{"id":9226,"date":"2017-05-01T00:07:19","date_gmt":"2017-04-30T21:07:19","guid":{"rendered":"http:\/\/109.232.216.219\/~bilimvegelecek\/?p=9226"},"modified":"2018-02-08T16:30:34","modified_gmt":"2018-02-08T13:30:34","slug":"cetin-ceviz-bir-problem-asal-ikizler","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2017\/05\/01\/cetin-ceviz-bir-problem-asal-ikizler","title":{"rendered":"\u00c7etin ceviz bir problem: Asal ikizler"},"content":{"rendered":"

Matematikte antik \u00e7a\u011fdan kalma \u00e7\u00f6z\u00fclememi\u015f bir problemdir asal ikizler hipotezi<\/strong>.<\/em> Bir ortaokul \u00f6\u011frencisinin anlayabilece\u011fi basitlikteki bu \u00f6nermeyi ya da olumsuzunu \u015fimdiye kadar hi\u00e7 kimse kan\u0131tlayamad\u0131. Asallar aras\u0131na gizlenmi\u015f mucizev\u00ee bir\u00e7ok problemden en eskisi olan asal ikizler hipotezini \u015f\u00f6yle a\u00e7\u0131klayabiliriz: Sadece 1\u2019e ve kendisine b\u00f6l\u00fcnebilen pozitif tamsay\u0131lara asal say\u0131<\/strong> denildi\u011fini biliyoruz. 1, teknik nedenlerden dolay\u0131 asal say\u0131 kabul edilmez.<\/p>\n

Y\u00fczy\u0131llard\u0131r matematik\u00e7ileri u\u011fra\u015ft\u0131ran hipotezi ifade etmeden \u00f6nce ilk 16 asal say\u0131ya g\u00f6z atal\u0131m:<\/p>\n

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53.<\/p>\n

Yukar\u0131da baz\u0131 ard\u0131\u015f\u0131k asallar\u0131 koyu siyahla belirtmemizin nedeni aralar\u0131ndaki fark\u0131n \u00a0olmas\u0131. \u015eimdi, bu say\u0131lar\u0131 birer \u00e7ift olarak yazal\u0131m:<\/p>\n

(3- 5),(5-7),(11- 13),(17-19),(29-31),(41-43).<\/p>\n

Aralar\u0131nda 2 fark olan bu asal \u00e7iftlerin her birine asal ikizler<\/strong> denir. Yukar\u0131da da g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi ilk asal say\u0131 aras\u0131nda \u00a0asal ikiz var. \u0130lk \u00a0asal say\u0131 aras\u0131nda \u00a0asal ikizin oldu\u011funu biliyoruz, hatta \"\"\u00a0\u2019den k\u00fc\u00e7\u00fck asal say\u0131lar aras\u0131nda 808.675.888.557.436\u00a0kadar asal ikizin oldu\u011fu bilgisayarla hesaplanm\u0131\u015f durumda. Asal ikiz hipotezi, sonsuz say\u0131da asal ikiz oldu\u011funu iddia eder.<\/p>\n

Y\u00fczy\u0131llard\u0131r yan\u0131tlanamayan soru: Asal ikizler sonsuz say\u0131da m\u0131d\u0131r?<\/strong><\/p>\n

Sonsuz say\u0131da asal say\u0131 oldu\u011funun kan\u0131t\u0131 ilk olarak, yakla\u015f\u0131k 2300 y\u0131l \u00f6nce matematik d\u00fcnyas\u0131n\u0131n en g\u00fczellerinden biri olarak kabul edilen, \u00e7ok yal\u0131n ve \u00e7ok \u015f\u0131k bir \u015fekilde \u00d6klid taraf\u0131ndan yap\u0131lm\u0131\u015ft\u0131r. Ama yukar\u0131daki sorunun yan\u0131t\u0131 hen\u00fcz verilememi\u015ftir. Sezgilerimiz bize sonsuz say\u0131da asal ikiz oldu\u011funu s\u00f6yleyebilir, fakat matematik\u00e7iler i\u00e7in b\u00f6ylesi bir inanc\u0131n hi\u00e7bir de\u011feri yoktur, \u00e7\u00fcnk\u00fc matematik\u00e7iler inanmaz, kan\u0131tlar! Matematikte ikna de\u011fil, kan\u0131t vard\u0131r.<\/p>\n

