Ge\u00e7enlerde kat\u0131ld\u0131\u011f\u0131m bir arkada\u015f toplant\u0131s\u0131nda konu\u015fuldu: Matematik ke\u015fif midir icat m\u0131d\u0131r?\u00a0 \u00d6nceki deneyimlerim bu yorgun tart\u0131\u015fman\u0131n verimli ge\u00e7emeyece\u011fini s\u00f6yl\u00fcyordu. Y\u00fczy\u0131llard\u0131r matematik\u00e7i ve felsefeciler taraf\u0131ndan y\u00fcr\u00fct\u00fclen \u00f6znel tart\u0131\u015fmalar\u0131n konusuydu. Ba\u015flang\u0131\u00e7ta b\u00f6ylesi bir sohbetin i\u00e7inde olmay\u0131 pek istemedim, ama konu\u015fmalar ilerledik\u00e7e olduk\u00e7a ilgin\u00e7 fikirler \u00e7\u0131kt\u0131 ortaya. Kimse birbirini ikna edemese de (ki gerekmiyordu) \u00e7ok yararland\u0131\u011f\u0131m bir zaman dilimiydi. Bu tart\u0131\u015fmay\u0131 kurgulayarak anlatabilir miyim diye d\u00fc\u015f\u00fcnd\u00fcm,\u201d icat\u00e7\u0131lar\u201d (\u0130) ve \u201cke\u015fif\u00e7ilerin\u201d (K) diyalogunu hem ke\u015fif hem icat diyenleri de ekleyerek kaleme almaya \u00e7al\u0131\u015ft\u0131m.<\/p>\n
\u00a0\u0130-<\/strong> Matematik kesinlikle insan taraf\u0131ndan yarat\u0131lm\u0131\u015ft\u0131r. \u0130nsan fiziksel d\u00fcnyay\u0131 m\u00fckemmel bir \u015fekilde soyutlayarak matemati\u011fi yaratm\u0131\u015ft\u0131r. Ke\u015ffedilen \u015fey fiziksel d\u00fcnyad\u0131r, matematik de\u011fil; \u00e7\u00fcnk\u00fc do\u011fada matematik yoktur. Ger\u00e7ek d\u00fcnyada matematiksel nesnelere rastlayamazs\u0131n\u0131z. \u00d6rne\u011fin do\u011fada matematiksel anlamda bir do\u011fru, bir \u00fc\u00e7gen veya bir \u00e7ember g\u00f6steremezsiniz. \u0130catla ke\u015fif aras\u0131ndaki farka bakarsak, zaten var olan bir \u015fey ke\u015ffedilir, olmayansa icat edilir. \u00d6rne\u011fin Kanarya Adalar\u0131 ke\u015ffedilirmi\u015ftir ama telefon icat edilmi\u015ftir, matematik de do\u011fada olmad\u0131\u011f\u0131ndan ke\u015fif de\u011fil icatt\u0131r.<\/p>\n K- <\/strong>Do\u011fay\u0131 sadece g\u00f6zlemleyebildi\u011fimiz, duyumsayabildi\u011fimiz \u015feylerle s\u0131n\u0131rlamayal\u0131m; g\u00f6r\u00fcp dokunamayaca\u011f\u0131m\u0131z, kendini \u201cf\u0131s\u0131lt\u0131yla\u201d anlatan bir\u00e7ok yan var do\u011fada.\u00a0\u00a0 Evet, matematiksel bir \u00e7ember yok, fakat ay\u0131n, g\u00fcne\u015fin g\u00f6r\u00fcn\u00fc\u015f\u00fc bir matematik\u00e7i i\u00e7in matematiksel \u00e7emberin modeli olabilir. \u00c7ember, do\u011fru, \u00fc\u00e7gen, say\u0131lar gibi kavramlar matemati\u011fin ke\u015ffinin (!) ba\u015flang\u0131c\u0131 i\u00e7in verilmesi gereken \u00f6rneklerdir. Sonras\u0131nda, matemati\u011fin geli\u015fimine bakt\u0131\u011f\u0131m\u0131zda k\u00fcmeler, fonksiyonlar, karma\u015f\u0131k say\u0131lar, fraktallar, \u00d6klid-d\u0131\u015f\u0131 