OpenAI, yakla\u015f\u0131k 90 y\u0131ld\u0131r \u00e7\u00f6z\u00fclememi\u015f olan Navier-Stokes varl\u0131k ve d\u00fczg\u00fcnl\u00fck problemini yapay zeka deste\u011fiyle \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc duyurdu. \u015eirket, hen\u00fcz kamuoyuna a\u00e7\u0131lmam\u0131\u015f yeni bir modelinin, yakla\u015f\u0131k 10 bin yapay zeka ajan\u0131n\u0131n koordineli \u00e7al\u0131\u015fmas\u0131yla problemin \u00e7\u00f6z\u00fcmlerinde sonlu zamanda tekillik olu\u015fabilece\u011fini g\u00f6steren bir kan\u0131t \u00fcretti\u011fini belirtti.<\/p>\n
Navier-Stokes denklemleri, su ve hava gibi ak\u0131\u015fkanlar\u0131n hareketlerinin matematiksel olarak tan\u0131mlanmas\u0131n\u0131 sa\u011flayan temel denklemlerdir. Problemin \u00f6z\u00fc ise, d\u00fczg\u00fcn ba\u015flang\u0131\u00e7 ko\u015fullar\u0131na sahip \u00fc\u00e7 boyutlu bir ak\u0131\u015f\u0131n her zaman d\u00fczg\u00fcn kal\u0131p kalmayaca\u011f\u0131d\u0131r; yani, belirli ko\u015fullar alt\u0131nda h\u0131zlar\u0131n s\u0131n\u0131rs\u0131z \u015fekilde b\u00fcy\u00fcyerek tekillik (sonsuz yo\u011funluk) olu\u015fturup olu\u015fturmayaca\u011f\u0131 sorgulanmaktad\u0131r. Bu sorun, 2000 y\u0131l\u0131nda Clay Matematik Enstit\u00fcs\u00fc taraf\u0131ndan \u2018\u2018Millennium Prize Problems\u2019\u2019 yani \u2018\u2018Bin Y\u0131l Problemleri\u2019\u2019 aras\u0131nda yer alm\u0131\u015f ve \u00e7\u00f6z\u00fcme ula\u015fanlara 1 milyon dolar \u00f6d\u00fcl vaat edilmi\u015ftir.<\/p>\n
OpenAI, 28 A\u011fustos\u2019ta matematik alan\u0131nda \u00f6nceki modellere k\u0131yasla \u00f6nemli bir geli\u015fme sa\u011flayan dahili bir modeli e\u011fitmeye ba\u015flad\u0131. 1 Eyl\u00fcl itibar\u0131yla, iki Millennium Prize Problem\u2019inin \u00e7\u00f6z\u00fclm\u00fc\u015f olabilece\u011fine dair s\u00f6ylentilerin ard\u0131ndan ekip, hen\u00fcz \u00e7\u00f6z\u00fclememi\u015f problemler \u00fczerinde \u00e7al\u0131\u015fmaya y\u00f6neldi. Sistem, ba\u015flang\u0131\u00e7ta yakla\u015f\u0131k 100 yapay zeka ajan\u0131yla Euler denklemleriyle ilgili daha basit bir probleme odakland\u0131 ve yakla\u015f\u0131k 50 saat i\u00e7inde ba\u015far\u0131l\u0131 oldu.<\/p>\n
Buradan elde edilen deneyimle OpenAI, kaynaklar\u0131n\u0131 Navier-Stokes problemine aktararak ajan say\u0131s\u0131n\u0131 yakla\u015f\u0131k 10 bine \u00e7\u0131kard\u0131. \u015eirket a\u00e7\u0131klamas\u0131na g\u00f6re Navier-Stokes probleminin \u00e7\u00f6z\u00fcm\u00fc i\u00e7in 88 saatlik bir \u00e7al\u0131\u015fma s\u00fcreci ya\u015fand\u0131. Bu s\u00fcre zarf\u0131nda yakla\u015f\u0131k 2,7 milyon mesaj al\u0131\u015fveri\u015fi yap\u0131ld\u0131 ve 130 milyar token \u00e7\u0131kt\u0131 \u00fcretildi. Kan\u0131t\u0131n do\u011frulu\u011funu teyit etmek amac\u0131yla Lean isimli bi\u00e7imsel do\u011frulama yaz\u0131l\u0131m\u0131 kullan\u0131ld\u0131 ve bu s\u00fcre\u00e7 GPT-6 Astra modeli ile desteklendi.<\/p>\n
OpenAI’n\u0131n sundu\u011fu geli\u015fme matematik camias\u0131nda b\u00fcy\u00fck ilgi uyand\u0131rd\u0131 ancak tart\u0131\u015fmalar da beraberinde geldi. New York \u00dcniversitesi \u00f6\u011fretim \u00fcyesi matematik profes\u00f6r\u00fc Tristan Buckmaster, OpenAI\u2019n\u0131n kendi ara\u015ft\u0131rma hatt\u0131ndaki \u00e7al\u0131\u015fmalar\u0131ndan faydalanm\u0131\u015f olabilece\u011fini belirtti. Buna kar\u015f\u0131n OpenAI, ortaya konan kan\u0131t\u0131n ba\u011f\u0131ms\u0131z olarak \u00fcretildi\u011fini ve tamamen yapay zeka tabanl\u0131 bir y\u00f6ntemle geli\u015ftirildi\u011fini savunuyor.<\/p>\n
Bu durum, matematik d\u00fcnyas\u0131nda sadece \u00fcretilen kan\u0131t\u0131n do\u011frulu\u011funu de\u011fil ayn\u0131 zamanda OpenAI\u2019n\u0131n bu sonuca nas\u0131l ula\u015ft\u0131\u011f\u0131n\u0131 da ayr\u0131nt\u0131l\u0131 \u015fekilde inceleme zorunlulu\u011funu do\u011furdu. Sonu\u00e7 ne olursa olsun, OpenAI\u2019n\u0131n yapay zekan\u0131n matematiksel problemlere uygulanabilirli\u011fine dair \u00f6nemli bir \u00f6rnek ortaya koydu\u011fu kesin.<\/p>\n
OpenAI, uzun s\u00fcredir \u00e7\u00f6z\u00fclemeyen Navier-Stokes varl\u0131k ve d\u00fczg\u00fcnl\u00fck problemine ili\u015fkin \u00f6nemli bir ad\u0131m att\u0131\u011f\u0131n\u0131 a\u00e7\u0131klad\u0131. Ancak matematik toplulu\u011fu h\u00e2l\u00e2 bu sonucun \u00f6zg\u00fcnl\u00fc\u011f\u00fc ve do\u011frulu\u011fu \u00fczerinde titizlikle \u00e7al\u0131\u015f\u0131yor. Yapay zeka destekli bu yeni y\u00f6ntem, matemati\u011fin en zor problemlerinin \u00e7\u00f6z\u00fcm\u00fcnde yeni ufuklar a\u00e7abilir. OpenAI\u2019n\u0131n yakla\u015f\u0131m\u0131, teknolojinin ve matemati\u011fin kesi\u015fiminde heyecan verici bir d\u00f6nemin habercisi olabilir.<\/p>\n