Bilgisayarla 2016\u2019da yap\u0131lan hesaplamalarda 808.675.888.557.436\u00a0basamakl\u0131 en b\u00fcy\u00fck iki asaldan olu\u015fan asal ikizin<\/p>\n

\"\"<\/p>\n

oldu\u011funu biliyoruz ve bundan sonra daha b\u00fcy\u00fck asal ikizler bulunabilir, fakat sonras\u0131 i\u00e7in, yani sonsuz say\u0131da asal ikiz i\u00e7in bilgisayarlar bize hi\u00e7bir \u015fey s\u00f6yleyemez.<\/p>\n

Ceviz k\u0131r\u0131labilecek mi?<\/strong><\/p>\n

Matemati\u011fin prensi olarak g\u00f6r\u00fclen Carl Friedrich Gauss, say\u0131lar teorisini \u201cmatemati\u011fin krali\u00e7esi\u201d olarak kabul eder. Gauss gibi bir\u00e7ok matematik\u00e7i onca hayal k\u0131r\u0131kl\u0131\u011f\u0131na kar\u015f\u0131n say\u0131lar kuram\u0131n\u0131n esrarengiz dehlizlerinde dola\u015fmaktan kendilerini alamam\u0131\u015flard\u0131r. Asal ikizler hipotezi de y\u00fczy\u0131llar boyunca binlerce say\u0131 kuramc\u0131s\u0131n\u0131 u\u011fra\u015ft\u0131rm\u0131\u015f, ama kimse bu \u00e7etin cevizi k\u0131rmay\u0131 ba\u015faramam\u0131\u015ft\u0131r.<\/p>\n

\u00dcnl\u00fc Alman matematik\u00e7i Edmund Landau, 1912\u2019de Uluslararas\u0131 Matematik\u00e7iler Kongresi\u2019nde verdi\u011fi konferansta asal ikizler hipotezi konusunda kayda de\u011fer bir geli\u015fmenin olmad\u0131\u011f\u0131n\u0131 ve belki de yak\u0131n gelecekte de olamayaca\u011f\u0131n\u0131 belirtmi\u015ftir.<\/p>\n

Matematik\u00e7iler, yakla\u015f\u0131k y\u00fczy\u0131ld\u0131r problemin \u00e7\u00f6z\u00fcm\u00fcnde \u00e7ok \u00f6nemli bir a\u015fama olarak kabul edilen bir \u201caltlimit\u201d hesab\u0131yla u\u011fra\u015fm\u0131\u015ft\u0131r. Bu hesab\u0131 pop\u00fcler bir matematik yaz\u0131s\u0131nda a\u00e7\u0131klaman\u0131n zorlu\u011fu y\u00fcz\u00fcnden bu \u201caltlimit\u201d sonucunu \u2206\u00a0ile g\u00f6sterirsek, matematik\u00e7iler \u2206=0\u00a0sonucuna ula\u015fmaya \u00e7al\u0131\u015fm\u0131\u015flard\u0131r. 1940\u2019ta Paul Erd\u00f6s\u00a0\u2206<1, 1954\u2019te Ricci \u2206<15\/16, 1986\u2019da Maier \u2206<0,2484\u2026, 2004\u2019te Goldston ve Y\u0131ld\u0131r\u0131m \u2206<0,085786\u2026\u00a0ve sonunda Goldston, Pintz ve Y\u0131ld\u0131r\u0131m \u2206=0\u00a0oldu\u011funu g\u00f6stermi\u015ftir. Matematik d\u00fcnyas\u0131nda Goldston, Pintz ve Y\u0131ld\u0131r\u0131m\u2019\u0131n (GPY) \u00e7al\u0131\u015fmalar\u0131 asal ikizler hipotezinin kan\u0131tlanmas\u0131 yolunda bir kilometre ta\u015f\u0131 olarak kabul ediliyor. GPY, bu ba\u015far\u0131s\u0131yla matematikte en prestijli \u00f6d\u00fcllerden biri olan ve daha \u00f6nce Erd\u00f6s, Langlands, Wiles gibi bir\u00e7ok \u00fcnl\u00fc matematik\u00e7iye verilen Cole \u00d6d\u00fcl\u00fc\u2019n\u00fcn sahibi olmu\u015ftur.<\/p>\n

