{"id":1008,"date":"2017-10-21T12:10:20","date_gmt":"2017-10-21T12:10:20","guid":{"rendered":"http:\/\/ragipsahin.com\/?p=1008"},"modified":"2017-10-21T12:09:59","modified_gmt":"2017-10-21T12:09:59","slug":"duelloda-olen-matematikci","status":"publish","type":"post","link":"https:\/\/www.ragipsahin.com.tr\/?p=1008","title":{"rendered":"D\u00fcelloda \u00d6len Matematik\u00e7i"},"content":{"rendered":"

Bu yak\u0131n \u00e7a\u011f yazarlar\u0131n\u0131n nas\u0131l bu kadar romantik olduklar\u0131na \u015fa\u015f\u0131rmamak gerekiyor. Adamlar\u0131n ya\u015fad\u0131\u011f\u0131 \u00e7a\u011f\u0131n gere\u011fi. Son as\u0131rda d\u00fcello s\u0131ras\u0131nda vurulup \u00f6len ka\u00e7 matematik\u00e7i biliyorsunuz ki ?<\/span><\/p>\n

S\u00f6z\u00fc fazla uzatmadan pek fazla tan\u0131nmayan bir matematik\u00e7iden bahstmek istiyorum.<\/p>\n

Frans\u0131z matematik\u00e7isi Galois, 1811-1832 y\u0131llar\u0131 aras\u0131nda ya\u015fad\u0131. Abel’in \u00e7a\u011fda\u015f\u0131 olan bu matematik\u00e7inin do\u011fum ve \u00f6l\u00fcm tarihlerine bakarsan\u0131z 21 y\u0131ll\u0131k bir \u00f6m\u00fcr s\u00fcrd\u00fc\u011f\u00fcn\u00fc g\u00f6r\u00fcr ve bu i\u015fte bir yanl\u0131\u015fl\u0131k oldu\u011funu d\u00fc\u015f\u00fcnebilirsiniz. Hi\u00e7bir yanl\u0131\u015fl\u0131k yok. Galois’n\u0131n hayat\u0131 Brezilya dizilerine konu olmaya aday \u015fanss\u0131zl\u0131klarla s\u00fcr\u00fcp gitmi\u015f ve 21 y\u0131lda t\u00fckenmi\u015ftir.Frans\u0131z matematik\u00e7isi Galois, 1811-1832 y\u0131llar\u0131 aras\u0131nda ya\u015fad\u0131. Abel’in \u00e7a\u011fda\u015f\u0131 olan bu matematik\u00e7inin do\u011fum ve \u00f6l\u00fcm tarihlerine bakarsan\u0131z 21 y\u0131ll\u0131k bir \u00f6m\u00fcr s\u00fcrd\u00fc\u011f\u00fcn\u00fc g\u00f6r\u00fcr ve bu i\u015fte bir yanl\u0131\u015fl\u0131k oldu\u011funu d\u00fc\u015f\u00fcnebilirsiniz. Hi\u00e7bir yanl\u0131\u015fl\u0131k yok. Galois’n\u0131n hayat\u0131 Brezilya dizilerine konu olmaya aday \u015fanss\u0131zl\u0131klarla s\u00fcr\u00fcp gitmi\u015f ve 21 y\u0131lda t\u00fckenmi\u015ftir.<\/span><\/p>\n

Paris yak\u0131nlar\u0131ndaki k\u00fc\u00e7\u00fck bir kasaban\u0131n belediye ba\u015fkan\u0131n\u0131n o\u011flu olan Galois, matemati\u011fe okul ya\u015fam\u0131 s\u0131ras\u0131nda ilgi duymaya ba\u015flam\u0131\u015f ve 14 ya\u015f\u0131ndayken Lagrange ve Abel’in eserlerini okumu\u015ftur.S\u0131n\u0131fta, b\u00fcy\u00fck matematik\u00e7ilerin kuramlar\u0131 \u00fczerine d\u00fc\u015f\u00fcnmesi, \u00f6devlerini unutmas\u0131 ve dikkatsizli\u011fi nedeniyle \u00f6\u011fretmenlerini k\u0131zd\u0131rd\u0131\u011f\u0131 bilinmektedir. Galois’in matemati\u011fe kar\u015f\u0131 duydu\u011fu sevgi o kadar b\u00fcy\u00fckt\u00fc ki birg\u00fcn \u00f6\u011fretmenlerinden birisi, “Anne-babas\u0131n\u0131n Galois’e sadece matematik dersi ald\u0131rmalar\u0131n\u0131n iyi olaca\u011f\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcyorum.” demi\u015ftir.<\/p>\n

