{"id":201,"date":"2016-10-28T08:31:37","date_gmt":"2016-10-28T08:31:37","guid":{"rendered":"http:\/\/ragipsahin.com\/?p=201"},"modified":"2016-10-22T09:57:09","modified_gmt":"2016-10-22T09:57:09","slug":"cahit-arf","status":"publish","type":"post","link":"https:\/\/www.ragipsahin.com.tr\/?p=201","title":{"rendered":"Cahit Arf"},"content":{"rendered":"

CAH\u0130T ARF\u0092IN HAYATI<\/strong><\/span><\/p>\n

1910`da Selanik`te do\u011fan Cahit Arf Y\u00fcksek\u00f6\u011frenimini Paris`te, Ecole Normale Superieure`de tamamlad\u0131.Galatasaray Lisesi`nde matematik \u00f6\u011fretmeni, \u0130stanbul \u00dcniversitesi Fen Fak\u00fcltesi`nde do\u00e7ent aday\u0131 olarak \u00e7al\u0131\u015ft\u0131.1938 y\u0131l\u0131nda G\u00f6ttingen \u00dcniversitesi`nden doktoras\u0131n\u0131 ald\u0131ktan sonra da \u0130stanbul \u00dcniversitesi`ndeki g\u00f6revini s\u00fcrd\u00fcrd\u00fc.1943`te profes\u00f6r, 1955`de ordinary\u00fcs profes\u00f6r oldu. Bu arada Maryland \u00dcniversitesi`nde misafir profes\u00f6r olarak \u00e7al\u0131\u015ft\u0131 ve Mainz Akademisi muhabir \u00fcyeli\u011fine se\u00e7ildi. 1962 y\u0131l\u0131nda \u0130stanbul \u00dcniversitesi`nden ayr\u0131larak bir y\u0131l s\u00fcreyle Robert Kolej`de \u00f6\u011fretim \u00fcyeli\u011fi yapt\u0131.1964-1966 y\u0131llar\u0131nda Princeton`da Institute for Advanced Study`de ara\u015ft\u0131r-malar\u0131n\u0131 s\u00fcrd\u00fcrd\u00fc. California \u00dcniversitesi`nde misafir \u00f6\u011fretim \u00fcyesi olarak bulundu.1967 y\u0131l\u0131nda yurda d\u00f6nerek Orta Do\u011fu Teknik \u00dcniversitesi Matematik B\u00f6l\u00fcm\u00fc`nde \u00e7al\u0131\u015fmaya ba\u015flad\u0131. T\u00fcrkiye Bilimsel ve Teknik Ara\u015ft\u0131rma Kurumu Bilim Kurulu Ba\u015fkanl\u0131\u011f\u0131nda bulundu, ve bu kuru- mun kurulmas\u0131 ve geli\u015fmesi y\u00f6n\u00fcnde emek harcad\u0131.1980 y\u0131l\u0131nda Orta Do\u011fu Teknik \u00dcniversitesi` nden kendi iste\u011fi ile emekli oldu.1985-1989 y\u0131llar\u0131 aras\u0131nda da T\u00fcrk Mtematik Derne\u011fi`nin ba\u015f- kanl\u0131\u011f\u0131n\u0131 y\u00fcr\u00fctt\u00fc, ayr\u0131ca T\u00dcB\u0130TAK`\u0131n \u201d Do\u011fa Turkish Journal of Mathematics\u201d ile \u201cTurkish Journal of Mathematics\u201d adl\u0131 dergilerinde yay\u0131n kurulu \u00fcyeliklerinde de bulundu.\u00d6l\u00fcm\u00fcne dek T\u00dcB\u0130TAK`\u0131n Marmara Ara\u015ft\u0131rma Merkezi`nde ve Bebek-\u0130stanbul`daki evinde matematik \u00e7al\u0131\u015f- malar\u0131n\u0131 s\u00fcrd\u00fcrd\u00fc.\u00d6l\u00fcm tarihi 26.12.1997 dir. 1939 y\u0131l\u0131nda yay\u0131nlanan ilk ara\u015ft\u0131rmas\u0131 ile ba\u015flayarak Ord. Prof. Dr. Cahit Arf , cebir, say\u0131lar kuram\u0131, elastisite kuram\u0131 ve analiz gibi matemati\u011fin de\u011fi\u015fik dallar\u0131nda yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalar\u0131nda \u00f6zg\u00fcn ve kal\u0131c\u0131 sonu\u00e7lar elde etmi\u015ftir.Matematik yaz\u0131n\u0131nda \u201cArf de\u011fi\u015fmezleri\u201d , \u201cArf halkalar\u0131\u201d gibi s\u00f6zc\u00fcklerle bug\u00fcnde de kar\u015f\u0131la\u015f\u0131l\u0131r.1948`de \u0130n\u00f6n\u00fc Arma\u011fan\u0131n\u0131, 1974`de T\u00fcrkiye Bilimsel ve Teknik Ara\u015ft\u0131rma Kurumu Bilim \u00d6d\u00fcl\u00fcn\u00fc kazanan Ord. Prof. Dr. Cahit Arf`a 1980 y\u0131l\u0131nda \u0130stanbul Teknik \u00dcniversitesi ve Karadeniz Teknik \u00dcniversitesi, 1981 y\u0131l\u0131nda da Orta Do\u011fu Teknik \u00dcniversi-tesi Onur Doktoras\u0131 vermi\u015flerdir.Arf, 1988`de Mustafa Parlar Bilim ve Onur \u00d6d\u00fcl\u00fcn\u00fc, 1989`da da Ege \u00dcniversitesi \u015e\u00fckran Plaketini alm\u0131\u015f, 1933`de T\u00fcrkiye Bilimler Akademisinde \u015eeref \u00dcyesi olmu\u015f, 1994`de Fransa` dan \u201cCommandeur des Palmes Academiques\u201d ni\u015fan\u0131n\u0131 alm\u0131\u015ft\u0131r.<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\nARF HALKALARI<\/strong><\/span><\/p>\n

