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Fermat's Enigma by Simon Singh

I bought this book in the same bag sale (books sold by the bag) at our local library. Proving Fermat's last theorem is one of the most crowning achievements of 20th century Mathematics. Knowing a bit about mathematics and writing/teaching proofs for a living, I am familiar that the actual proof of the theorem is extremely complex. Even for an amateur Mathematician, understanding all the nuts and bolts of the proof itself would take several years. I was of the opinion that this book might be full of superficial pop culture mumbo-jumbo and was skeptical to pick it up. Of course, if one wants to write a book on Fermat's last theorem that can be understood by a layman, then everything has to be watered down, except for the statement. Once I started reading the book, I understood that this book was not just about the theorem, but more about the endeavor of Mathematics itself. 

The book takes us through the journey of the origins of proof based mathematics (Greeks), to Fermat, to Euler, Germain, Kummer, Taniyama and Shimura, to Ribet, to Wiles, to Galois, and finally back to Wiles. In each of the personalities introduced by Simon, he does not shy away from showing both the positive and the negative aspects of the life of mathematicians and the society they lived in. For example, the Greek mathematician Pythagoras who is considered as father of proof based mathematics killed Hippasus for demonstrating the existence of irrational numbers. Sophie Germain had to use a pseudonym of Le Blanc while sending letters/homeworks to other mathematicians because a woman was not legally allowed to enroll in mathematics classes.

More than anything, this book shows that mathematics is essentially a tradition that has been ongoing for 2000 years. This book explains how one mathematical discovery is based on the previous contributions of other mathematicians. This unbroken chain, while it holds true for all aspects of modern civilization, it particularly easy to see in the case of proof based mathematics. This social aspect of mathematics is often hidden in works dealing with "great men". The stereotype is that "great men" do everything by themselves. The fact that proving Fermat's last theorem required not only the tenacity and perseverance of  Andrew Wiles, but also the contributions by many other skilled mathematicians, makes it even more impressive. There is no one "great man" in mathematics, but rather, many great people. 

I think this is probably one of the very few popular books that can be written about a theorem. The simplicity of the statement of the theorem, the attempts for over 300 years by other mathematicians, the radical decision of Andrew Wiles to work by himself and not share his ideas with other mathematicians, the seven years of struggle, the flaw in the preliminary proof, one year of revision, all of this makes for a wonderful story and it is indeed well narrated by Simon. I can imagine only two such propositions, first on Goldbach Conjecture, second on 3n+1 problem, that share similar features as Fermat's last theorem. If and when they get solved, I hope someone writes a similar beautiful book. There are some trivial puzzles sprinkled to make it a bit more interesting for people who can solve some high school mathematics. Overall, a very nice and pleasant read.

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