現代数学の系譜工学物理雑談古典ガロア理論も読む46

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164: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2017/11/14(火) 20:42:07.06 ID:agSxZaXK

>>159

ガロア語録 "On jugera"：「証明は思いつくであろう」（＾＾
スレ4 https://uni.5ch.net/test/read.cgi/math/1335598642/229
229 返信：現代数学の系譜11 ガロア理論を読む[] 投稿日：2012/05/11(金) 07:53:48.30
下記"On jugera"について
the crucial lemmaは、>>3では、第III節の定理で
"On jugera"：「証明は思いつくであろう」と守屋は訳している
”My opinion is in paragraph 37" (freely translated)”は、Edwards (著) Galois Theory>>174の序文 ページixの通りなので、この文はここから採ったのだろう

http://www2.ee.ufpe.br/codec/BITOFHISTORY.html
A BIT OF HISTORY: GALOIS' LIFE.

ON THE STATEMENT "On jugera".

This famous passage is the one where Galois proves the crucial lemma stating that any rational function of the roots can be expressed as a rational function of the Galois resolvent.
Poisson (What about him?) had called Galois' prove insufficient. Galois, rather than elucidate his proof, laconically replied, "That remains to be seen.
My opinion is in paragraph 37" (freely translated).
It is easy to understand Poisson's position. Galois' proof can be regarded as as, at best, a sketch, and therefore is certainly "insufficient" if one is in any doubt as to the correctness of his theory and the accuracy of his reasoning.
In his report to the Academy, Poisson said of Galois' memoir as a whole that
<< We have made every effort to understand Mr. Galois' proof. His argument are not clear enough, nor developed enough, for us to be able to judge their correctness... >>.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1510442940/164

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