{"id":68467,"date":"2026-06-04T00:00:29","date_gmt":"2026-06-03T21:00:29","guid":{"rendered":"https:\/\/bilimvegelecek.com.tr\/?p=68467"},"modified":"2026-06-03T21:05:06","modified_gmt":"2026-06-03T18:05:06","slug":"yanlis-da-matematige-dahil","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2026\/06\/04\/yanlis-da-matematige-dahil","title":{"rendered":"Yanl\u0131\u015f da matemati\u011fe dahil!"},"content":{"rendered":"

Ali T\u00f6r\u00fcn<\/strong><\/p>\n

SAT, \u00fcniversitelere kabul i\u00e7in yayg\u0131n olarak kullan\u0131lan ve uluslararas\u0131 ge\u00e7erlili\u011fi olan Amerika Birle\u015fik Devletleri merkezli bir test s\u0131nav\u0131d\u0131r.<\/p>\n

1982 SAT\u2019de sorulan yanl\u0131\u015f bir matematik sorusu SAT\u2019ye k\u00f6t\u00fc bir \u015f\u00f6hret kazand\u0131rmakla kalmay\u0131p 300.000 \u00f6\u011frencinin s\u0131nav sonu\u00e7lar\u0131n\u0131n yeniden de\u011ferlendirilmesine yol a\u00e7ar:<\/p>\n

\u201cA \u00e7emberinin yar\u0131\u00e7ap\u0131, B \u00e7emberinin yar\u0131\u00e7ap\u0131n\u0131n 1\/3’\u00fcd\u00fcr. A \u00e7emberi, ba\u015flang\u0131\u00e7 \u200b\u200bkonumuna d\u00f6nene kadar B \u00e7emberi etraf\u0131nda d\u00f6n\u00fcyor. A \u00e7emberi toplamda ka\u00e7 devir yapm\u0131\u015ft\u0131r?\u201d<\/p>\n

\"\"<\/p>\n

SAT\u2019de d\u00f6rt yanl\u0131\u015f bir do\u011fruyu g\u00f6t\u00fcrmedi\u011finden bo\u015f b\u0131rakan olmaz ve bu s\u0131nava giren herkes bu soruyu yanl\u0131\u015f cevaplar; \u00e7\u00fcnk\u00fc se\u00e7eneklerde do\u011fru cevap yoktur!<\/p>\n

Sorunun do\u011fru cevab\u0131n\u0131n se\u00e7eneklerde olmad\u0131\u011f\u0131 s\u0131nav sonras\u0131nda \u00fc\u00e7 \u00f6\u011frencinin itiraz\u0131 \u00fczerine anla\u015f\u0131l\u0131r ve soru t\u00fcm s\u0131nav kat\u0131l\u0131mc\u0131lar\u0131 i\u00e7in iptal edilir.<\/p>\n

Soruyu haz\u0131rlayanlar, k\u00fc\u00e7\u00fck \u00e7emberin b\u00fcy\u00fck \u00e7emberin \u00e7evre uzunlu\u011fu kadar bir yol kat edece\u011fini d\u00fc\u015f\u00fcnerek cevab\u0131 3 a\u00e7arak yan\u0131lm\u0131\u015flard\u0131r.<\/p>\n

E\u011fer k\u00fc\u00e7\u00fck \u00e7ember, d\u00fcz bir yol boyunca b\u00fcy\u00fck \u00e7emberin \u00e7evresi kadar bir mesafeyi d\u00f6nerek kat etmi\u015f olsayd\u0131 bu sonu\u00e7 do\u011fruydu. (A\u015fa\u011f\u0131daki \u015fekilde 1. durum)<\/p>\n

Ama k\u00fc\u00e7\u00fck \u00e7ember b\u00fcy\u00fck \u00e7emberin \u00e7evresi etraf\u0131nda d\u00f6nd\u00fc\u011f\u00fcnde durum de\u011fi\u015fiyor ve 1 tur daha eklenerek sonu\u00e7 4 oluyor. (A\u015fa\u011f\u0131daki \u015fekilde 2. durum)<\/p>\n

