《費馬大定理》费马大定理：数学历史的趣味探索

(n+1)^2 - n*2=2n+1，会遍历所有奇数。而奇数中含有无穷多的完全平方数。 - 支线: Stoicheia, geometry - find the first irrational number: proved √2 is irrational using reductio ad absurdum - fundamental theorem of arithmetics: 质因数分解是唯一的

Fermat（1607） - 主线: (1) 提出费马大定理 (2) 使用 method of inifinite descent 证明了 n=4 的情况

Leonhard Euler（1707-1783） - 主线：利用17世纪发明的复数，解决 n=3 的问题 - 支线：欧拉猜想，和费马大定理形式类似。是一个有趣的错误的猜想：反例非常难找，于1966年才被推翻。1988年才找到 n=4 的反例。

Johann Carl Friedrich Gauss（1777-1855） - 主线：帮助女性数学家 Sophie Germain(1776-1831)，使后者 proved the theorem for n=p−1, where p is a prime number of the form p=8k+7, with a weak assumption - 支线：PNT Prime nummber theorem - a) Primes become less common as they become larger. Precise quantification proved in 1896. - b) 还有一个有关超难找的反例的故事：There is a Gausss formula which underestimated the number of the primes. However, the counterexample is extremely large. Its like the total number of games when using all the particles in the universe (10^87) to play chess. (P179) 1931 - c) 还有一个：31，331，3331，一直到33333331都是质数，但333333331=117*19608843.

Ernst Eduard Kummer(1801-1893) - 主线：In 1848, Cauchy & Lamé were competing for proving Fermats Last Theorem. But Kummer pointed out a crucial mistake: in the field of complex numbers, Euclids fundamental theorem of arithmetics doesnt hold. The factorization of complex numbers is not unique. For example, 12=(1+√-11)(1-√-11), which leads to the failure of their proofs for irregular primes.

Cantor（