Lies ve y\u00fcksek\u00f6\u011frenimini Fransa\u2019da tamamlad\u0131. T\u00fcrkiye\u2019ye d\u00f6nd\u00fckten sonra bir s\u00fcre Galatasaray Lisesi\u2019nde \u00f6\u011fretmenlik yapt\u0131. Do\u00e7ent aday\u0131 olarak \u0130stanbul \u00dcniversitesi Matematik B\u00f6l\u00fcm\u00fc\u2019ne ge\u00e7i\u015fin ard\u0131ndan 1937\u2032de doktora yapmak i\u00e7in G\u00f6ttingen\u2019e gitti. Burada yapt\u0131\u011f\u0131 doktora \u00e7al\u0131\u015fmas\u0131, onun d\u00fcnya \u00e7ap\u0131nda tan\u0131nmas\u0131na yol a\u00e7t\u0131.<\/span><\/p>\n

Alman matematik dehas\u0131 Hasse\u2019nin uyar\u0131lar\u0131na kar\u015f\u0131n Non-kom\u00fctatif Class Field \u00fczerinde tek ba\u015f\u0131na bir bu\u00e7uk y\u0131l \u00e7al\u0131\u015farak doktoras\u0131n\u0131 tamamlad\u0131. Arf\u2019in bu \u00e7al\u0131\u015fmas\u0131yla elde etti\u011fi sonu\u00e7lar\u0131n bir k\u0131sm\u0131 literat\u00fcre \u0091\u0091Hasse-Arf Teoremi\u0092\u0092 olarak ge\u00e7ti.<\/span><\/p>\n

Doktora tezini 1938\u2032de bitirdikten sonra Hasse\u2019nin \u00f6nerisiyle bir y\u0131l daha G\u00f6tting\u2019de kald\u0131. Bu ise onun i\u00e7in yeni bir \u00e7al\u0131\u015fma d\u00f6nemi oldu ve matematik\u00e7i E. Witt\u2019in, ilk ad\u0131m\u0131n\u0131 att\u0131\u011f\u0131 Kuadratik Formlar teorisini \u00f6nemli \u00f6l\u00e7\u00fcde tamamlad\u0131. Bu \u015fekilde d\u00fcnya literat\u00fcr\u00fcne \u0091\u0091Arf Invaryantan\u0131\u0092\u0092 olarak ge\u00e7en invaryant\u0131 ortaya \u00e7\u0131kard\u0131. Cahit Arf\u2019\u0131 d\u00fcnyaya tan\u0131tan bu bulu\u015f olmu\u015ftu.<\/span><\/p>\n

Sava\u015f y\u0131llar\u0131 s\u0131ras\u0131nda \u0130stanbul \u00dcniversitesi\u0092ne gelen Du Val isimli \u0130ngiliz matematik\u00e7i, Arf\u2019in ya\u015fam\u0131nda \u00f6nemli olacak bir sayfan\u0131n daha a\u00e7\u0131lmas\u0131n\u0131 sa\u011flad\u0131. Du Val\u2019in anlatt\u0131\u011f\u0131 teoride, geometrik argumanlar\u0131n arkas\u0131nda etkin cebirsel kavramlar\u0131n varl\u0131\u011f\u0131ndan s\u00f6z eden Arf, bu iddiay\u0131 kan\u0131tlamak i\u00e7in bir hafta eve kapand\u0131. Evden \u00e7\u0131kt\u0131\u011f\u0131nda, birtak\u0131m halkalardan s\u00f6z etti. O halkalara \u0091\u0091Arf Halkalar\u0131\u0092\u0092 kapan\u0131\u015flar\u0131na da \u0091\u0091Arf Kapan\u0131\u015f\u0131\u0092\u0092 denildi.<\/span><\/p>\n