\"\"<\/p>\n

Bu bir tur fazlal\u0131\u011f\u0131 g\u00f6rmenin en kolay yolu k\u00fc\u00e7\u00fck \u00e7emberin ba\u015flang\u0131\u00e7 konumuna gelebilmesi i\u00e7in merkezinin ald\u0131\u011f\u0131 yolu g\u00f6zlemlemektir; \u00e7\u00fcnk\u00fc k\u00fc\u00e7\u00fck \u00e7emberin ba\u015flang\u0131\u00e7 noktas\u0131na gelebilmesi i\u00e7in a\u015fa\u011f\u0131daki \u015fekilde g\u00f6r\u00fclen \u00fc\u00e7 nokta (k\u00fc\u00e7\u00fck ve b\u00fcy\u00fck \u00e7emberin merkezleri ve de\u011fme noktas\u0131) do\u011frusal olmal\u0131d\u0131r.<\/p>\n

\"\"<\/p>\n

Bu durumda k\u00fc\u00e7\u00fck \u00e7emberin merkezi yar\u0131\u00e7ap\u0131 4 birim olan bir \u00e7ember \u00fczerinde dola\u015farak ba\u015flang\u0131\u00e7 noktas\u0131na gelir ve dolay\u0131s\u0131yla 4 tur atam\u0131\u015f olur.<\/p>\n

1982 SAT\u2019nin haz\u0131rlayanlar\u0131n\u0131 da yan\u0131ltan bu soru, sezgisel yakla\u015f\u0131mla matematiksel d\u00fc\u015f\u00fcnme aras\u0131ndaki farka i\u015faret eden ve matematiksel ak\u0131l y\u00fcr\u00fctmenin zarif, bazen de sezgisel olmayan do\u011fas\u0131n\u0131 ortaya koyan g\u00fczel bir \u00f6rnek. Belki de bu y\u00fczden yaz\u0131n\u0131n ba\u015fl\u0131\u011f\u0131n\u0131 tekrarlamak gerekir: Yanl\u0131\u015f da matemati\u011fe dahil!<\/p>\n

Be\u015fer \u015fa\u015far ustalar da \u015fa\u015far.<\/p>\n

Matematik tarihine g\u00f6z att\u0131\u011f\u0131m\u0131zda bir\u00e7ok b\u00fcy\u00fck matematik\u00e7inin \u201ciyi hatalar\u0131yla\u201d kar\u015f\u0131la\u015f\u0131r\u0131z. \u0130yi hatalar yeni fikirlerin \u00fcretilmesine, yeni matematik alanlar\u0131n\u0131n do\u011fmas\u0131na yol a\u00e7m\u0131\u015ft\u0131r. Bu iyi hatalar\u0131n \u00fc\u00e7\u00fcn\u00fcn hikayesi a\u015fa\u011f\u0131daki gibidir.<\/p>\n

\u00a0<\/strong>Bu durumda k\u00fc\u00e7\u00fck \u00e7emberin merkezi yar\u0131\u00e7ap\u0131 4 birim olan bir \u00e7ember \u00fczerinde dola\u015farak ba\u015flang\u0131\u00e7 noktas\u0131na gelir ve dolay\u0131s\u0131yla 4 tur atam\u0131\u015f olur.<\/p>\n

1982 SAT\u2019nin haz\u0131rlayanlar\u0131n\u0131 da yan\u0131ltan bu soru, sezgisel yakla\u015f\u0131mla matematiksel d\u00fc\u015f\u00fcnme aras\u0131ndaki farka i\u015faret eden ve matematiksel ak\u0131l y\u00fcr\u00fctmenin zarif, bazen de sezgisel olmayan do\u011fas\u0131n\u0131 ortaya koyan g\u00fczel bir \u00f6rnek. Belki de bu y\u00fczden yaz\u0131n\u0131n ba\u015fl\u0131\u011f\u0131n\u0131 tekrarlamak gerekir: Yanl\u0131\u015f da matemati\u011fe dahil!<\/p>\n

Be\u015fer \u015fa\u015far ustalar da \u015fa\u015far.<\/p>\n

Matematik tarihine g\u00f6z att\u0131\u011f\u0131m\u0131zda bir\u00e7ok b\u00fcy\u00fck matematik\u00e7inin \u201ciyi hatalar\u0131yla\u201d kar\u015f\u0131la\u015f\u0131r\u0131z. \u0130yi hatalar yeni fikirlerin \u00fcretilmesine, yeni matematik alanlar\u0131n\u0131n do\u011fmas\u0131na yol a\u00e7m\u0131\u015ft\u0131r. Bu iyi hatalar\u0131n \u00fc\u00e7\u00fcn\u00fcn hikayesi a\u015fa\u011f\u0131daki gibidir.<\/p>\n

