Customer Reviews

Fermat's Last Theorem for Amateurs

5 star:		(1)
4 star:		(3)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

If, like me, you were fascinated to hear that Fermat's so-called "last theorem" had been proven in 1995, then read Simon Singh or Amir Aczel's books popularizing the proof in outline, you probably wanted something more.

If, like me, you are a person who took some math in college, enjoys recreational mathematics books of the Douglas Hofstadter and Ian Stewart genre, and even sometimes picks up the odd number-theory book, you might consider yourself an "amateur."

If...if... this might seem like the book for you. I'd suggest that its not.

The mathematics in this book and its level of presentation was simply impenetrable by me. Not slow going... "no" going. That's frustrating to admit, but in a way fine, since it affirms of my admiration at a distance of the work that professional mathematicians do. I have seen many cited who state that Wiles' proof is simply beyond the ken of even 95% of working mathematicians. I believe this book must really be intended to serve some fraction of that group. Perhaps within the fold of mathematics these would consider themselves "amateurs". My two stars are offered only for them.

The book is simply not for the "lay" amateur. And Ribenboim's titling of it suggests that he does not even know that this lower caste, containing those of us who enjoy recreational mathematics and would describe ourselves as "amateurs", even exists. We know we exist as something mathematically distinct from the general population by the simple fact of the universally raised eyebrows that confront any mention of our interest in mathematics. Nevertheless, like any other species in a niche, we will have to continue to feed on a sparse supply of intellectual sustenance and learn to avoid the over-rich and indigestible fare of the higher forms.

Finally, if you haven't read Singh or Aczel I'd offer the former 5 stars and the latter 3 but recommend both. A truly fascinating story.

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.

I find that this is a great book if you are an instructor or have a solid background in algebraic number theory. If you are unfamiliar with the Legendre Symbol, Gaussian integers, or the Law of Quadratic Reciprocity, you may wish to start out with a book such as Elementary Number Theory. If your are familiar with Algebraic Number Theory and wish to study in detail the Fermat Last Theorem proofs up to Kummer's Theory, this is a great book. I would recommend starting out with Edward's Book (Fermat's Last Theorem), for analysis of Euclid's proof of N=3. I found this very useful as an example of applications of Gaussian integers and Eisenstein integers. Ribenboim is one of the top experts about Fermat's Last Theorem and he is to praised for putting these beautiful proofs down. Even so, I would recommend purchasing other books to help explain this one. I found Stark's book very helpful in understanding Quadratic Fields.

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.