Matematik \u00e7\u00f6z\u00fcmlerinin mekanik problemlerine uygulanmas\u0131n\u0131n en iyi \u00f6rneklerini veren Arf, gen\u00e7 bir matematik\u00e7i ku\u015fa\u011f\u0131n\u0131n yeti\u015fmesine katk\u0131da bulundu. Arf, bilimi T\u00fcrkiye\u2019ye sevdirmek i\u00e7in \u00e7ok u\u011fra\u015ft\u0131.<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\n\u00c7\u00dcNK\u00dc \u00d6L\u00dcM\u00dc UNUTUYORUZ<\/strong><\/span><\/p>\n

Matemati\u011fi \u0091\u0091t\u00fcmevar\u0131msal bir bilim\u0092\u0092 olarak tan\u0131mlayan Arf, bu bilimin sonsuz k\u00fcmeler i\u00e7in ge\u00e7erli oldu\u011funu alt\u0131n\u0131 \u00e7izerek matematik-\u00f6l\u00fcms\u00fczl\u00fck ili\u015fkisini \u015f\u00f6yle a\u00e7\u0131kl\u0131yordu: \u0091\u0091Bu sonsuzluklar\u0131 t\u00fcmevar\u0131msal bir \u015fekilde kavr\u0131yoruz ve kavrad\u0131\u011f\u0131m\u0131z zaman da o sonsuzlu\u011fu hissediyoruz. Ve bu bize mutluluk veriyor. \u00c7\u00fcnk\u00fc \u00f6l\u00fcm\u00fc unutuyoruz.. Herkes \u00f6l\u00fcms\u00fcz oldu\u011fu alanda \u00e7al\u0131\u015fmak ister. Ben de matematikte kendimi \u00f6l\u00fcms\u00fcz hissettim\u2026\u0092\u0092<\/span><\/p>\n

Bilim adaml\u0131\u011f\u0131n\u0131 bir ya\u015fam bi\u00e7imi olarak s\u00fcrd\u00fcren Arf, 90 ya\u015f\u0131nda \u00f6l\u00fcrken bile matematik \u00e7al\u0131\u015fmalar\u0131na devam ediyordu.<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\nHASSE-ARF TEOREM\u0130<\/strong><\/span><\/p>\n

Cahit Arf\u2019\u0131n Almanya\u2019da \u00fcnl\u00fc bir matematik dergisi olan Crelle Journal\u2019da 1939 y\u0131l\u0131nda yay\u0131mlanm\u0131\u015f olan ilk \u00e7al\u0131\u015fmas\u0131, G\u00f6ttingen \u00dcniversitesi\u2019nde, 1938 y\u0131l\u0131nda haz\u0131rlad\u0131\u011f\u0131 son derece parlak olan doktora tezidir. Cahit Arf\u2019\u0131n Almanya\u2019ya gelmeden \u00f6nce d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fc ve proje haline getirdi\u011fi \u00e7ok kapsaml\u0131 bir problem vard\u0131: \u00c7\u00f6z\u00fclebilen cebirsel denklemlerin bir listesini yapmak. Bu ama\u00e7la G\u00f6ttingen\u2019e gitti ve orada \u00fcnl\u00fc matematik\u00e7i Hasse\u2019nin doktora \u00f6\u011frencisi oldu. Hasse\u2019ye projesinden bahsetti. Hasse, problemi \u00f6nce \u00f6zel hallerde \u00e7\u00f6zmesini sal\u0131k verdi\u011fini, bunun \u00fczerine birka\u00e7 ay gibi k\u0131sa bir s\u00fcre Cahit Arf\u2019\u0131n hi\u00e7 g\u00f6z\u00fckmedi\u011fini ve o s\u00fcre sonunda problemi tamamen \u00e7\u00f6z\u00fcp kendisine getirdi\u011fini 1974\u2032te yine Silivri\u2019de bir Cebir ve Say\u0131lar Teorisi toplant\u0131s\u0131nda anlatm\u0131\u015ft\u0131. Bu olay Cahit Arf\u2019\u0131n \u00fcst\u00fcn matematik yetene\u011fini g\u00f6stermenin yan\u0131 s\u0131ra daha G\u00f6ttingen\u2019e gelirken matematik bak\u0131m\u0131ndan ne kadar olgun oldu\u011funu da g\u00f6stermektedir. Cahit Arf bu \u00e7al\u0131\u015fmas\u0131yla say\u0131lar teorisinde \u00e7ok \u00f6zel bir yeri olan lokal cisimlerde dallanma teorisine \u00e7ok \u00f6nemli yap\u0131sal bir katk\u0131da bulunmu\u015ftur. Burada buldu\u011fu sonu\u00e7lardan bir b\u00f6l\u00fcm\u00fc bug\u00fcn d\u00fcnya matematik literat\u00fcr\u00fcnde ve kitaplarda Hasse-Arf Teoremi olarak ge\u00e7mektedir.<\/span><\/p>\n