Poincare makalesini \u00e7ekiyor, \u00f6d\u00fclden vaz ge\u00e7iyor
\n<\/em><\/strong>19. y\u00fczy\u0131l\u0131n b\u00fcy\u00fck Frans\u0131z matematik\u00e7isi Henri Poincare\u2019nin \u201c\u00dc\u00e7 cisim problemi ve dinamik denklemler\u201d isimli makalesindeki hatan\u0131n ortaya \u00e7\u0131k\u0131\u015f\u0131 ve sonras\u0131 \u00e7ok ilgin\u00e7tir.<\/p>\n

\u0130sve\u00e7 ve Norve\u00e7\u2019i y\u00f6neten kral II. Oscar 1888\u2019de astrofizik ve matematik dallar\u0131na ait kendi ad\u0131yla an\u0131lan bir \u00f6d\u00fcl koyar. Weierstrass ve Hermite gibi \u00fcnl\u00fc matematik\u00e7iler taraf\u0131ndan haz\u0131rlanm\u0131\u015f d\u00f6rt problemden herhangi birini \u00e7\u00f6zen \u00f6d\u00fcl\u00fcn sahibi olacakt\u0131r.<\/p>\n

Bu sorulardan ilki g\u00fcne\u015f sistemiyle ilgilidir ve kabaca \u015f\u00f6yle ifade edilebilir: G\u00fcne\u015f sistemi Newton fizi\u011fi yasalar\u0131yla a\u00e7\u0131kland\u0131\u011f\u0131 \u00fczere sonsuza dek d\u00fczenli olarak i\u015fleyebilecek mi, yoksa bir gezegen g\u00fcne\u015fe veya ba\u015fka bir gezegene \u00e7arpabilir mi? Ba\u015fka bir deyi\u015fle, ba\u015flang\u0131\u00e7ta gezegenlerin k\u00fctle, yer, h\u0131z, zaman ve hareket y\u00f6nlerini biliyor olmam\u0131z onlar\u0131n \u201csonsuza dek\u201d nas\u0131l hareket edeceklerini belirlememizi sa\u011flar m\u0131?<\/p>\n

Poincar\u00e9, haz\u0131rlad\u0131\u011f\u0131 makaledeki g\u00f6r\u00fc\u015f ve d\u00fc\u015f\u00fcnceleriyle bu soruyu k\u0131smen yan\u0131tlayarak 1890\u2019da \u00f6d\u00fcl\u00fcn sahibi olur. J\u00fcri ba\u015fkan\u0131 Weierstrass, Poincar\u00e9\u2019nin \u00e7al\u0131\u015fmas\u0131 hakk\u0131ndaki g\u00f6r\u00fc\u015flerini \u00f6d\u00fcl organizasyonunu yapan Mittag-Leffler\u2019e \u015fu c\u00fcmlelerle bildirir: \u201cKral\u0131n\u0131za, asl\u0131nda bu \u00e7al\u0131\u015fman\u0131n \u00f6ne s\u00fcr\u00fclen soruya tam bir \u00e7\u00f6z\u00fcm getirmi\u015f oldu\u011funun kabul edilemeyece\u011fini, ancak yine de yay\u0131mlanmas\u0131 halinde g\u00f6k mekani\u011finde yeni bir d\u00f6nem ba\u015flatacak kadar \u00f6nemli bir \u00e7al\u0131\u015fma oldu\u011funu s\u00f6yleyebilirsiniz.\u201d<\/p>\n

Poincar\u00e9\u2019nin makalesi g\u00f6k cisimlerinin hareketlerinin d\u00fczenli ve belirlenebilir oldu\u011funu g\u00f6steriyordur ama Poincare, g\u00fcn\u00fcm\u00fczde kelebek etkisi<\/strong> olarak bilinen, ba\u015flang\u0131\u00e7 ko\u015fullar\u0131na duyarl\u0131 ba\u011f\u0131ml\u0131l\u0131k<\/strong> kavram\u0131n\u0131 g\u00f6z ard\u0131 etti\u011finin fark\u0131nda de\u011fildir.<\/p>\n

