Customer Reviews

The World's Most Famous Math Problem: The Proof of Fermat's Last Theorem and Other Mathematical Mysteries

5 star:		(4)
4 star:		(1)
3 star:		(4)
2 star:		(3)
1 star:		(23)

 

 

Like many of us, there are some elements of mathematics that Ms. Vos Savant doesn't understand. Unfortunately, instead of investigating these subjects or asking questions of experts, the author concludes that there must be something wrong with the mathematics. Although this book purports to be about Wiles's proof of Fermat's Last Theorem, it is really a description of all the things that are "wrong" in mathematics, including some comments on Wiles's work. This can make for some entertaining reading, like her argument against the imaginary number i, but it can also be quite annoying, like her incredibly disrespectful comment (under the heading "a possible fatal flaw [in Wiles's proof]") that Wiles ought to check and make sure that his "proof" doesn't also rule out solutions to the equation with exponent 2, since we know that there are solutions in this case. A big plus for this book is the evidence it provides for the relative unimportance of I.Q.

So, there's this thing, it's called math. Actually, it's called mathematician's math. In this kind of math, everything has to proven rigorously, nothing is taken for granted - all this to avoid fallacies in logic and paradoxes. This is the right way to do mathematics, at least from the modern point of view.

Physicists, they also need to use math. However, they're only interested in math to describe Nature. So they may not do everything rigorously - perhaps they extend the results of a theorem to a place where the hypotheses do not strictly hold, or say something is "intuitively obvious". The brilliant physicists are normally right, and many physicists are also great mathematicians.

Chemists (primarily physical chemists) use math too, since they need a way to describe whatever they're working on accurately. But they don't care about proof at all. They'll just use whatever works, and ignore all the theory. This is okay, except that they don't get a complete understanding of the underlying mathematics, and as such, don't know much about math.

Now, philosophers, they use mathematics and logic to try to bring validity to their arguments. The majority of them fail miserably, and end up stumbling all over their words. This isn't to say that all philosophers don't know what they're talking about - a few do, the best example being Bertrand Russell, who was a great mathematician and philosopher. But most philosophers that use math don't use it in the correct spirit.

Now, I have discovered a new low in mathematics. I'll call it "Savant mathematics", in honor of the person who originated it. In this book, she makes blatantly false statements about fundamental aspects of mathematics (for example, claiming that philosophical induction (not mathematical) is a valid method of mathematical proof, or that proof by contradiction is wrong - I know constructivists the latter is false but they're a minority of mathematicians) and, despite a lack of training in mathematics, claims that Wiles' proof may be wrong. Sure, the proof was incorrect, at first, but not for the reasons she claimed. She wouldn't even be able to understand why the proof was wrong!

It is simply appalling to me that she would dare make all these statements without knowing the least bit of mathematics. The fact that she had the nerve to confront Andrew Wiles, if not the entire mathematical community, without knowing a single iota about what they do, is simply wrong, and even more so for a person with her status in the public's eye.

I can only hope that no person takes this book seriously. If you want to learn about the incredible story of Fermat's Last Theorem and it's proof, I recommend you get some of the other books out there. The one I personally recommend is Simon Singh's Fermat's Last Enigma.

This book was written hastily to cash in on the publicity surrounding FLT. It qualifies as something of a scam, since the author not only has no expertise in the area, but the book itself has little to do with the actual proof. It consists mainly of simple explanations of basic mathematical methods and traditional math problems. The book's short length is padded by extensive quotes from other books. For a much better book on the same topic, I recommend "Fermat's Enigma" by Simon Singh.

I've mentioned to my brother that this book (in my own field of number theory, alas!) may be the worst popular book on a mathematical topic ever written. His response was to buy it for me as a Christmas present.

If you are a mathematician or at all knowledgeable about mathematics, you will probably respond in one of the following three ways:

(1) Laugh

(2) Throw up

(3) Laugh until you throw up

If you are a number theorist and actually know what a semistable elliptic curve is, it only gets better-or worse, depending on your point of view. Is Marilyn vos Savant the World's Stupidest Person? Considering that she undoubtedly made a tidy sum for her minimal efforts in writing this book, I am forced to doubt it. Will you be a candidate for the World's Stupidest Person if you buy this book? Only if you take it seriously.

Ms. Savant is a skeptic to Andrew Wiles' FLT proof. She did not explicitly say why she takes that stand. I assume it is because of her knowledge that many bogus FLT proofs have surfaced in the past. She did not mention if she herself had read or understood the proof or those sketches of the proof by Karl Rubin reproduced in the appendix. Further, she amateurishly tries to debunk some centuries-old foundations of mathematics, such as imaginary numbers and the "proof by contradiction/induction" methods. Her superficial attempts at doing so is really quite laughable. Then, she arrogantly suggests that she might have found a "fatal flaw" to Wiles' proof, which is nothing more than validity testing for the base cases, something any college student would know to do. One thing this book clearly reflects is the limitations of one's IQ measure. I advice Ms. Savant to leave the writing of math-related books to those better versed in math, even if the book is just meant for the general public. This book is not worthy of the shelve-space of anyone who is even remotely interested in math.

