Fermat's Last Theorem
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.