Baz\u0131 g\u00f6kbilimciler makaledeki bu a\u00e7\u0131k \u00fczerine itiraz ederler ve bir s\u00fcre sonra Poincar\u00e9 hatal\u0131 oldu\u011funu kabul eder, yapt\u0131\u011f\u0131 hatan\u0131n \u00e7al\u0131\u015fmas\u0131n\u0131n t\u00fcm\u00fcn\u00fc \u00e7\u00fcr\u00fctt\u00fc\u011f\u00fcn\u00fc anlar. \u00d6te yandan, 2500 Kronluk \u00f6d\u00fclle birlikte alt\u0131n madalyay\u0131 alm\u0131\u015ft\u0131r ve makale enstit\u00fcn\u00fcn b\u00fclteninde \u00e7oktan yay\u0131mlanm\u0131\u015ft\u0131r.<\/p>\n

B\u00fclten toplat\u0131l\u0131r, Poincar\u00e9 bir y\u0131l sonra yeni bir \u00e7al\u0131\u015fmayla bu kez tam tersine, zaman i\u00e7inde gezegenlerin hareketlerinin g\u00fcvenilir bir \u015fekilde tahmin edilemeyece\u011fini, \u00e7\u00fcnk\u00fc ba\u015flang\u0131\u00e7 de\u011ferlerinin sonsuz bir do\u011fruluk derecesiyle bilmenin m\u00fcmk\u00fcn olamayaca\u011f\u0131n\u0131 savunur. Sonras\u0131nda ilgin\u00e7 bir sonu\u00e7 ortaya \u00e7\u0131kar; \u00e7\u00fcnk\u00fc Poincar\u00e9\u2019nin bu son \u00e7al\u0131\u015fmas\u0131 g\u00fcn\u00fcm\u00fczde kaos teorisi<\/strong> olarak bilinen kuram\u0131n temellerini olu\u015fturmu\u015ftur.<\/p>\n

Bu olayda Poincar\u00e9\u2019nin bilimsel bak\u0131mdan ya\u015fad\u0131\u011f\u0131 hayal k\u0131r\u0131kl\u0131\u011f\u0131n\u0131n maddi sonu\u00e7lar\u0131 da olmu\u015ftur. Enstit\u00fc, Poincar\u00e9\u2019den toplat\u0131l\u0131p imha edilen hatal\u0131 versiyonun bask\u0131 giderlerinin kar\u015f\u0131l\u0131\u011f\u0131 olarak 3500 Kron talep eder. B\u00f6ylece Poincar\u00e9, ald\u0131\u011f\u0131 2500 Kronluk \u00f6d\u00fclden 1000 Kron daha fazlas\u0131n\u0131 \u00f6deyerek kaos teorisinin \u00f6nc\u00fcleri aras\u0131nda yer al\u0131r.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><\/em><\/p>\n

Euler\u2019in yan\u0131lg\u0131s\u0131 ve say\u0131lar teorisi
\n<\/strong><\/em>Matematik tarihinin en \u00fcretken matematik\u00e7isi ve bir matematik dehas\u0131 olan Leonhard Euler\u2019in say\u0131lar teorisi, sonsuz seriler, limit gibi kavramlar\u0131 kullan\u0131rken yapt\u0131\u011f\u0131 hatalar g\u00fcn\u00fcm\u00fcz matematik\u00e7ilerine sa\u00e7 ba\u015f yolduracak niteliktedir.<\/em><\/p>\n

Euler, 1769\u2019da bilinen en \u00fcnl\u00fc teoremlerden biri olan Fermat\u2019n\u0131n Son Teoremi\u2019nin bir genellemesi olarak, n>2\u00a0<\/em><\/p>\n

a^n+b^n+c^n=d^n<\/p>\n

e\u015fitli\u011fini sa\u011flayan <\/span>a, b, c, d <\/span>pozitif tamsay\u0131lar\u0131n\u0131n bulunamayaca\u011f\u0131n\u0131 \u00f6ne s\u00fcrer ve \u00f6zellikle <\/span>n <\/span>= 4 i\u00e7in bu denklemin <\/span>\u00e7\u00f6z\u00fcm\u00fcn\u00fcn olamayaca\u011f\u0131n\u0131 ifade eder. <\/span>Bu san\u0131 200 y\u0131l\u0131 a\u015fk\u0131n bir s\u00fcre ge\u00e7erlili\u011fini korur ama <\/span>1988\u2019de Amerikal\u0131 matematik\u00e7i Noam Elkies d\u00f6rd\u00fcnc\u00fc <\/span>kuvvetler i\u00e7in Euler\u2019in varsay\u0131m\u0131na uymayan bir kar\u015f\u0131 \u00f6rnek bulur:<\/span><\/p>\n

