Book review: Fermat’s Last Theorem – Simon Singh

I had just finished a mathematics book called Fermat’s Last Theorem by mathematics and science writer Dr. Simon Singh. I am impressed that the author has a PhD in Particle Physics, I thought he is just a journalist!

The book is about Fermat’s Last Theorem. Pierre de Fermat was an “amateur” mathematician, also called the Prince of Amaterus, published several notes on the margin of the mathematics textbook, Arithmetica. These notes gave hints of how to solve some problems in the Arithmetica, mathematicians after him had studied these notes and are able to rediscover his proofs.

However, one question remained unsolved. The question gives a statement and asks people to prove it. The statement states that there is no solution for the equation  x^{n}+y^{n}=z^{n} for n>2. This question is aptly called Fermat’s Last Theorem because it is the last to be solved (actually it should be called conjecture, because it is not yet proven to be a theorem).

There is a well made documentary by BBC on this particular topic, it is made by the author of this book. The documentary, as well as the book, chronicled the journey of Professor Andrew Wiles in proving the Fermat’s Last Theorem. I am impressed that they can lay out all the essential points in 1 hour, watching the documentary gave me about 80% of the knowledge of the book.

I like the chronological development from the ancient to modern mathematics, as well as the ingenious methods of mathematics used in proving the theorem. From Frey’s linking the Fermat’s Last Theorem to Taniyama-Shimura Conjecture, Ken Ribet’s successful proving of the linkage, and finally the proof of Taniyama-Shimura Conjecture by Andrew Wiles. Truly remarkable.

I had to forgo my dinner to finish reading the book (truly a big sacrifice).

Edit (15/March/2015): Prof Andrew Wiles just won the Abel Prize, one of the biggest prize in the field, congratulations!

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