Fermat’s Last Theorem for Amateurs by Paulo Ribenboim (PDF)

Description

In 1995, Andrew Wiles completed a proof of Fermat’s Last Theorem. Although this was certainly a great mathematical feat, one shouldn’t dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.

User’s Reviews

Editorial Reviews: Review From the reviews:MATHEMATICAL REVIEWS”The history of elementary approaches to Fermat is very rich indeed, and Ribenboim has arranged these approaches in a way that makes them accessible to interested readers without extensive mathematical backgrounds…both readable and fairly comprehensive. This book would likely be of great interest to an enthusiastic undergraduate with a basic knowledge of rings and fields. In addition to describing the history of one of the great problems in number theory, the book provides a gentle and well-motivated introduction to some important ideas in modern number theory…any reader who spends a few hours with this book is guaranteed to learn something new and interesting about Fermat’s last theorem.”

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

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