Monday, September 14, 2020

Fermat's Enigma - Simon Singh (1997)

Enigma was the German crypto system that has been decoded by the allied forces surreptitiously to win over the axis powers' every secret move. Fermat's last theorem is in a sense a similar puzzle that baffled the mathematical community over 350 years. The books is written for common understanding without dabbling into mathematical details and hence very useful. The first part is about the development of mathematical system and development of scientific temperament from Pythogoras to Fermat. The last part is about development of systems and how Andrew Wiles managed to tackle the problem. The book has a few interesting puzzles talked about as well. The game theoretic truel is particularly interesting one. 

What is there in Fermat's theorem?  x^n + y^n = z^n does not have any integral solution for n > 2. 

Fermat in a margin note has teased to the mathematical community that he had a proof for the same but too long to be mentioned in the margin notes. It's called the last conjecture not because it's the last one he mentioned but it's the last one that mathematical community proved. With several attempts taken to solve the conjecture it was established the theorem has relations to:

1. Elliptical equations
2. Modular computations
3. Galois groups

While Andrew Wiles approach was to relate between several of these seemingly unrelated mathematical islands and bring home a 20th century solution to a 17th century puzzle. Skeptics are still engaged in finding out further solution to the 17th century solution for the 17th century puzzle. As much as Andrew Wiles was responsible for the solution of the theorem who eventually proved a dual Taniyama-Shimura conjecture, the Japanese scientists Taniyama and Shimura cannot be discounted for their efforts in establishing a dual of the Fermat's Last Theorem. 

Simon Singh has done an excellent job in keeping things simple for a complex problem and ensuring common man can appreciate the mathematical hard work. But do not expect any mathematical details in the book. 

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