Friday, June 01, 2012

Fermat's Last Theorem by Amir D. Aczel

After reading Longitude, I decided on another book in the same genre: thin history of science books.  This book, subtitled "Unlocking the Secret of an Ancient Mathematical Problem" begins with Andrew Wiles' alleged proof of of Fermat's Last Theorem.  FLT is simple to understand but was, for nearly three centuries, impossible to prove. 

The theorem states that equations like a^2 + b^2 = c^2 can't be solved for exponents larger than 2.  Fermat, mathematician in the 1600's, stated this theorem with an innocent note indicating he had proven it but didn't have space in the margin of his notebook to write out the entire proof.  Since then, mathematicians had struggled to find a proof, and in 1993 Wiles was so sure that he had that he presented it at a large conference. 

Wiles' original proof of FLT was erroneous, so the book picks up the story there, ultimately unraveling the politics and characters involved in the lead-up to the proof as well as the correction that Wiles ultimately presented to successfully prove the theorem.  However, to appreciate the entire story, the author uses most of the book to provide a history of the math behind the story, starting long before Fermat, with the Greek mathematicians up through modern times.

I liked the book but I didn't love it.  I guess as a math person I craved better explanations of some of the mathematical concepts.  I wanted to understand the basic layout of the proof, and instead I got a narrative of the people involved as well as this history, but not enough math.  Some sections (like on non-Euclidean geometry) were at a level of detail I was looking for, but once he got into the elliptical math at the basis of the proof, Aczel's descriptions were not complete enough for my taste.

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