Lokal cisimler teorisi, daha \u00f6nce de belirtildi\u011fi gibi, H. Hasse taraf\u0131ndan \u00e7ok efektif olarak kullan\u0131lmaya ba\u015flanm\u0131\u015ft\u0131. Ancak, o zamanki lokal cisimler teorisi, daha ziyade say\u0131-cisimleri ve (sonlu katsay\u0131l\u0131) cebrik fonksiyon-cisimleri \u00fczerine uygulanmak maksad\u0131yla geli\u015ftirildi\u011fi i\u00e7in, daima kalan s\u0131n\u0131f cisminin sonlu bir cisim oldu\u011fu kabul edilerek kurulmu\u015f idi. Dolay\u0131s\u0131yla, bu olduk\u00e7a s\u0131n\u0131rl\u0131 \u015fart\u0131n yerine daha genel bir \u015fart alt\u0131nda bu teorinin kurulmas\u0131 \u00e7ok arzu edilen bir husus idi. Herhalde onun i\u00e7indir, Cahit Bey\u2019in G\u00f6ttingen\u2019de Hasse ile yapt\u0131\u011f\u0131 ilk g\u00f6r\u00fc\u015fmede, Hasse ona hemen bu problemi doktora konusu olarak tavsiye etmi\u015ftir. Cahit Bey\u2019in bana anlatt\u0131\u011f\u0131na g\u00f6re, bu g\u00f6r\u00fc\u015fmeden sonra, kendisi bir daha hi\u00e7 Hasse ile g\u00f6r\u00fc\u015fmemi\u015f, ta bir y\u0131l sonra doktora tezini bitirinceye kadar. \u201cUntersuchungen \u00dcber Reinverzweigte Erweiterungen Diskret bewerteter Perfekter K\u00f6rper\u201d adl\u0131 Cahit Bey\u2019in tezinde, kalan s\u0131n\u0131f cisminin sonlu olmas\u0131 \u015fart\u0131 yerine daha \u00e7ok genel bir \u015fart alt\u0131nda lokal cisimler teorisi kurulmu\u015ftur. Cahit Bey\u2019in tezinde \u015fekillenmi\u015ftir diyebiliriz. \u00d6zelikle, bu tez i\u00e7inde yer alan ve daha \u00f6nce J. Herbrand taraf\u0131ndan incelenmi\u015f olan y\u00fcksek mertebeden dallanma gruplar\u0131n\u0131n indisleri ile ilgili Hasse Arf teoremi \u00e7ok me\u015fhurdur. Bu teorem, yukar\u0131da belirtilen indisler aras\u0131nda s\u0131\u00e7ramalara tekab\u00fcl edenlerin tam say\u0131lar oldu\u011funu ifade etmekte olup, Arf\u2019\u0131n temsillerinin varl\u0131\u011f\u0131n\u0131n ispat i\u00e7in de kilit nokta te\u015fkil etti\u011finden \u00fcn kazanm\u0131\u015ft\u0131r. B\u00f6ylece Cahit Bey, bir y\u0131l gibi k\u0131sa bir zaman i\u00e7inde m\u00fckemmel bir doktora tezi haz\u0131rlayarak, kendisinin ola\u011fan \u00fcst\u00fc kabiliyetini kan\u0131tlam\u0131\u015f oluyordu.Ayr\u0131ca G\u00f6ttingen\u2019deki se\u00e7kin matematik\u00e7iler ile kayna\u015fm\u0131\u015f olan gen\u00e7 Cahit Bey, say\u0131lar teorisine ait zaman\u0131n en u\u00e7 ara\u015ft\u0131rma havas\u0131n\u0131 bol bol teneff\u00fcs etmi\u015ftir. Fakat ayn\u0131 zamanda bu zonelerin, \u0130kinci D\u00fcnya Sava\u015f\u0131\u2019na do\u011fru s\u00fcr\u00fcklenen Almanya i\u00e7in uzun karanl\u0131k zamanlar\u0131n ba\u015flang\u0131c\u0131 oldu\u011funu da ilave etmemiz gerekir.<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\nCAH\u0130T ARF\u0092IN \u00c7ALI\u015eMALARININ KISA B\u0130R TANITIMI<\/strong><\/span><\/p>\n