2682440<\/span>4^4<\/span>+15365639<\/span>4^4<\/span>+18796760<\/span>4^4 <\/span>= 20615673<\/span>4^4<\/span>.<\/span><\/p>\n

Elkies, yukar\u0131daki say\u0131lar\u0131n denklemi sa\u011flayan en k\u00fc\u00e7\u00fck de\u011ferler oldu\u011funu g\u00f6stermekle birlikte sonsuz say\u0131da kar\u015f\u0131 \u00f6rnek \u00fcretmenin y\u00f6ntemini de yay\u0131mlar.<\/em><\/p>\n

Euler\u2019in bu yan\u0131lg\u0131s\u0131 say\u0131lar teorisinde<\/strong> bir\u00e7ok ara\u015ft\u0131rman\u0131n \u00f6n\u00fcn\u00fc a\u00e7arak g\u00fcn\u00fcm\u00fcz matematik\u00e7ilerinin bu alanda ara\u015ft\u0131rma yapmas\u0131na olanak sa\u011flam\u0131\u015ft\u0131r.<\/em><\/p>\n

Frege\u2019yi y\u0131kan hata ve entelekt\u00fcel d\u00fcr\u00fcstl\u00fck<\/strong>
\n<\/strong><\/em>Analitik felsefenin ve \u00e7a\u011fda\u015f dil felsefesinin kurucular\u0131 aras\u0131nda yer alan Alman as\u0131ll\u0131 matematik\u00e7i ve mant\u0131k\u00e7\u0131 Gottlob Frege, 1893\u2019te \u00fcnl\u00fc Aritmeti\u011fin Temelleri<\/em> adl\u0131 yap\u0131t\u0131n\u0131n birinci cildini yay\u0131mlar. Bu \u00e7al\u0131\u015fmas\u0131yla aritmeti\u011fin temelleri \u00fczerine bir mant\u0131k sistemi geli\u015ftiren Frege bekledi\u011fi ilgiyi g\u00f6remez.<\/p>\n

Aritmeti\u011fin Temelleri<\/em>\u2019nin ilk cildinin yay\u0131mlanmas\u0131ndan dokuz y\u0131l sonra ikinci cildini tamamlar, bask\u0131ya g\u00f6nderir.<\/p>\n

Birka\u00e7 g\u00fcn sonra Bertrand Russell\u2019dan bir mektup al\u0131r. Russell, mektubunda Aritmeti\u011fin Temelleri<\/em>\u2019ni okudu\u011funu, \u00e7ok be\u011fendi\u011fini ve \u00e7ok yararland\u0131\u011f\u0131n\u0131 \u00f6vg\u00fc dolu c\u00fcmlelerle anlatarak ikinci cildin yay\u0131mlanmas\u0131n\u0131 sab\u0131rs\u0131zl\u0131kla bekledi\u011fini belirtir. Sonras\u0131nda da ke\u015ffetti\u011fi bir paradokstan (Russell paradoksu) s\u00f6z eder.<\/p>\n

Frege bu paradoksun \u00f6nemini b\u00fcy\u00fck bir \u00fcz\u00fcnt\u00fcyle hemen kavray\u0131p \u00fczerinde dokuz y\u0131l boyunca \u00e7al\u0131\u015farak ula\u015ft\u0131\u011f\u0131 sonu\u00e7lar\u0131n temellerinin sars\u0131ld\u0131\u011f\u0131n\u0131 anlar.<\/p>\n

Hayat\u0131n\u0131 adad\u0131\u011f\u0131, y\u0131llarca \u00e7al\u0131\u015farak ortaya \u00e7\u0131kard\u0131\u011f\u0131 kuram\u0131n\u0131n sa\u011flam olmad\u0131\u011f\u0131n\u0131 g\u00f6r\u00fcr. Kitab\u0131n bask\u0131 plakalar\u0131 haz\u0131rlanm\u0131\u015ft\u0131r, temel de\u011fi\u015fikler yapabilmesi i\u00e7in \u00e7ok ge\u00e7tir. Sadece bir sons\u00f6z yazmakla yetinmek zorunda kal\u0131r.<\/p>\n

