Most helpful critical review
2Two-third of the book is irrelevant to the �epic quest�
ByAmazon Customeron March 10, 2001
I may have to apologize for not as raving as other reviewers on this book by Simon Singh. To be fair to the book and thus the author, I do find a fairly fluent narration on the mathematicians who attempted or contributed to solve the Fermat's Last Theorem. Meanwhile, I personally don't find the writing style and the organization of the materials to be particularly appealing.
We never hold any slightest hope that a 285-page book (the paperback edition) would offer us a clear understanding on how the proof, that incorporates so much of the techniques in the modern number theory, is devised. The book basically steers itself all clear from the mathematics.
These below are what significantly push my rating of this book to a low range:
1. Too much on who the mathematicians were rather what they did to the proof. Approximately two-thirds of the book is on stories behind those mathematicians who one way or the other got involved in the Last Theorem. Those may be interesting from a historical perspective but are simply irrelevant to how we came to the proof.
2. The author starts quite early in the book to tout mathematical proof as an "absolute proof" that "[m]athematical theorems rely on this logical process and once proven are true until the end of time. Mathematical proofs are absolute." By contrast, "... the scientific theory can never be proved to the same absolute level of a mathematical theorem ... So-called scientific proof relies on observation and perception." An account on the differences between the two is beyond the scope here. Apparently, the author either doesn't know those are apples and oranges or, worse, attempts to elevate mathematical proof to an "absolute" level it might not need at all.
3. Throughout the book, the author has mentioned more than once how important logical proof is in a mathematical proof. At least he cites the two events with the first in Wolfskehl's finding of "a gap in the logic" by Kummer then the second in Katz's checking of Wiles' proof. Unfortunately, the author allows such a gap of logic in the proof of Pythagoras's Theorem shown in Appendix I: "... four identical right-angled triangles are combined with one tilted square to build a large square." The author only states so but fails to provide any proof that the inside four-sided shape formed by the four hypotenuses IS a square. (Certainly we do know it is and can plug the proof. Otherwise Pythagoras's Theorem won't hold.)