1樓：十七畫
雖然Artin不是在做習題，但其心路歷程或許對題主有所啟發。所以我摘過來這個故事。他提到的互反律今天我們稱作Artin互反律，是那個時代最璀璨的定理之一
I will tell you a story about the Reciprocity Law. After my thesis, I had the
idea to define L-series for non-abelian extensions. But for them to agree with
the L-series for abelian extensions, a certain isomorphism had to be true. I
could show it implied all the standard reciprocity laws. So I called it the General
Reciprocity Law and tried to prove it but couldn』t, even after many tries.
Then I showed it to the other number theorists, but they all laughed at it, and
I remember Hasse in particular telling me it couldn』t possibly be true. Still, I
kept at it, but nothing I tried worked. Not a week went by — for three years
! — that I did not try to prove the Reciprocity Law. It was discouraging, and
meanwhile I turned to other things. Then one afternoon I had nothing special
to do, so I said, 「Well, I try to prove the Reciprocity Law again.」 So I went out
and sat down in the garden. You see, from the very beginning I had the idea to
use the cyclotomic fields, but they never worked, and now I suddenly saw that
all this time I had been using them in the wrong way — and in half an hour I
had it.
Emil Artin, as recalled by Mattuck (in Recountings: Conversations with
MIT Mathematicians 2009).
考研數學三可以不去看證明題嗎
白日夢想家 我跟你想法類似，現在只做計算。但可能後面會一些典型證明的專題，直接扔了還是有點慌 才發現是一年前的問題，請問你最後怎麼選擇了呢？可否傳授一些經驗 like you 巧了，我也是。基本上每一道都不會，但是我還是認真看完答案理解，並重新做了一遍。畢竟這個對提公升邏輯能力有很大幫助。我想送你一...
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予一人 儘管你在很多書上或者從你的老師口中聽到的都是，洛必達法則只適用於 的情形。但事實上，對於後面一種情形，並不需要分子也是 只要分母 就夠了，這就是說，對於 的情形也可以使用洛必達。至於理由，要回歸到洛必達法則的證明，在那個證明裡並沒有用到分子趨於 的條件。如果你不滿意這樣的證明方式，你可以換一...