Frege, kitab\u0131n s\u00f6n s\u00f6z\u00fcnde \u015fu c\u00fcmlelere yer verir: \u201cBir biliminsan\u0131n\u0131n ba\u015f\u0131na gelebilecek en talihsiz \u015fey, \u00e7al\u0131\u015fmas\u0131 bittikten sonra, kurdu\u011fu yap\u0131n\u0131n temellerinin sars\u0131lmas\u0131d\u0131r. Kitab\u0131m\u0131n ikinci cildinin tamamlanmas\u0131na yak\u0131n, Say\u0131n Bertrand Russell\u2019dan ald\u0131\u011f\u0131m mektupla, ben bu duruma d\u00fc\u015ft\u00fcm.\u201d<\/p>\n

Sonras\u0131nda Russell bu olayla ilgili d\u00fc\u015f\u00fcncelerini \u015fu s\u00f6zlerle anlatacakt\u0131r: \u201cEntelekt\u00fcel d\u00fcr\u00fcstl\u00fck ve do\u011fru s\u00f6zl\u00fcl\u00fck \u00f6rneklerini d\u00fc\u015f\u00fcnd\u00fck\u00e7e \u015funu anl\u0131yorum ki, Frege\u2019nin kendini hakikate adanm\u0131\u015fl\u0131\u011f\u0131yla kar\u015f\u0131la\u015ft\u0131rabilecek bildi\u011fim hi\u00e7bir \u00f6rnek yok. […] Temel varsay\u0131m\u0131n\u0131n hatal\u0131 oldu\u011funu fark etmesi \u00fczerine ki\u015fisel hayal k\u0131r\u0131kl\u0131\u011f\u0131n\u0131 ve duygular\u0131n\u0131 hi\u00e7 kimselere g\u00f6stermeden entelekt\u00fcel bir zevkle bana yan\u0131t verdi. Bu, egemenlik kurma ve tan\u0131nma yolunda s\u0131\u011f \u00e7abalar harcamak yerine kendini yarat\u0131c\u0131 yap\u0131tlara ve bilgiye adamas\u0131 durumunda insan\u0131n nelere kadir olabilece\u011finin dokunakl\u0131 bir g\u00f6stergesi ve neredeyse insan\u00fcst\u00fc bir davran\u0131\u015f \u00f6rne\u011fiydi.\u201d<\/p>\n

Frege\u2019nin hatas\u0131 matematik tarihinde dramatik bir d\u00f6n\u00fcm noktas\u0131d\u0131r; \u00e7\u00fcnk\u00fc Russell Paradoksu<\/strong> olarak adland\u0131r\u0131lan, \u201cKendisini eleman olarak i\u00e7ermeyen t\u00fcm k\u00fcmelerin k\u00fcmesi kendisini i\u00e7erir mi?\u201d sorusunun yan\u0131ts\u0131z kalmas\u0131yla matemati\u011fin temelleri adeta tehdit alt\u0131nda kalm\u0131\u015ft\u0131r.<\/p>\n

Russell Paradoksundan sonra matematik\u00e7iler \u201cHangi k\u00fcmelerin var olmas\u0131na izin verece\u011fiz?\u201d sorusunu daha dikkatli sormaya ba\u015flarlar ve bu s\u00fcre\u00e7 felsefi sonu\u00e7lar\u0131n\u0131n yan\u0131 s\u0131ra, tan\u0131mlar\u0131n a\u015f\u0131r\u0131 dikkatli yaz\u0131lmas\u0131, aksiyomlar\u0131n daha a\u00e7\u0131k belirtilmesi ve bi\u00e7imsel ispat sistemlerinin kurulmas\u0131yla aksiyomatik k\u00fcmeler kuram\u0131n\u0131n in\u015fas\u0131 sonucunu do\u011furur.<\/p>\n

Hatalar neden \u00f6nemli?
\n<\/em><\/strong>Matematikte yap\u0131lan hatalar\u0131 sadece \u201cyanl\u0131\u015f sonu\u00e7lar\u201d olarak de\u011fil de matemati\u011fin nas\u0131l geli\u015fti\u011fini anlaman\u0131n anahtar\u0131 olarak g\u00f6rmek gerekir ve hatta matematik tarihi, bir bak\u0131ma yanl\u0131\u015f sezgilerin<\/strong>, eksik tan\u0131mlar\u0131n<\/strong>, ba\u015far\u0131s\u0131z ispatlar\u0131n<\/strong>, kar\u015f\u0131 \u00f6rneklerin<\/strong> giderek daha sa\u011flam yap\u0131lara d\u00f6n\u00fc\u015fmesinin tarihidir.<\/p>\n

