Fermat's Last Theorem

Simon Singh

For $n$ larger than $3$ , the equation $z^{n} = x^{n} + y^{n}$ does not have an integer solution.

Bluffer’s guide to Fermat’s Last Theorem

페르마의 메모

p90 그는 ‘아리스메티카’ 8번 문제 다음에 있는 여백에 다음과 같은 주석을 달아놓았다.

Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duoso eiusdem nominis fas est dividere. 임의의 세제곱수는 다른 두 세제곱수의 합으로 표현될 수 없다. 임의의 네제곱수 역시 다른 두 네제곱수의 합으로 표현될 수 없다. 일반적으로, 3이상의 지수를 가진 정수는 이와 동일한 지수를 가진 다른 두 수의 합으로 표현될 수 없다.

… 문제의 개요를 소개하는 그의 주석 밑에는 또 하나의 장난기 어린 주석�� 달려 ��다. 이것이야말로 향후 300여 년 간 전세계 수학자들의 자존심을 여지없이 짓밟아 놓은 역사적인 주석이었다.

Cuitus rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet. 나는 경이적인 방법으로 이 정리를 증명했다. 그러나 책의 여백이 너무 좁아 여기에 옮기지는 않겠다.

p297 그 당시 뉴욕 8번가의 지하철역에서는 다음과 같은 낙서가 발견되기도 했다.

이 방정식에는 정수해가 없다. 나는 경이적인 방법으로 이 정리를 증명했다. 그러나 지금 내가 탈 기차가 오고 있기 때문에 여기 적을 만한 시간이 없다.

Gauss

p.142 Gauss is widely acknowledged as being the most brilliant mathematician who has ever lived. While E. T. Bell referred to Fermat as the Prince of Amateurs, he called Gauss the Prince of Mathematicians.

In one letter he even displayed contempt for the problem. His friend the German astronomer Heinrich Olbers had written to Gauss encouraging him to compete for a prize which had been offered by the Paris Academy for a solution to Fermat’s challenge:

It seems to me, dear Gauss, that you should get busy about this.” Two weeks later Gauss replied, “I am very much obliged for your news concerning the Paris prize. But I confess that Fermat’s Last Theorem as an isolated proposition has very little interest for me, for I could easily lay down a multitude of such propositions, which one could neither prove nor disprove.

Gauss was entitled to his opinion, but Fermat had clearly stated that a proof existed. Historians have suspect that in the past Gauss had tried and failed to make any impact on the problem, and his response to Olbers was merely a case of intellectual sour grapes. Nonetheless when he received Germain’s letters he was sufficiently impressed by her breakthrough that he temporarily forgot his ambivalence towards Fermat’s Last Theorem.

But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe. A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: one is not astonished at it: the enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it. But when a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius. Indeed nothing could prove to me in so flattering and less equivocal manner that the attractions of this science, which has enriched my life with so many joys, are not chimerical, as the predilection with which you have honored it.