u015f\u00fcn say\u0131 kuramc\u0131lar\u0131 aras\u0131nda pek taraftar\u0131 yoktur. Her ne olursa olsun, bu hipotezi ister kan\u0131tlanabilir, ister kan\u0131tlanamaz bir \u00f6nerme olarak kabul edelim, kan\u0131t u\u011frunda yap\u0131lan \u00e7al\u0131\u015fmalar bir\u00e7ok yeni matematiksel kuram\u0131n ortaya \u00e7\u0131kmas\u0131na neden oldu\u011fundan, sonu\u00e7ta matematik ve dolay\u0131s\u0131yla insanl\u0131k kazan\u0131yor!<\/p>\n","protected":false},"excerpt":{"rendered":" Say\u0131lar teorisi \u00fczerine yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalarla tan\u0131nan Christian Goldbach\u2019\u0131n, \u00fcnl\u00fc \u0130svi\u00e7re\u2019li matematik\u00e7i Leonhard Euler\u2019le d\u00fczenli olarak mektupla\u015ft\u0131\u011f\u0131 bilinmektedir. Goldbach, 1742\u2019de g\u00f6nderdi\u011fi mektuplar\u0131n birinde \u015f\u00f6yle bir \u00f6nermeden s\u00f6z eder: 2\u2019den b\u00fcy\u00fck her tamsay\u0131 3 asal say\u0131n\u0131n toplam\u0131 olarak yaz\u0131labilir. Goldbcah, (1 say\u0131s\u0131n\u0131 asal say\u0131 kabul ederek!), 3=1+1+1, 4=2+1+1 gibi pek \u00e7ok tamsay\u0131y\u0131 inceledi\u011fini, hepsinde de b\u00f6ylesi e\u015fitliklerin […]<\/p>\n","protected":false},"author":375,"featured_media":13622,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[195,25,514],"tags":[208,1008,1503],"class_list":["post-13621","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-158-sayi","category-matematik","category-matematik-sohbetleri","tag-matematik","tag-matematik-sohbetleri","tag-sayi-teorisi"],"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