xn+yn=zn: no solutions
'x^n+y^n=z^n: no solutions
'I have discovered a truly remarkable proof of this, but I can't write it now because my train is coming.'
Graffiti on New York's Eighth street subway station.
The equation x^n+y^n=z^n looks petty straightforward. After all n=2 is the classic Pythagoras theorem, but for any value of n greater than 2 there are no whole number solutions. Around 1637 Pierre de Fermat discovered this and mentioned it as a margin note along with the enigmatic remark that would haunt mathematicians for three centuries to come 'I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain'. It was another 358 before the English mathematician Andrew Wiles could finally prove Fermat's proposition. This book is the story of Fermat's last Theorem, from it's origins in ancient Greece, through to it's final solution. Although covering some rather complex, indeed mind boggling ideas this book is an excellent read. Rather like 'The Mummy Congress' it laces the academic material with colourful sketches of the personalities involved. For the more mathematically minded there are a series of appendixes illustrating various proofs. My favourite was Bertrand Russell's paradox of the meticulous librarian who discovers in his library a number of catalogues of catalogues. He creates two additional catalogues one listing those catalogues that list themselves and one those which do not, and then become stuck on the question 'should the catalogue that lists all catalogues that do not list themselves be listed in itself?'
362 pages, published by Fourth Estate
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