Cahit Arf, Hasse\u2019nin \u00f6nerisi \u00fczerine ba\u015fka bir zor problemle u\u011fra\u015fmak \u00fczere bir y\u0131l daha G\u00f6ttingen\u2019de kald\u0131. Yeni u\u011fra\u015ft\u0131\u011f\u0131 problem, matematikte \u201ckuadratik formlar\u201d olarak bilinen konuda idi. Uzayda konisel y\u00fczey denklemleri buna basit bir \u00f6rnek olarak g\u00f6sterilebilir. Bu konudaki temel problem, kuadratik formlar\u0131n birtak\u0131m invariantlar, yani de\u011fi\u015fmezler yard\u0131m\u0131yla s\u0131n\u0131fland\u0131r\u0131lmas\u0131d\u0131r. Bu s\u0131n\u0131fland\u0131rma Witt ad\u0131nda \u00fcnl\u00fc bir Alman matematik\u00e7i taraf\u0131ndan karakteristi\u011fi ikiden farkl\u0131 olan cisimler i\u00e7in 1937\u2032de yap\u0131lm\u0131\u015ft\u0131. Karakteristik iki olunca problem \u00e7ok daha zorla\u015f\u0131yor ve Witt\u2019in y\u00f6ntemi uygulanam\u0131yordu. Cahit Arf bu problemle u\u011fra\u015ft\u0131 ve karakteristi\u011fi iki olan cisimler \u00fczerindeki kuadratik formlar\u0131 \u00e7ok iyi bir bi\u00e7imde s\u0131n\u0131fland\u0131rd\u0131. Bunlar\u0131n invariantlar\u0131n\u0131, yani de\u011fi\u015fmezlerini in\u015fa etti. Bu invariantlar bug\u00fcn d\u00fcnya matematik literat\u00fcr\u00fcnde Arf invariantlar\u0131 olarak ge\u00e7mektedir. G\u00fcn\u00fcm\u00fcz cebirsel ve diferansiyel topolojisinde ve geometride hala yerini koruyan bu \u00e7al\u0131\u015fma 1941 y\u0131l\u0131nda yine Crelle dergisinde yay\u0131mland\u0131 ve Cahit Arf\u2019\u0131 d\u00fcnyaya tan\u0131tt\u0131. O y\u0131l\u0131n sonunda T\u00fcrkiye\u2019ye d\u00f6nen Cahit Arf ayn\u0131 problemi bu kez aritmetik a\u00e7\u0131dan inceledi, yani problemi bu kez karakteristi\u011fi iki olan bir cisim \u00fczerindeki formel seriler halkas\u0131 \u00fczerinde ele ald\u0131. Bu \u00e7al\u0131\u015fmas\u0131 1943\u2032te \u201c\u0130stanbul \u00dcniversitesi Fen Fak\u00fcltesi Mecmuas\u0131\u201dnda yay\u0131mland\u0131.<\/span><\/p>\n