geometriler gibi bir\u00e7ok matematiksel kavram nesneldir, varl\u0131klar\u0131 onlar hakk\u0131ndaki bilgilerimizden ba\u011f\u0131ms\u0131zd\u0131r. Onlar, biz bilsek de bilmesek de vard\u0131r. Ku\u015fkusuz, bu nesneler fiziksel ya da maddi de\u011fildir, mek\u00e2n ve zaman\u0131n d\u0131\u015f\u0131nda var olurlar, ama de\u011fi\u015fmezdirler, yarat\u0131lmam\u0131\u015flard\u0131r, yok olmayacaklard\u0131r. \u00d6rne\u011fin, ke\u015ffinden sonra Pisagor\u2019un tanr\u0131lara \u015f\u00fckran ifadesi olarak bir \u00f6k\u00fcz kurban etti\u011fi rivayet edilen Pisagor Teoremi, Pisagor\u2019dan bin y\u0131l \u00f6nce Babiller taraf\u0131ndan da biliniyordu ve bu teoremin kan\u0131t\u0131 ilk kez Pisagor\u2019dan yakla\u015f\u0131k iki y\u00fcz y\u0131l sonra \u00d6klid taraf\u0131ndan yap\u0131ld\u0131. \u015eimdi bu noktada sorabiliriz: Pisagor Teoremi ne zaman do\u011fruluk kazand\u0131? Babiller d\u00f6neminde mi, yani M\u00d6 1900-1600\u2019de mi? Pisagor\u2019un ya\u015fad\u0131\u011f\u0131 \u00e7a\u011fda m\u0131, yani M\u00d6 500\u2019de mi? Yoksa \u00d6klid kan\u0131tlad\u0131\u011f\u0131nda m\u0131, yani M\u00d6 300\u2019de mi? Biz do\u011fru oldu\u011funu bilmesek de bu \u00f6nerme \u201cnesnel bir ger\u00e7ek\u201d olarak hep do\u011fruydu. Matematik b\u00f6ylesi binlerce \u00f6nermeden olu\u015fuyor, biz onlar\u0131n do\u011fru oldu\u011funu bilmezken bile do\u011fru olan!<\/p>\n \u0130-<\/strong> Matemati\u011fin ke\u015fif oldu\u011fu g\u00f6r\u00fc\u015f\u00fc olduk\u00e7a zorlama, u\u00e7uk zihinsel bir hayal \u00fcr\u00fcn\u00fcd\u00fcr. Matematiksel ara\u015ft\u0131rma Platonculu\u011fa indirgenemez. Bu g\u00f6r\u00fc\u015fe g\u00f6re matematiksel ger\u00e7ekler bir k\u00e2\u011f\u0131t par\u00e7as\u0131na \u00e7izilen do\u011fru, \u00e7ember ve \u00fc\u00e7genden ibaret de\u011fildir. As\u0131l ger\u00e7ek kusursuz matematiksel nesnelerin yer ald\u0131\u011f\u0131 hayali \u201cidealar d\u00fcnyas\u0131ndad\u0131r\u201d.\u00a0 Oysa ara\u015ft\u0131rma yapan bir matematik\u00e7i hayali bir d\u00fcnyada \u00e7al\u0131\u015fmaz. Bu y\u00fczden, olmayan bir d\u00fcnyada olmayan nesneleri ke\u015ffetmesi m\u00fcmk\u00fcn de\u011fildir. Ke\u015ffedilmeyi bekleyen, haz\u0131r yap\u0131lm\u0131\u015f bir d\u00fcnya yoktur. Pisagor Teoremi gibi b\u00fct\u00fcn matematiksel nesneler insanlar taraf\u0131ndan tasarlanm\u0131\u015f icatlard\u0131r. Bu ger\u00e7e\u011fi \u00fcnl\u00fc Alman matematik\u00e7i Kronecker\u2019in \u015fu s\u00f6z\u00fc \u00e7ok iyi anlat\u0131r: Tamsay\u0131lar Tanr\u0131 taraf\u0131ndan yarat\u0131lm\u0131\u015flard\u0131r, gerisi insan i\u015fidir\u201d.