Book Description
June 23, 1993. A Princeton mathematician announces that he has unlocked, after thousands of unsuccessful attempts by others, the greatest mathematical riddle in the world. Dr. Wiles demonstrates to a group of stunned mathematicians that he has provided the proof of Fermat's Last Theorem (the equation x" + y" = z", where n is an integer greater than 2, has no solution in positive numbers), a problem that has confounded scholars for over 350 years.Here in this brilliant new book, Marilyn vos Savant, the person with the highest recorded IQ in the world explains the mathematical underpinnings of Wiles's solution, discusses the history of Fermat's Last Theorem and other great math problems, and provides colorful stories of the great thinkers and amateurs who attempted to solve Fermat's puzzle. ... Read more

Customer Reviews (34)

Blame the publisher for Marilyn's mistakes
I picked this up cheaply at a used book shop based on Marilyn Vos Savant's reputation, she has the world's highest I.Q., and I was curious as to what her writing was like. It's quite good, as you would expect from a professional magazine writer. The subject was topical at the time (1993) and the book was quickly published to cash in on the announcement of a proof of Fermat's Last Theorem. Unfortunately, no one with college math was around to correct some repeated blunders. Just to pick one: Vos Savant confuses inductive knowledge, which she understands well, with inductive proof, which she doesn't.

Inductive knowledge is when we think we "know" something because we've seen it time and again. She illustrates it quite well with the phrase "all wheels are round". Why do we believe this? Because every time we see a wheel, it's round. Repeated exposure. Now to push things a little further, if "all wheels are round" then "something that's not round isn't a wheel". So logically every time we see a knife, which is not round, then this inductively confirms the earlier statement. Vos Savant's illustration drives the point home that this isn't really satisfying logically and that inductive knowledge doesn't really work when it comes to proofs.

What Vos Savant fails to realize is that an inductive proof is a completely different animal. It's an accident that both concepts use the same label (i.e. inductive). Inductive proof is a mechanical process, an algorithm, a method, by which we can show the truth of many mathematical theorems. To use the method, the theorem we're trying to prove must be about something we can count. We look at the first case and usually, it's fairly simple to show it to be true. Then we look at the second case, and again we often easily prove it to be true. Then we look at the third, fourth, fifth cases and we notice that we can generalize the next case from the one we are looking at now. So we do just that, we generalize: if we can show that the (n+1)th case (i.e. the next case) is true whenever the nth case (i.e. the case now) is true, AND if we explicitly show the first case to be true, then and only then is our theorem always true.

There is nothing weird or special about this, it only takes a little time and effort to understand. Proof by induction is not usually taught before college, and then only to those who take calculus, and then only superficially (analysis and abstract algebra courses examine this method (one of Peano's natural number axioms actually) in more depth). There's no denying that Ms. Vos Savant is an accomplished intelligent human being. But she only has, as we all only have, so much time alloted to her to enjoy life and pursue her interests. Mathematics is obviously not among these and shame on the publisher for thinking that Vos Savant's high I.Q. automatically made her a mathematical authority.

Vincent Poirier, Tokyo

A review of these reviews
Ah, these poor little threatened egos on display:How dare anyone contradict the university professionals?How dare anyone have an opinion outside the status quo?How dare any publisher even consider a book not from a fully affiliated tenured and chaired professor of mathematics?Where is peer review when we need it?I especially enjoyed the brag of vandalism.Savonarola would be proud.

Im SO excited
Isn't it just marvelous, finally a chance to polish up my knowledge of the worlds most famous maths problem. I can't tell you how much me and my wife have enjoyed, and been entregued by this. Night-after-night, just laying down on the hay, having a laugh with this top quality piece of material. Maths world here I come.

the world's IQest woman?
I have no problem to admit that the world's IQest person, is a female person. But as I browsed this book, I would be hard pressed to grant Madame Marilyn Vos Savant the title,as the world's IQest woman.

Excellent, honest book
This is a fantastic book!I especially like the fact that she highlights several problems with the current state of mathematics, drawing this field (and maybe all of modern science) into question.

Few people dare to question science, but Marilyn has done so, and she has good reason for it.If half of the scientists of the world were in politics, the world would be a much better place.Politics is in dire need of minds capable of flexible, yet rigorous thinking, and scientists are experts at this sort of thing.

Bravo, Marilyn! ... Read more

Book Description
Four volumes in one: Famous Problems of Elementary Geometry, byKlein. A fascinating, simple, easily understandable account ofthe famous problems of Geometry---The Duplication of the Cube,Trisection of the Angle, Squaring of the Circle---and the proofsthat these cannot be solved by ruler and compass. Suitablypresented to undergraduates, with no calculus required. Also,the work includes problems about transcendental numbers, theexistence of such numbers, and proofs of the transcendence of$e$.

From Determinant to Tensor, by Sheppard. A novel and simpleintroduction to tensors.

"An excellent little book, the aim of which is to familiarize thestudent with tensors and to give an idea of their applications.We wish to recommend the book heartily ... The beginner willfind the book a valuable introduction and the expert aninteresting review with a refreshing novelty of presentation."

---Bulletin of the AMS

Chapter headings: 1: Origin of Determinants; 2: Properties ofDeterminants; 3: Solution of Simultaneous Equations; 4:Properties; 5: Tensor Notation; 6: Sets; 7: Cogredience, etc. 8:Examples from Statistics; 9: Tensors in Theory of Relativity.

Introduction to Combinatory Analysis, by MacMahon. Anintroduction to the author's two-volume work.

Three Lectures on Fermat's Last Theorem, by Mordell. This famousproblem is so easy that a high-school student might notunreasonably hope to solve it: it is so difficult that as of the1962 publication date of this book, tens of thousands of amateurand professional mathematicians, Euler and Gauss among them,failed to find a complete solution. Mordell himself had asolution (as he said he did). This work is one of themasterpieces of mathematical exposition. ... Read more