1945\u2032lere gelindi\u011finde d\u00fczlem bir e\u011frinin herhangi bir kolundaki \u00e7okkat noktalar\u0131n \u00e7okkatl\u0131l\u0131klar\u0131n\u0131n yaln\u0131z aritmeti\u011fe ait bir y\u00f6ntem ile nas\u0131l hesaplanaca\u011f\u0131 iyi bilinmekteydi. D\u00fczlem halde, algoritman\u0131n ba\u015flad\u0131\u011f\u0131 say\u0131lar e\u011fri kolunun parametreli denklemlerinden bilinen bir kanuna g\u00f6re elde ediliyordu. Genel durumda ise b\u00f6yle bir sonu\u00e7 hen\u00fcz bulunamam\u0131\u015ft\u0131. Bu s\u0131ralarda \u0130stanbul\u00d5da Patrick du Val ad\u0131nda bir \u0130ngiliz matematik\u00e7i bulunuyordu. Du Val genel halde algoritman\u0131n ba\u015flad\u0131\u011f\u0131 say\u0131lara \u201ckarakter\u201d ad\u0131n\u0131 vermi\u015f ve e\u011frinin t\u00fcm geometrik \u00f6zellikleri bilindi\u011fi zaman bu karakterlerin nas\u0131l bulunaca\u011f\u0131n\u0131 g\u00f6stermi\u015fti. Bunun tersi de do\u011fruydu: bu karakterler bilinirse e\u011frinin \u00e7okkatl\u0131l\u0131k dizisi, yani geometrik \u00f6zellikleri de bulunabiliyordu. Burada a\u00e7\u0131k kalan problem ise bir e\u011frinin parametreli denklemleri verildi\u011finde karakterlerini bulabilmek idi. Cevap d\u00fczlem e\u011friler i\u00e7in bilinmekte, ama y\u00fcksek boyutlu uzaylarda bulunan tekil e\u011friler i\u00e7in bilinmemekte idi. Ayr\u0131ca y\u00fcksek boyutlu bir uzayda tan\u0131mlanm\u0131\u015f bir tekil e\u011frinin \u00e7okkatl\u0131l\u0131k \u00f6zelliklerini, yani geometrik \u00f6zelliklerini bozmadan en d\u00fc\u015f\u00fck ka\u00e7 boyutlu uzaya sokulabilece\u011fi de bu problemle beraber d\u00fc\u015f\u00fcn\u00fclen bir soru idi. Bu \u00e7e\u015fit sorular, matematiksel bak\u0131\u015f a\u00e7\u0131s\u0131n\u0131n temel problemi olan s\u0131n\u0131fland\u0131rma probleminin e\u011frilere uygulanmas\u0131 bak\u0131m\u0131ndan son derece \u00f6nemli ve zor sorulard\u0131r. Cahit Arf bu problemi 1945\u2032te tamam\u0131yla \u00e7\u00f6zm\u00fc\u015f ve tek boyutlu tekil cebirsel kollar\u0131n s\u0131n\u0131fland\u0131r\u0131lmas\u0131 problemini kapatm\u0131\u015ft\u0131r. Bu sonucun zorlu\u011fu hakk\u0131nda fikir elde edebilmek i\u00e7in d\u00fczg\u00fcn varyetelerin s\u0131n\u0131fland\u0131r\u0131lmas\u0131 probleminin bug\u00fcne kadar yaln\u0131z 1, 2 ve k\u0131smen 3 boyutlu varyeteler i\u00e7in \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fcn\u00fc, tekilliklerin s\u0131n\u0131fland\u0131r\u0131lmas\u0131 probleminin ise 1 boyutlu varyeteler, e\u011friler i\u00e7in Cahit Arf taraf\u0131ndan \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fcn\u00fc g\u00f6z \u00f6n\u00fcne almak gerekir. Cahit Arf bu problemi \u00e7\u00f6zerken \u00f6nemini g\u00f6zledi\u011fi ve problemin \u00e7\u00f6z\u00fcm\u00fcnde en \u00f6nemli rol\u00fc oynad\u0131\u011f\u0131n\u0131 fark etti\u011fi baz\u0131 halkalara \u201ckarakteristik halka\u201d ad\u0131n\u0131 vermi\u015f ve daha sonra gelen yabanc\u0131 ara\u015ft\u0131rmac\u0131lar bu halkalara \u201cArf halkalar\u0131\u201d ve bunlar\u0131n kapan\u0131\u015flar\u0131na \u201cArf kapan\u0131\u015flar\u0131\u201d ad\u0131n\u0131 vermi\u015flerdir. Bug\u00fcn matematik literat\u00fcr\u00fcnde bu halkalar bu adlar\u0131 ta\u015f\u0131maktad\u0131r. Cahit Arf\u2019\u0131n bu \u00e7al\u0131\u015fmas\u0131 1949\u2032da Proceedings of London Mathematical Society dergisinde yay\u0131mlanm\u0131\u015ft\u0131r.<\/span><\/p>\n

Bundan sonra, bir d\u00f6nem Cahit Arf m\u00fchendislik problemleri ile ilgilendi. B\u00fct\u00fcnl\u00fc\u011f\u00fc bozmamak i\u00e7in onlar\u0131n ayr\u0131ca ele al\u0131nmas\u0131 uygun olacakt\u0131r.<\/span><\/p>\n

1955 y\u0131l\u0131nda Almanya\u2019da yay\u0131mlanan bir \u00e7al\u0131\u015fmas\u0131 lokal cisimlerle ilgili \u00e7ok \u00f6nemli bir in\u015fa problemidir. \u015eunu belirtmek gerekir ki bu \u00e7al\u0131\u015fmas\u0131 onun hedefledi\u011fi ve tutku haline getirdi\u011fi birka\u00e7 problemden birisi olan \u201cabelyen olmayan s\u0131n\u0131f cisimleri teorisi\u201d i\u00e7in bir \u00e7\u0131k\u0131\u015f noktas\u0131 olmu\u015ftur ve bu problem hala a\u00e7\u0131k bir problemdir. 1957 y\u0131l\u0131nda yine Almanya\u2019da \u201cRiemann-Roch Teoremi\u201d adl\u0131 \u00e7al\u0131\u015fmas\u0131 yay\u0131mlanm\u0131\u015ft\u0131r. Riemann\u2019\u0131n doktora tezinden \u00e7\u0131kan bu teorem \u00d4Kompleks Analizin\u2019 temel teoremlerinden biridir. 1938 y\u0131l\u0131nda Weil bu teoremi fonksiyon cisimleri y\u00f6n\u00fcnden, 1957 y\u0131l\u0131nda Cahit Arf say\u0131 cisimleri y\u00f6n\u00fcnden in\u015fa etmi\u015ftir.<\/span><\/p>\n