<\/p>\n E\u011fer ak\u0131l, zek\u00e2 insana de\u011fil de ba\u015fka bir canl\u0131 t\u00fcr\u00fcne bah\u015fedilmi\u015f olsayd\u0131, \u00f6rne\u011fin bir bal\u0131k t\u00fcr\u00fc taraf\u0131ndan mant\u0131ksal \u00e7\u0131kar\u0131mlar yap\u0131labilseydi, o zaman ortaya matematikle hi\u00e7 ilgisi olmayan sadece suyla ilgili ve sadece hareket, \u0131s\u0131, su bas\u0131nc\u0131 gibi kavramlar \u00e7\u0131kacakt\u0131. Bu durumda, bu bal\u0131k t\u00fcr\u00fcn\u00fcn \u201cmatemati\u011fi\u201d g\u00fcn\u00fcm\u00fcz matemati\u011fini kapsamayacak, ya\u015fad\u0131\u011f\u0131 d\u00fcnyayla s\u0131n\u0131rl\u0131 kalacakt\u0131. O halde demek ki insan i\u00e7ine do\u011fdu\u011fu d\u00fcnyay\u0131 soyutlayarak matemati\u011fi yarat\u0131yor. Ge\u00e7mi\u015fte matematikte ya\u015fanan krizler matemati\u011fin sorunlar\u0131n\u0131n insan kaynakl\u0131 oldu\u011funu, iddia edildi\u011fi gibi matematik\u00e7ilerin kusursuz bir \u201cidealar d\u00fcnyas\u0131nda\u201d ke\u015ffe \u00e7\u0131kmad\u0131klar\u0131n\u0131 g\u00f6sterir. \u00d6rne\u011fin G\u00f6del\u2019in Birinci Eksiklik Teoremi matemati\u011fin \u00e7eli\u015fkisiz oldu\u011funun kan\u0131tlanamayaca\u011f\u0131n\u0131 s\u00f6yler. Nas\u0131l oluyor da insandan ba\u011f\u0131ms\u0131z, o \u201cnesnel ger\u00e7ekler\u201d d\u00fcnyas\u0131nda ke\u015ffedilen matemati\u011fin \u00e7eli\u015fkisiz oldu\u011fu kan\u0131tlanam\u0131yor?<\/p>\n K-<\/strong> 1880\u2019lerde \u00fcnl\u00fc Alman matematik\u00e7i Cantor, \u201cSay\u0131lar insan zek\u00e2s\u0131n\u0131n \u00f6zg\u00fcr bulu\u015flar\u0131d\u0131r,\u00a0 matemati\u011fin \u00f6z\u00fc, tamamen \u00f6zg\u00fcrl\u00fc\u011f\u00fcndedir.\u201d s\u00f6z\u00fcyle matemati\u011fin temellerini sarsan\u00a0 \u201ck\u00fcmeler kuram\u0131n\u0131\u201d in\u015fa etmi\u015fti. Cantor\u2019un att\u0131\u011f\u0131 s\u0131ra d\u0131\u015f\u0131 ad\u0131mlar, o d\u00f6nemde matemati\u011fin \u201ckeyfi kurallara\u201d dayanan bir icat oldu\u011fu d\u00fc\u015f\u00fcncesini g\u00fc\u00e7lendirmi\u015fti, fakat k\u0131sa s\u00fcrede durum de\u011fi\u015fti. Bir\u00e7ok matematik\u00e7i matemati\u011fin ba\u011f\u0131ms\u0131z bir ger\u00e7ekler d\u00fcnyas\u0131n\u0131n varl\u0131\u011f\u0131n\u0131 kabul etti, \u00e7\u00fcnk\u00fc Cantor\u2019un daha \u00f6nce hi\u00e7bir matematik\u00e7inin akl\u0131na gelmeyen b\u00fcy\u00fck bir ke\u015ffi ba\u015far\u0131yla sonu\u00e7land\u0131rd\u0131\u011f\u0131 inanc\u0131 yerle\u015fti. Matematik tarihine g\u00f6z att\u0131\u011f\u0131m\u0131zda bir\u00e7ok matematik\u00e7i ke\u015ffe denk olan \u201csezgi\u201d yetene\u011fi sayesinde matematiksel do\u011frulukla kar\u015f\u0131la\u015ft\u0131\u011f\u0131 hissini ya\u015fad\u0131\u011f\u0131n\u0131 ifade etmi\u015ftir.