Yukar\u0131daki tarihlere dikkat edilirse \u2206<1\u2019in kan\u0131t\u0131ndan \u2206=0\u00a0kan\u0131t\u0131na kadar 60 y\u0131ldan fazla bir zaman ge\u00e7mi\u015ftir. Bu s\u00fcre, matematiksel ara\u015ft\u0131rman\u0131n ne denli me\u015fakkatli ve yo\u011fun \u00e7abalar sonunda adeta bir bayrak yar\u0131\u015f\u0131 gibi ortaya \u00e7\u0131kt\u0131\u011f\u0131n\u0131n \u00e7ok \u00e7arp\u0131c\u0131 bir \u00f6rne\u011fi olsa gerek. Matematiksel ara\u015ft\u0131rma, \u00f6yle bir anda gelen esin perisiyle ortaya \u00e7\u0131km\u0131yor!<\/p>\n

Goldston ve Y\u0131ld\u0131r\u0131m isimlerine dikkatinizi \u00e7ekmek isterim. Her ikisinin de asal ikizler hipoteziyle \u00e7eyrek as\u0131rdan fazla bir s\u00fcredir u\u011fra\u015ft\u0131klar\u0131n\u0131 biliyoruz. Halen Bo\u011fazi\u00e7i \u00dcniversitesi\u2019nde \u00f6\u011fretim \u00fcyesi olan Cem Yal\u00e7\u0131n Y\u0131ld\u0131r\u0131m, verdi\u011fi bir r\u00f6portajda asal ikizler problemiyle lise y\u0131llar\u0131nda tan\u0131\u015ft\u0131\u011f\u0131n\u0131 ve doktora sonras\u0131 bu problemle daha yo\u011fun u\u011fra\u015ft\u0131\u011f\u0131n\u0131 belirtiyor. Bir matematik\u00e7i i\u00e7in \u00e7eyrek as\u0131r boyunca azimle yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalar\u0131n ilk meyvesini alm\u0131\u015f olmas\u0131 b\u00fcy\u00fck bir mutluluk olsa gerek!<\/p>\n

2013\u2019te matematik d\u00fcnyas\u0131n\u0131 adeta \u015fok eden ilgin\u00e7 bir geli\u015fme ya\u015fan\u0131r. \u00c7in as\u0131ll\u0131 Amerikal\u0131 matematik\u00e7i Y. Zhang, ikiz asallar\u0131 de\u011fil ama aralar\u0131ndaki fark 70 milyon olan asal \u00e7iftlerin sonsuz say\u0131da oldu\u011funu kan\u0131tlar. Bu sonucun as\u0131l \u00e7arp\u0131c\u0131 yan\u0131 Zhang\u2019\u0131n y\u0131llarca i\u015f bulamayan, motel, lokanta gibi yerlerde \u00e7al\u0131\u015fmak zorunda kalm\u0131\u015f bir matematik\u00e7i olmas\u0131d\u0131r. Matematik \u00e7evrelerinden uzak, ara\u015ft\u0131rmalar\u0131n\u0131 izole bir \u015fekilde s\u00fcrd\u00fcren Zhang\u2019\u0131n b\u00f6ylesi \u00f6nemli bir makaleye imza atm\u0131\u015f olmas\u0131 matematik\u00e7iler aras\u0131nda \u015fa\u015fk\u0131nl\u0131k yaratm\u0131\u015ft\u0131r.<\/p>\n