Erken d\u00f6nem matemati\u011finde sonsuz seriler, limit, s\u00fcreklilik, sonsuz k\u00fc\u00e7\u00fckler gibi bir\u00e7ok kavram \u201csezgisel\u201d olarak do\u011fru kabul ediliyordu ve sonras\u0131nda bu kabuldeki hatalar\u0131n \u00f6zellikle Weierstarss, Cauchy, Bolzana gibi matematik\u00e7iler taraf\u0131ndan ortadan kald\u0131r\u0131lmas\u0131yla matematiksel kesinli\u011fin temelleri \u00fczerinde modern analiz do\u011fdu. \u00d6nceki hatalar olmasayd\u0131 belki de modern analiz bu denli sa\u011flam bir yap\u0131ya kavu\u015famayacakt\u0131.<\/p>\n

19. y\u00fczy\u0131la kadar bir\u00e7ok matematik\u00e7i \u201cDo\u011fru g\u00f6r\u00fcnen \u015fey b\u00fcy\u00fck ihtimalle do\u011frudur\u201d yakla\u015f\u0131m\u0131na daha yak\u0131nd\u0131 ve bu yakla\u015f\u0131m\u0131n sonucu olarak hatalar\u0131n artmas\u0131yla tam ispat, a\u00e7\u0131k varsay\u0131m matematik yapman\u0131n olmazsa olmaz\u0131 haline geldi.<\/p>\n

Matematikteki hatalar\u0131n pozitif bilimlerdeki hatalardan farkl\u0131 olarak kesin bir bi\u00e7imde te\u015fhis edilebilip d\u00fczeltilebiliyor olmalar\u0131 bu hatalar\u0131 daha de\u011ferli k\u0131lmaktad\u0131r.<\/p>\n

Sonu\u00e7 olarak matematik yaparken olu\u015fan hatalar ister bir SAT s\u0131nav\u0131nda ortaya \u00e7\u0131ks\u0131n isterse bir teoremin ispat\u0131nda veya bir kuram\u0131n in\u015fas\u0131 s\u00fcrecinde hi\u00e7 fark etmiyor asla bir \u201cson\u201d de\u011fil hep daha derin bir ba\u015flang\u0131ca yol a\u00e7\u0131yor.<\/p>\n

\"\"<\/p>\n

KAYNAKLAR<\/span><\/b><\/p>\n

1) A. Nesin, A. T\u00f6r\u00fcn, Matematik\u00e7i Portreleri<\/i>, Nesin Yay\u0131nevi, 2025.<\/span><\/p>\n

2) https:\/\/kskedlaya.org\/putnam-archive<\/span>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Ali T\u00f6r\u00fcn SAT, \u00fcniversitelere kabul i\u00e7in yayg\u0131n olarak kullan\u0131lan ve uluslararas\u0131 ge\u00e7erlili\u011fi olan Amerika Birle\u015fik Devletleri merkezli bir test s\u0131nav\u0131d\u0131r. 1982 SAT\u2019de sorulan yanl\u0131\u015f bir matematik sorusu SAT\u2019ye k\u00f6t\u00fc bir \u015f\u00f6hret kazand\u0131rmakla kalmay\u0131p 300.000 \u00f6\u011frencinin s\u0131nav sonu\u00e7lar\u0131n\u0131n yeniden de\u011ferlendirilmesine yol a\u00e7ar: \u201cA \u00e7emberinin yar\u0131\u00e7ap\u0131, B \u00e7emberinin yar\u0131\u00e7ap\u0131n\u0131n 1\/3’\u00fcd\u00fcr. A \u00e7emberi, ba\u015flang\u0131\u00e7 \u200b\u200bkonumuna d\u00f6nene kadar B […]<\/p>\n","protected":false},"author":375,"featured_media":68472,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10536,38,514,510],"tags":[3562,6482],"class_list":["post-68467","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-266-sayi","category-dergi-sayilari","category-matematik-sohbetleri","category-surekli-bolumler","tag-ali-torun","tag-matematik-sohbetler"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/68467","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=68467"}],"version-history":[{"count":2,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/68467\/revisions"}],"predecessor-version":[{"id":68474,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/68467\/revisions\/68474"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/68472"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=68467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=68467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=68467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}