Bu arada, \u015funu hat\u0131rlatmak gerekir: Matemati\u011fe her konuda temel katk\u0131lar\u0131yla unutulmaz bir 19. y\u00fczy\u0131l matematikcisi olan Riemann\u2019\u0131n 1859\u2032da b\u0131rakt\u0131\u011f\u0131 ve b\u00fct\u00fcn matematik\u00e7ileri heyecanland\u0131ran bir problem hala \u00e7\u00f6z\u00fcm beklemektedir. \u201cRiemann Hipotezi\u201d olarak bilinen bu problem, yine Riemann\u2019\u0131n tan\u0131mlad\u0131\u011f\u0131 ve \u201czeta fonksiyonu\u201d ad\u0131yla bilinen bir fonksiyonun b\u00fct\u00fcn s\u0131f\u0131rlar\u0131n\u0131n reel k\u0131s\u0131mlar\u0131n\u0131n 1\/2 olup olmad\u0131\u011f\u0131 problemidir. Cahit Arf 1980 y\u0131l\u0131ndan sonra \u00e7ok geni\u015f kapsaml\u0131 bir problem \u00fczerinde \u00e7al\u0131\u015f\u0131yordu. Bu problem \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fc takdirde yan \u00fcr\u00fcn olarak Riemann hipotezi de \u00e7\u00f6z\u00fclm\u00fc\u015f olacakt\u0131. Benim bildi\u011fim kadar\u0131yla sonlu cisim \u00fczerinde in\u015fa etti\u011fi ve bizim \u201cArf Zeta Fonksiyonu\u201d olarak adland\u0131rd\u0131\u011f\u0131m\u0131z bir fonksiyon Riemann hipotezini sa\u011flamakta idi, yani s\u0131f\u0131rlar\u0131n\u0131n reel k\u0131s\u0131mlar\u0131 1\/2 oluyordu. Cahit Arf bu projenin di\u011fer basamaklar\u0131 \u00fczerinde \u00e7al\u0131\u015fmalar\u0131n\u0131 s\u00fcrd\u00fcrd\u00fc, ancak hangi a\u015famaya kadar geldi\u011fini bilemiyorum. Ke\u015fke bu g\u00f6rkemli projeyi tamamlayabilseydi!<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\nBEM\u0130M G\u00d6Z\u00dcMLE CAH\u0130T ARF<\/strong><\/span><\/p>\n

Cahit Arf bilim d\u00fcnyas\u0131n\u0131n tart\u0131\u015fmas\u0131z en b\u00fcy\u00fck<\/strong><\/span><\/p>\n

adamlar\u0131ndan biriydi. D\u00fcnyaca tan\u0131n\u0131yordu. Ordinaryus<\/strong><\/span><\/p>\n

olmu\u015ftu.Bilimi herkese sevdirmeye \u00e7al\u0131\u015fm\u0131\u015ft\u0131. \u00d6ld\u00fc\u011f\u00fcnde<\/strong><\/span><\/p>\n

\u00e7al\u0131\u015fmalar\u0131 yar\u0131m kalm\u0131\u015ft\u0131; yani, b\u00fct\u00fcn \u00f6mr\u00fcn\u00fc matemati\u011fe<\/strong><\/span><\/p>\n

adam\u0131\u015ft\u0131. Kendi ad\u0131 verilen halka teorisi ile matematikte<\/strong><\/span><\/p>\n

koskoca bir y\u00fcz y\u0131la damgas\u0131n\u0131 vurmu\u015ftu.<\/strong><\/span><\/p>\n

\u0130lkokul \u00e7a\u011f\u0131nda hemen hemen herkes gibi O\u0092 da matemati\u011fi sevmiyordu.O\u0092 nu soka\u011fa oynamas\u0131 i\u00e7in g\u00f6ndermiyorlard\u0131. O\u0092 da kendi i\u00e7inde bir \u015feyler yapm\u0131\u015ft\u0131. Kendi oyununu kendi kuruyordu. \u00c7ocuklu\u011funda daima ka\u011f\u0131ttan oyuncaklar yapard\u0131. Bu bir bak\u0131ma iyi olmu\u015ftu. Oyuncak icat ediyor daima etraf\u0131n\u0131 inceliyordu.<\/span><\/p>\n