GPY\u2019nin elde etti\u011fi ba\u015far\u0131 ve Zhang\u2019\u0131n ula\u015ft\u0131\u011f\u0131 sonu\u00e7la olu\u015fan heyecan sonras\u0131, tan\u0131nm\u0131\u015f matematik\u00e7i Terence Tao\u2019nun giri\u015fimiyle 70 milyon say\u0131s\u0131n\u0131 k\u00fc\u00e7\u00fclterek, m\u00fcmk\u00fcnse fark\u0131n 2 oldu\u011fu asal \u00e7iftlerin, yani asal ikizlerin sonsuz say\u0131da oldu\u011funu kan\u0131tlamak amac\u0131yla bir\u00e7ok matematik\u00e7inin kat\u0131ld\u0131\u011f\u0131 bir imece projesi ba\u015flat\u0131lm\u0131\u015ft\u0131r. Matematik\u00e7ilerin i\u015fbirli\u011fine ve bilgi payla\u015f\u0131m\u0131na a\u00e7\u0131k, internet \u00fczerinden y\u00fcr\u00fct\u00fclen bu \u00e7al\u0131\u015fmalar sayesinde fark, bilgisayar yard\u0131m\u0131yla \u00f6nce 4680\u2019e d\u00fc\u015f\u00fcr\u00fclm\u00fc\u015f ve sonras\u0131nda gen\u00e7 matematik\u00e7i James Maynard, Goldston ve Y\u0131ld\u0131r\u0131m\u2019\u0131n 2000\u2019lerin ba\u015f\u0131nda yay\u0131mlad\u0131klar\u0131 ve hatal\u0131 oldu\u011fu anla\u015f\u0131lan makalesinden yararlanarak fark\u0131 600\u2019e indirmi\u015ftir. Son olarak imece projesiyle fark\u0131n 252\u2019ye d\u00fc\u015ft\u00fc\u011f\u00fcn\u00fc ve farkl\u0131 hipotezler yard\u0131m\u0131yla fark\u0131n 12\u2019ye kadar indi\u011fini biliyoruz.<\/p>\n

B\u00fct\u00fcn bu geli\u015fmeler asal ikizler probleminin beyaz bayrak sallayaca\u011f\u0131 g\u00fcn\u00fcn \u00e7ok da uzak olmad\u0131\u011f\u0131n\u0131 g\u00f6steriyor, fakat belki de \u00e7\u00f6z\u00fcme birka\u00e7 y\u00fczy\u0131l sonra ula\u015f\u0131lacak. Ne var ki hi\u00e7 \u00f6nemli de\u011fil, \u00e7\u00fcnk\u00fc en b\u00fcy\u00fck zafer, matematik\u00e7ilerin sayg\u0131de\u011fer \u00e7abalar\u0131n\u0131n insan\u0131n insansalla\u015fmas\u0131na yapt\u0131\u011f\u0131 ola\u011fan\u00fcst\u00fc katk\u0131d\u0131r!<\/p>\n

Kaynaklar<\/strong><\/p>\n

– Terzio\u011flu, T, \u0130kiz Asallar San\u0131s\u0131 ve Cole \u00d6d\u00fcl\u00fc<\/em>, Matematik D\u00fcnyas\u0131, Say\u0131 98, 2014.
\n– Wikipedia
\n– Say, C, Bu yaz\u0131yla matemati\u011fi seveceksiniz<\/em>, Odatv.com.<\/p>\n","protected":false},"excerpt":{"rendered":"

Matematikte antik \u00e7a\u011fdan kalma \u00e7\u00f6z\u00fclememi\u015f bir problemdir asal ikizler hipotezi. Bir ortaokul \u00f6\u011frencisinin anlayabilece\u011fi basitlikteki bu \u00f6nermeyi ya da olumsuzunu \u015fimdiye kadar hi\u00e7 kimse kan\u0131tlayamad\u0131. Asallar aras\u0131na gizlenmi\u015f mucizev\u00ee bir\u00e7ok problemden en eskisi olan asal ikizler hipotezini \u015f\u00f6yle a\u00e7\u0131klayabiliriz: Sadece 1\u2019e ve kendisine b\u00f6l\u00fcnebilen pozitif tamsay\u0131lara asal say\u0131 denildi\u011fini biliyoruz. 1, teknik nedenlerden dolay\u0131 asal […]<\/p>\n","protected":false},"author":375,"featured_media":15081,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[516,25,514],"tags":[566,208],"class_list":["post-9226","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-159-sayi","category-matematik","category-matematik-sohbetleri","tag-asal-sayi","tag-matematik"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/9226","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/users\/375"}],"replies":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/comments?post=9226"}],"version-history":[{"count":0,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/9226\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/15081"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=9226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=9226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=9226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}