Fermat’s Last Theorem for Amateurs

First, I give this book for 4 stars because the title is misleading. The background needed to understand this book is a major in mathematics at the undergrad level. If you were a math major and earned your degree several years ago, you may still have trouble following the book. It is for "amateurs" with a math degree and who are still "in touch" with the math they learnt. The book is however quite good; give a good historical narrative along with enough mathematics to satisfy the reader.The problem is mathematics has gotten so much abstract and complicated during the last 50 years that it is impossible for someone not trained in the exact specialized field to follow what is going on. Since Fermat's last theorem has caught the public attention, people want to know what the fuss is all about. Alas, they really cannot understand it or even appreciate the mathematics in general without strong background in number theory, Galois theory, elliptic curves, and so on. All books that try to cater to the layman have to decide where to draw the line. If they water down the mathematics, then they really cannot explain how the proof was got satisfactorily; and if they throw in one too many equations, it becomes incomprehensible to many--even mathematicians not in that specialized field. My advice to the general public is to watch the video on Fermat's last theorem. I think for the layman visual media is better than a book. Just Google the excellent UKTV documentary on Fermat's last theorem.

Solid coverage of proofs relating to Fermat's Last Theorem up to Kummer's Theory. You will find proofs for n=2, n=3, n=4, n=5, and n=7. Requires solid background in Algebraic Number Theory. For example, you should already have a good understanding of the Quadratic Law of Reciprocity, Quadratic Fields, and Congruences. If you don't, I recommend Elementary Number Theory for Congruences and the Quadratic Law of Reciprocity and Stark's An Introduction to Number Theory for Quadratic Fields. I would also recommend starting out with Edward's Book on Fermat's Last Theorem which includes detailed coverage of Kummer's Theory.

I am a math instructor and graduate student at PVAMU, and am working on a thesis detailing the history of attempts to prove and the Wiles proof of FLT. The text was easily readable and the proofs were very well done. I was able to follow the logic and math of all the presented proofs very well.