Daha 16 ya\u015f\u0131nda iken pek \u00e7ok matematik klasi\u011fini okumu\u015f olmas\u0131na ra\u011fmen \u00fcniversiteye kabul edilmedi. Kendisini kan\u0131tlayabilmek i\u00e7in 17 ya\u015f\u0131nda zaman\u0131n tan\u0131nm\u0131\u015f matematik\u00e7ilerinden Cauchy’ye verdi\u011fi makalesini Cauchy kaybetti. 18 ya\u015f\u0131ndayken bir yar\u0131\u015fmaya soktu\u011fu bir di\u011fer makalesi de, yar\u0131\u015fman\u0131n hakemi Fourier \u00f6l\u00fcnce kayboldu. Zorla girebildi\u011fi \u00f6\u011fretmen okulundan, okul y\u00f6netimini ele\u015ftirdi\u011fi i\u00e7in kovuldu. Bir dergiye sundu\u011fu bir ba\u015fka makalesi, hakem ispatlar\u0131n i\u00e7inden \u00e7\u0131kamad\u0131\u011f\u0131 i\u00e7in reddedildi. Bir taraftan matematik dersleri vererek hayat\u0131n\u0131 kazanmaya \u00e7al\u0131\u015fan Galois bir tarfatan da siyasete bula\u015fm\u0131\u015ft\u0131r. 1830 Devrimi’ne Cumhuriyet\u00e7i olarak kat\u0131ld\u0131. Siyasi nedenlerle de iki kez hapse girip \u00e7\u0131kt\u0131.<\/p>\n

Ve nihayet, ertesi sabah d\u00fcello edece\u011fi, o so\u011fuk may\u0131s gecesi gelip \u00e7atar. Galois hen\u00fcz 21 ya\u015f\u0131ndad\u0131r. T\u00fcm hayat\u0131 siyasi fikirler ve matematik teorileriyle ge\u00e7mi\u015f bir gen\u00e7 elbette insan \u00f6ld\u00fcrme ‘sanat\u0131’ \u00fczerine bilgisizdir. \u00d6ld\u00fcr\u00fclece\u011fini anlar. Oysa daha kafas\u0131ndaki matematik fikirlerini olgunla\u015ft\u0131racak zaman\u0131 olmam\u0131\u015ft\u0131r. \u00d6l\u00fcm\u00fcn bekleme odas\u0131nda volta vurdu\u011fu bir saatte bu gen\u00e7 adam insano\u011flunun \u00f6l\u00fcms\u00fczler listesine ad\u0131n\u0131 yazd\u0131rmak i\u00e7in son kez hamle yapar. Bu son gece arkada\u015f\u0131 Chavelier’e bir mektup yazar. Bu mektupta Gauss’un kulland\u0131\u011f\u0131 baz\u0131 teknikleri genelle\u015ftirerek, derecesi d\u00f6rtten b\u00fcy\u00fck olan her polinom i\u00e7in \u00e7al\u0131\u015facak bir ‘k\u00f6k bulma y\u00f6ntemi’ bulman\u0131n neden imkans\u0131z oldu\u011funu anlat\u0131r. \u0130\u00e7inde k\u00f6kleri arad\u0131\u011f\u0131m\u0131z say\u0131 sistemleri “cisimler” ile k\u00f6kleri kendi aras\u0131nda d\u00f6nd\u00fcren perm\u00fctasyon “gruplar\u0131” aras\u0131nda daha \u00f6nce g\u00f6zlenmemi\u015f ili\u015fkiler bulur. Bu ili\u015fkiler yuma\u011f\u0131na bug\u00fcn genel olarak Galois teorisi denir.<\/p>\n

Denklemin katsay\u0131lar\u0131n\u0131 i\u00e7ine alan say\u0131 sistemine denklemin t\u00fcm k\u00f6klerini teker teker katarak sistemi b\u00fcy\u00fctt\u00fc\u011f\u00fcm\u00fcz\u00fc d\u00fc\u015f\u00fcnelim. \u00d6te yandan t\u00fcm k\u00f6kleri kendi aras\u0131nda d\u00f6n\u00fc\u015ft\u00fcren perm\u00fctasyon grubu ve onun baz\u0131 k\u00f6kleri sabit b\u0131rakan alt gruplar\u0131n\u0131 d\u00fc\u015f\u00fcnelim. Galois bu iki d\u00fcnya aras\u0131nda k\u00f6pr\u00fc kurar ve bir taraftaki k\u00f6k bulma problemini, \u00f6b\u00fcr tarafta bir grubun yap\u0131s\u0131n\u0131 inceleme problemine d\u00f6n\u00fc\u015ft\u00fcr\u00fcr. G\u00f6r\u00fcr ki, e\u011fer bu tarafta k\u00f6k bulunabiliyorsa \u00f6b\u00fcr tarafta da grubun \u00f6zel bir yap\u0131s\u0131 olmas\u0131 gerekir. Oysa bu \u00f6zel yap\u0131n\u0131n, derecesi d\u00f6rtten b\u00fcy\u00fck denklemelere kar\u015f\u0131l\u0131k gelen gruplarda, her zaman olmad\u0131\u011f\u0131n\u0131 tespit eder.<\/p>\n

