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A riproaring romp through the history of maths
am 15. September 1998
Pierre de Fermat was a state official in seventeenth century France. Forbidden from fraternizing with the locals (whom he might meet in the course of business) he resorted to a solitary hobby -- mathematics. His talent was prodigious, but he was notorious for leaving only sketches of the proofs of his conjectures for others to complete. Over the centuries, all his conjectures were proved correct by others -- except one, that defied all attempts to crack it. Musing on equations in a tome on arithmetic by classical mathematician Diophantus, Fermat looked at the equation x^n + y^n = z^n, and conjectured that there would be no whole-number solutions for x, y or z where n is any whole number greater than 2. He hinted that he had found a proof -- but never delivered. So simply stated, yet so hard to crack, the problem tantalized generations of mathematicians and would-be-mathematicians. Simon Singh tells the story of how a British-born mathematician working in the US, Andrew Wiles, worked in secret for 7 years, throwing every 20th-century technique at Fermat's puzzle, and eventually solving it. But did he? An error was found in his huge proof, hundreds of pages long, that took "a year of hell" to solve. Writing engagingly about maths is very hard, but Singh cuts through the technicalities to deliver a page-turner worthy of every airport lounge. I cried real tears at the part where Wiles descends from his attic den to announce to his (presumably long-suffering) wife that he had solved the 350-year-old riddle. I did have one or two puzzles of my own: first, I think Singh skates a little too much over certain mathematical technicalities that it would have done no harm to delve into a little, such as the critical field of modular forms. Ian Stewart does not shy from these in his (admittedly terser) 'From here To Infinity'. Second, the puzzle still lingers -- Wiles solved the problem with modern maths that would have been unavailable to Fermat. So did Fermat really have a proof in mind -- or didn't he?