Matemati\u011fe hevesi olmamakla birlikte lineer (do\u011frusal) denkleme dayal\u0131 problemleri \u00e7\u00f6zmekte zorlanmayan Arf, kendisindeki bu yetene\u011fi be\u015finci s\u0131n\u0131fta okurken kar\u015f\u0131la\u015ft\u0131\u011f\u0131 lise mezunu bir \u00f6\u011fretmen ortaya \u00e7\u0131karm\u0131\u015ft\u0131. Bu \u00f6\u011fretmen Arf\u0092\u0131n kendine g\u00fcven duymas\u0131n\u0131 sa\u011flad\u0131. Arf bu h\u0131zla okulda b\u00fcy\u00fck ba\u015far\u0131lar elde etti ve babas\u0131 taraf\u0131ndan Fransa\u0092 ya g\u00f6nderildi.<\/span><\/p>\n

YAZININ DEVAMI \u0130\u00c7\u0130N SAYFA NUMARALARINI TIKLAYINIZ<\/strong><\/span><\/p>\n


\nArf , matematik \u0096 \u00f6l\u00fcms\u00fczl\u00fck ili\u015fkisini \u015f\u00f6yle s\u00f6yledi:<\/strong><\/span><\/p>\n

\u0093Bu sonsuzluklar\u0131 t\u00fcmevar\u0131msal yani , bilinen birtak\u0131m g\u00f6zlemlere dayanarak bunlar\u0131 a\u00e7\u0131klayan bir \u00f6nermeye ge\u00e7me i\u015flemi , gibi bir \u015fekilde kavr\u0131yoruz ve bu bize mutluluk veriyor. \u00c7\u00fcnk\u00fc \u00f6l\u00fcm\u00fc unutmuyoruz\u2026 Herkes \u00f6l\u00fcms\u00fcz oldu\u011fu alanda \u00e7al\u0131\u015fmak ister. Ben de matematikte kendimi \u00f6l\u00fcms\u00fcz hissettim\u2026\u0094<\/span><\/p>\n

Profes\u00f6r Arf, \u201cHasse – Arf teoremi\u201d ile matematik d\u00fcnyas\u0131nda tan\u0131nd\u0131. Geometri problemlerini cetvel ve pergelle \u00e7\u00f6z\u00fclebilir olup olmad\u0131klar\u0131na g\u00f6re s\u0131n\u0131fland\u0131rmay\u0131 tasarlayan Arf, yaln\u0131zca ikinci dereceden cebirsel denklemlere indirgenebilen problemlerin cetvel ve pergel yard\u0131m\u0131yla \u00e7\u00f6z\u00fclebilece\u011fini saptad\u0131. Baz\u0131 cisimleri s\u0131n\u0131fland\u0131r\u0131p, de\u011fi\u015fmezlerini saptad\u0131. Bu \u00e7al\u0131\u015fmada ortaya \u00e7\u0131kan \u201cArf de\u011fi\u015fmezi\u201d terimi onun matematik d\u00fcnyas\u0131ndaki \u00fcn\u00fcn\u00fc artt\u0131rd\u0131. Ayr\u0131ca, \u201cArf halkalar\u0131\u201d ve \u201cArf kapan\u0131\u015flar\u0131\u201d kavramlar\u0131yla tan\u0131nd\u0131. Arf, son y\u0131llarda da matemati\u011fin biyoloji bilimi i\u00e7indeki olas\u0131 uygulamalar\u0131 \u00fczerinde \u00e7al\u0131\u015fmalar yap\u0131yordu.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

CAH\u0130T ARF\u0092IN HAYATI 1910`da Selanik`te do\u011fan Cahit Arf Y\u00fcksek\u00f6\u011frenimini Paris`te, Ecole Normale Superieure`de tamamlad\u0131.Galatasaray Lisesi`nde matematik \u00f6\u011fretmeni, \u0130stanbul \u00dcniversitesi Fen Fak\u00fcltesi`nde do\u00e7ent aday\u0131 olarak \u00e7al\u0131\u015ft\u0131.1938 y\u0131l\u0131nda G\u00f6ttingen \u00dcniversitesi`nden doktoras\u0131n\u0131 ald\u0131ktan sonra da \u0130stanbul \u00dcniversitesi`ndeki g\u00f6revini s\u00fcrd\u00fcrd\u00fc.1943`te profes\u00f6r, 1955`de ordinary\u00fcs profes\u00f6r oldu. Bu arada Maryland \u00dcniversitesi`nde misafir profes\u00f6r olarak \u00e7al\u0131\u015ft\u0131 ve Mainz Akademisi muhabir \u00fcyeli\u011fine se\u00e7ildi. …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[57,58,56],"class_list":["post-201","post","type-post","status-publish","format-standard","hentry","category-genel","tag-10-liranin-arkasindaki-matematikci","tag-arf-teoremi","tag-cahit-arf"],"aioseo_notices":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2YBEC-3f","jetpack_sharing_enabled":true,"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/201","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=201"}],"version-history":[{"count":0,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/201\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}