Sonu\u00e7 olarak insanl\u0131\u011f\u0131n iki bin y\u0131ld\u0131r arad\u0131\u011f\u0131 k\u00f6kler, basit cebirsel y\u00f6ntemlerle bulunamaz. \u0130\u015fte Galois teorisinin basit bir \u00f6zeti. Belki bu ‘basit’ a\u00e7\u0131klama size gere\u011finden fazla ayr\u0131nt\u0131l\u0131 ve teknik gelmi\u015f olabilir. Daha k\u0131sa ve daha \u00f6z Galois teorisini neden anlatamayaca\u011f\u0131m\u0131 Galois teorisi hakk\u0131nda s\u00f6ylenen bir s\u00f6zle a\u00e7\u0131klayay\u0131m; “Galois teorisi sar\u0131msa\u011fa benzer, az\u0131 olmaz…”<\/p>\n

Galois’n\u0131n mektubu \u00f6l\u00fcms\u00fczl\u00fc\u011fe do\u011fru f\u0131rlat\u0131lm\u0131\u015f bir \u00e7\u0131\u011fl\u0131kla biter: ” B\u00fct\u00fcn bu karma\u015f\u0131k hesaplar\u0131 a\u00e7makta kendisine yarar g\u00f6recek birilerinin \u00e7\u0131kaca\u011f\u0131n\u0131 umar\u0131m.” Ertesi g\u00fcn d\u00fcelloda vurulur. Hastanede bir g\u00fcn can \u00e7eki\u015ftikten sonra \u00f6l\u00fcr. Arkada\u015f\u0131 bu mektubu \u00fc\u00e7 ay sonra yay\u0131nlarsa da mektup ilgi g\u00f6rmez. makalelerinin \u00e7o\u011fu 1846’da yay\u0131mlan\u0131ncaya kadar g\u00fcn \u0131\u015f\u0131\u011f\u0131na \u00e7\u0131kmam\u0131\u015ft\u0131r. Bu tarihte Cauchy, grup kuram\u0131 hakk\u0131nda yay\u0131nlar yapmaya ba\u015flay\u0131nca, Galois’in \u00e7al\u0131\u015fmalar\u0131 da matematik\u00e7ilerin ilgisini \u00e7ekmi\u015ftir.<\/p>\n

Galois’in \u00f6neminin tam olarak anla\u015f\u0131lmas\u0131, Camille Jordan’\u0131n 1870 y\u0131l\u0131ndaki yay\u0131mlar\u0131yla ger\u00e7ekle\u015fmi\u015ftir. E\u011fer Galois, Newton ya da Gauss gibi uzun y\u0131llar ya\u015fam\u0131\u015f olsayd\u0131, matemati\u011fe yapaca\u011f\u0131 katk\u0131lar\u0131n \u00e7ok daha fazla olaca\u011f\u0131 kesindir.<\/p>\n

Bu arada \u00f6lmeden \u00f6nce yazm\u0131\u015f oldu\u011fu notta bahsetti\u011fi hesaplamal\u0131 ve teoremi hen\u00fcz hesaplayan bir matematik\u00e7i yoktur…<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Bu yak\u0131n \u00e7a\u011f yazarlar\u0131n\u0131n nas\u0131l bu kadar romantik olduklar\u0131na \u015fa\u015f\u0131rmamak gerekiyor. Adamlar\u0131n ya\u015fad\u0131\u011f\u0131 \u00e7a\u011f\u0131n gere\u011fi. Son as\u0131rda d\u00fcello s\u0131ras\u0131nda vurulup \u00f6len ka\u00e7 matematik\u00e7i biliyorsunuz ki ? S\u00f6z\u00fc fazla uzatmadan pek fazla tan\u0131nmayan bir matematik\u00e7iden bahstmek istiyorum. Frans\u0131z matematik\u00e7isi Galois, 1811-1832 y\u0131llar\u0131 aras\u0131nda ya\u015fad\u0131. Abel’in \u00e7a\u011fda\u015f\u0131 olan bu matematik\u00e7inin do\u011fum ve \u00f6l\u00fcm tarihlerine bakarsan\u0131z 21 y\u0131ll\u0131k …<\/p>\n","protected":false},"author":1,"featured_media":19654,"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":[409,410],"class_list":["post-1008","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-genel","tag-duelloda-olen-matematikci","tag-galois"],"aioseo_notices":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.ragipsahin.com.tr\/wp-content\/uploads\/2016\/11\/d%C3%BCelloda-%C3%B6len-matematik%C3%A7i.png?fit=741%2C486&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/p2YBEC-gg","jetpack_sharing_enabled":true,"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/1008","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=1008"}],"version-history":[{"count":0,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/posts\/1008\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=\/wp\/v2\/media\/19654"}],"wp:attachment":[{"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ragipsahin.com.tr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}