Having read and appreciated a few layman books on physics in general and quantum physics in particular, I was looking for a good book with a little bit of ’comprehendible mathematics’.
The book by Simon Singh, an Englishman of Punjabi descent, provided me with all that I wanted. In fact, I had come across the Fermat’s Last Theorem during my twelfth year of study in an encyclopedia, but unlike Andrew Wiles, who went on to prove it beyond any doubt, I was just happy to know that a riddle so simple and elegantly stated( the sum of x to the power of n and y to the power of n can never equal another whole number, say z, to the same power of n for n greater than 2) could challenge mathematicians for centuries altogether. When I picked up the book....I wondered, with a good amount of skepticism, about the necessity for someone to write a whole book of more than 350 pages. But then, the first few pages of the preface was sufficient to convince me that the story of the fermat’s theorem was inextricably linked with the history of mathematics, more specifically with the history of number theory. As the author himself states, ’The Last Theorem is at the heart of an intriguing saga of courage, skulduggery, cunning and tragedy, involving all the greatest heroes of mathematics.’
The exciting story starts with Pythagoras and his famous theorem which forms the cornerstone of Trigonometry. The theorem which states that the square on the hypotenuse of every right angled triangle is equal to the sum of the squares on the other two sides, has been recorded in the Guiness book of records as the theorem that has the maximum number of different proofs, 108 in all, and one by an American President too! Not only does the author touch upon the mathematical significance of the theorem but also shares with his readers, a certain amount of social history of those times as well as the personality of mathematicians in context. In the first few chapters the reader would find interesting facets of number theory like the concept of perfect numbers, irrational numbers, friendly numbers. Also provided are a few snippets which make reading the book much more enthralling. The journey continues with Pierre de Fermat’s characterisation followed by attempts to prove it, starting from Leonard Euler, Sophie Germain, Augustin Cauchy, Alan Turing to our dear Andrew Wiles. Significantly each attempt to solve the Theorem not only provided the future generation of mathematicians powerful ideas and tools but also lead towards igniting sufficient amount of passion towards a vision of grand unified mathematics.
A significant portion of the book is dedicated to the Taniyama-Shimura conjecture, a work of Goro Shimura and Yutaka Taniyama, two young Japanese mathematicians, the proof of which implied absolute truth of the Fermat’s conundrum. The author has undoubtedly captured the creativity and heroism involved in the quest for the truth. Apart from this the book gives a brief account of the existing unsolved riddles of mathematics along with a series of appendices which expand on the mathematical ideas contained in the text. This popular book makes each reader realise that there is a world of beauty and intellectual challenge in a field considered dull by most of us. Thanks Simon Singh!