The World's Most Famous Math Problem by Marilyn vos Savant

[If you're looking for information on famous mathematical problems, see Famous Math Problems.]

The World's Most Famous Math Problem by Marilyn vos Savant (St. Martin's Press, 1993) discusses Fermat's Last Theorem and Andrew Wiles' proof, the latter of which had been announced shortly prior to this book being written.

It is mentioned in the acknowledgements that this book took three weeks to write and, in two words, it shows. Vos Savant's thesis seems to be to show that Wiles' proof of Fermat's Last Theorem is wrong. Now vos Savant, despite having the highest measured IQ in the world, and being skilled at explaining things such as the Monty Hall problem, is not trained in the sort of mathematics required to understand Wiles' proof of Fermat's last theorem, and it just isn't the sort of stuff you can learn in just three weeks. So, to her credit, she doesn't attack Wiles' proof on mathematical grounds. Rather, she starts by attacking it based on some sort of risk assessment model, which doesn't seem unreasonable, but a far more reasonable idea to me would have been to talk with people who understand the mathematics and could provide intelligent commentary on it.

As it turns out, Wiles' initial proof was in fact incorrect, but not for any reason that vos Savant offered, and Wiles was able to fix the problem shortly thereafter.

The book, with the exception of a brief section on the history of Fermat's Last Theorem which is a reasonable summary of the problem's history, goes downhill from there. There are two main problems. The first is that vos Savant gives equal weight to both speculative, antiquated or fringe views and modern, mainstream views. For example, she deprecates proof by contradiction as "rejected entirely by some." Sure, some people do reject it, but most don't. Proof by contradiction has been a fundamental part of logic for the past 2,300 years. Similarly, her views on imaginary numbers are a few hundred years behind the times. There are a few other parts of the book that will cause mathematicians to cringe.

The second problem with the book is that it is rather disjoint; there is no coherent argument, just a bunch of random points thrown together, and the relationship between one point and another, and between most of the points and Fermat's Last Theorem, is obscure at best. My favourite is on page 62, where she writes, "A possible fatal flaw in Wiles' proof is whether the same basic arguments could be constructed to hold true for all exponents, instead of just the exponents equal to or greater than 3" (emphasis hers). Um, yeah, I'm pretty sure that if you're publishing some groundbreaking mathematical paper, you'd check to make sure that it doesn't contradict basic mathematical truths such as 1¹ + 1¹ = 2¹ (i.e. 1 + 1 = 2).

The book is quite thin (80 pages) and a fair bit of it consists of quotes from other works. If you can get the book cheaply and are just interested in a brief introduction to Fermat's Last Theorem, this book might just be worthwhile, although there are lots of other better resources now. It is also useful if you want practice in refuting incorrect ideas. Not recommended as an introduction to any of the mathematics discussed in the book, including Euclidean geometry and proof.

Rating: 2.5/10