<\/p>\n 1894\u2019te \u00fcnl\u00fc Frans\u0131z matematik\u00e7i Hermite yazd\u0131\u011f\u0131 bir mektupta matematiksel kavramlar\u0131n her birinin insandan ba\u011f\u0131ms\u0131z nesnel ger\u00e7ekler oldu\u011funu belirterek, \u201cBiz t\u0131pk\u0131 fizik\u00e7iler, kimyac\u0131lar ya da zoologlar gibi onlar\u0131 ke\u015ffediyoruz\u201d s\u00f6z\u00fcn\u00fc ekledi. Sonras\u0131nda, 1920\u2019lerde \u0130ngiliz matematik\u00e7i Hardy ise matematik\u00e7iyi uzaktaki bir da\u011f s\u0131ras\u0131n\u0131 g\u00f6z\u00fcne kestiren bir k\u00e2\u015fife benzeterek, matemati\u011fin bizden ba\u011f\u0131ms\u0131z bir ger\u00e7eklik oldu\u011funu \u015fu s\u00f6zlerle ifade etti: \u201cKan\u0131tlad\u0131\u011f\u0131m\u0131z ve bizim s\u00fcsl\u00fc p\u00fcsl\u00fc s\u00f6zc\u00fcklerle a\u00e7\u0131klad\u0131\u011f\u0131m\u0131z teoremler, yaln\u0131zca g\u00f6zlemlerimizin notlar\u0131d\u0131r. 317 asal bir say\u0131d\u0131r, bizim onu b\u00f6yle d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcm\u00fczden veya akl\u0131m\u0131z b\u00f6yle bi\u00e7imlenmi\u015f oldu\u011fundan de\u011fil, ama b\u00f6yle oldu\u011fundan b\u00f6yledir, \u00e7\u00fcnk\u00fc matematiksel ger\u00e7eklik b\u00f6yle kurulmu\u015ftur\u201d.<\/p>\n G\u00f6del\u2019in Eksiklik Teoremi bize matematiksel nesnelerin nas\u0131l var oldu\u011fu hakk\u0131nda bir \u015fey s\u00f6ylemez, bilinen aksiyomatik sistemlerin s\u0131n\u0131rlar\u0131na i\u015faret eder. G\u00f6del matematiksel Platonculu\u011fun \u00fcnl\u00fc temsilcilerindendir, matematiksel sezginin fiziksel duyu alg\u0131lar\u0131 kadar g\u00fcvenilir oldu\u011funu savunarak matematikte \u201cnesnel ger\u00e7ekler\u201d d\u00fcnyas\u0131na dikkat \u00e7ekmi\u015ftir. G\u00f6del\u2019in b\u00f6ylesi bir felsefi sonuca Eksiklik Teoremleri sonras\u0131nda ula\u015ft\u0131\u011f\u0131 bilinir.<\/p>\n Konu\u015ftuklar\u0131m\u0131z asl\u0131nda matematik felsefesinde Platonist ve Formalist gibi iki ana ak\u0131m\u0131n temel tezlerine dayan\u0131r. Y\u00fczy\u0131llard\u0131r matematiksel ontoloji \u00fczerinden tart\u0131\u015f\u0131lan olduk\u00e7a kapsaml\u0131 bir konu. Platoncu g\u00f6r\u00fc\u015f matemati\u011fin evrensel niteli\u011fine dikkat \u00e7eker, e\u011fer Evren\u2019de d\u00fcnya d\u0131\u015f\u0131 ya\u015fam s\u00f6z konusuysa uzayl\u0131larla ayn\u0131 matematiksel kavramlara sahip olaca\u011f\u0131m\u0131z\u0131 savunur. Bu sav\u0131n belirsizli\u011fi s\u0131k\u0131c\u0131 olabilir, ancak tek ba\u015f\u0131na hi\u00e7bir icat, atomalt\u0131 par\u00e7ac\u0131klar\u0131n hareketinden tutun da \u00fcremeye kadar her alanda d\u00fcnyay\u0131 ve evreni anlamam\u0131za yetmez.<\/p>\n K\u0130- <\/strong>\u201cMatematik bir ke\u015fif mi yoksa icat m\u0131?