I say, I like to consider myself somewhat of a cosmopolitan and, as such, delight in the undertaking of a novel or tale of interest... but the self-proclaimed 'Savant' of mathematics has gone too far! This infernal, bug-addled, mephitic clodhopping ninny has committed the following insults:

1.) Inscribing her picture near Fermat's on the front cover, implying by the most subtle of means that she dares rival one of the world's greatest mathematicians.

2.) Claiming to have found several errors with (not only Andrew Wiles' proof, but) mathematics in general

However, I may mention that despite the fact this book induced me to vomit with rage, I still retain a copy to convince my associates that IQ is completely unrelated to intelligence. I am still in disbelief that the publishers can live with themselves, knowing that they are spreading ANTI-information; bring this book in too close contact with an actual book on mathematics, and both will vaporize instantly.

The main lesson to be learned from this book is that there is no correlation between IQ and personal character. According to the Mathematical Association of America, their president wrote to Ms. Savant shortly after her public proclamation that the proof was incorrect, and explained to her that no competent mathematician would have ever made the error which she attributed to Wile. He received a short and "ungracious" response. (I might add that I am slightly acquainted with the man who was the president of the MAA at the time, and he is an uncommonly courteous and gracious gentleman himself. So Ms. vos Savant's reaction can have been triggered only by her own ignorance and defensiveness.)

Needless to say, Savant's argument is too silly to waste your time with, but I really do need to address the preposterous claim made in the previous review. The fact that Wile's proof was found to have a flaw, does absolutely NOTHING, in even the most miniscule degree, to justify vos Savant's foolishness. It wasn't as if there was a flaw hidden somewhere, and she saw it but just slightly mis-located it. Her entire thesis demonstrated that she didn't know the first thing about the theorem, the proof, or the mathematics which surround it. She was simply writing about a subject of which she had no knowledge, and was arrogant enough to believe that her IQ and her personal fame would compensate for her ignorance.

For the time and money you will invest in reading about Fermat's last theorem, you can do a whole lot better than this book. I recommend Simon Singh's _Fermat's Engima_ (Bantam, 1998), a non-technical book that gives the reader a good overview of how the problem was approached by other mathematicians, and how it was finally proved by Andrew Wiles. _Fermat's Enigma_ does not require anything beyond a high school-level math background. Another good work is Amir Aczel's _Fermat's Last Theorem_ (Delacorte, 1997). Aczel takes the reader slightly deeper into the theoretical realm, but it too is a non-technical account.

Contrary to the review below, Wiles' proof of Fermat's last theorem did NOT involve the use of computers. Second, Marilyn vos Savant's purported insight that Wiles' proof can not be the same as Fermat's proof is rather innocuous. Again, if this observation is what entices the reader to pick up a book on Fermat's last theorem, try one of the other two titles which I recommended; both provide explanations of why Wiles' proof and Fermat's proof (if he truly had one) are not identical. Third, if Wiles' proof is correct, then he did indeed "solve" Fermat's last theorem. One should not confuse the NAME given to a theorem with the particular APPROACH used to prove it. In this case, Wiles has proved Fermat's last theorem, even though he may not have reproduced Fermat's proof.

But my complaints with this book don't really have anything to do with the previous paragraph. Instead, Marilyn vos Savant's book has two significant shortcomings. First, the book spends very little time actually discussing _The World's Most Famous Math Problem_, contrary to what the title suggests. There is little meat on the bones, so to speak. Second, the story is not complete. At the time Marilyn vos Savant wrote this book, Wiles' proof was under review. A problem was later discovered in the proof and Wiles headed back to the drawing board, emerging with a corrected proof a few years later. None of this amazing drama is recounted in Marilyn vos Savant. For this reason, more than any other, I strongly encourage the interested reader to invest their valuable money and time in either Singh's book or Aczel's, but please, not this one.

Savant, I used to believe in you. I've been a big fan of you and read most of your articles. I know you've made mistakes before, but they've been insignificant to the amount of knowledge you've put forth.

I currently go to high school, and when I heard that you released a new book, I went ahead and got it. When I first read it, I was in disbelief; I thought maybe I wasn't smart enough to understand the logic, because it didn't make any sense to me. When I showed it to my high school math teacher, she said that you were wrong, but I didn't believe them. I went to my local college and asked the professors there, and they all said that you were wrong. I've searched and searched online and everyone says you're wrong.

I've tried to tell myself "this is just like the Monte Carlo goat-door problem; everyone said 1/2, but you said 1/3, and you were right." But if you're right, then why does math still work at all? You disprove it in your book! If it turns out that you were wrong on such a large magnitude, then I don't know what role models to believe in anymore.

I stumbled upon this book while browsing in a bookstore long ago. I imagined from the title that she was attempting to explain to the public Sir Andrew Wiles' great accomplishment in proving Fermat's Last Theorem, but when I started reading her book, I couldn't believe my eyes.

In addition to the errors other reviewers have pointed out, she claims that non-Euclidean geometry is "false." I would send her my book on that subject but I doubt that she would read it.

I say that because a mathematician I know sent her a polite letter pointing out her errors. She replied:

"My mathematical friends and I had a good laugh over your missive. Keep those cards and letters coming."

Yes, she was smart enough to give the correct solution to the Monty Hall problem, but when she errs, she is either too arrogant or too ignorant or too corrupt to admit it.