\u201d sorusu yanl\u0131\u015f bir sorudur, \u00e7\u00fcnk\u00fc matematik k\u0131smen ke\u015fif, k\u0131smen icatt\u0131r. Matematik\u00e7iler matematiksel nesneleri icat ederler, sonra da bu nesneler aras\u0131ndaki ili\u015fkileri ke\u015ffederler. \u00d6rne\u011fin 3, 4, 5 gibi say\u0131lar birer icatt\u0131r, ama \u00a0e\u015fitli\u011fi bir ke\u015fiftir. Dolay\u0131s\u0131yla matematiksel tan\u0131m ve aksiyomlar icat, teorem ve kuramlar birer ke\u015fiftir. T\u0131pk\u0131 satran\u00e7 oyununun ve kurallar\u0131n\u0131n bir icat olup, oyunda en iyi stratejinin bulunmas\u0131n\u0131n bir ke\u015fif olmas\u0131 gibi; \u00f6rne\u011fin geometride a\u00e7\u0131, do\u011fru, \u00fc\u00e7gen gibi kavramlar birer icat olup, \u00fc\u00e7genin i\u00e7 a\u00e7\u0131lar\u0131n\u0131n \u00f6l\u00e7\u00fclerinin toplam\u0131n\u0131n 180 derece olmas\u0131 gibi teoremler birer ke\u015fiftir. Ku\u015fkusuz ki matematik, insan\u0131n s\u0131radan bir etkinli\u011fi de\u011fildir; ancak \u00f6nce yaratman\u0131z gerekir, yoksa matematiksel bir ke\u015ffe \u00e7\u0131kamazs\u0131n\u0131z, t\u0131pk\u0131 \u015fu soru gibi: Ormandaki a\u011fa\u00e7lar\u0131n ka\u00e7 tane oldu\u011funu g\u00f6steren say\u0131 var, ama o a\u011fa\u00e7lar\u0131 sayacak kimse yoksa o say\u0131 var m\u0131d\u0131r?<\/p>\n Kaynaklar<\/strong><\/p>\n –\u00a0<\/strong>Ali Nesin, Matematik ve Do\u011fa<\/em>, Nesin Yay\u0131nevi, 2007.<\/p>\n – Mario Livio, Tanr\u0131 Matematik\u00e7i mi<\/em>?, Alt\u0131n Kitaplar, 2005.<\/p>\n","protected":false},"excerpt":{"rendered":" Ge\u00e7enlerde kat\u0131ld\u0131\u011f\u0131m bir arkada\u015f toplant\u0131s\u0131nda konu\u015fuldu: Matematik ke\u015fif midir icat m\u0131d\u0131r?\u00a0 \u00d6nceki deneyimlerim bu yorgun tart\u0131\u015fman\u0131n verimli ge\u00e7emeyece\u011fini s\u00f6yl\u00fcyordu. Y\u00fczy\u0131llard\u0131r matematik\u00e7i ve felsefeciler taraf\u0131ndan y\u00fcr\u00fct\u00fclen \u00f6znel tart\u0131\u015fmalar\u0131n konusuydu. Ba\u015flang\u0131\u00e7ta b\u00f6ylesi bir sohbetin i\u00e7inde olmay\u0131 pek istemedim, ama konu\u015fmalar ilerledik\u00e7e olduk\u00e7a ilgin\u00e7 fikirler \u00e7\u0131kt\u0131 ortaya. Kimse birbirini ikna edemese de (ki gerekmiyordu) \u00e7ok yararland\u0131\u011f\u0131m bir zaman […]<\/p>\n","protected":false},"author":375,"featured_media":13954,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[192,25,514],"tags":[237,1598,426,208],"class_list":["post-14151","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-155-sayi","category-matematik","category-matematik-sohbetleri","tag-felsefe","tag-icat","tag-kesif","tag-matematik"],"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