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

by Marilyn vos Savant

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.

Genres: Science, Mathematics, Nonfiction

80 pages, Paperback

First published October 15, 1993

About the author

Marilyn vos Savant is an American magazine columnist, author, lecturer and playwright who rose to fame through her listing in the Guinness Book of World Records under "Highest IQ". Since 1986 she has written Ask Marilyn, a Sunday column in Parade magazine in which she solves puzzles and answers questions from readers on a variety of subjects.

Reviews

[Kai · Rating 1 out of 5]

Do not write math if you do not know math. Math is a subject to be rigorous and respectable that should be as consistent and complete as possible under the same logic mother. Presenting the text in non-mathematical and casual way is not a guilt. However, it is an indecency to mess up with the basics of math and claims that there is a fallacy is a proof without any detailed examination but by 'persuading' with references to articles. If such kind of manner to math was ever promoted through this book, I'm not surprised to see planes fall and electronics crash one day.

For example, if we all agree on a direct proof of p implies q, we have to accept proof by contradiction for consistency. Assumes that p implies not q, if we can arrive to a contradiction, i.e., p implies not q is always false, after few arguments, then p implies q must be true, which works the same as a direct proof, or a proof by contrapositive etc. (Here I do not give a proof, please explore the subject itself with respect if you are interested in it.)

However, the author rejects the proof to be valid by saying it 'is rejected by entirely by some' that I have to doubt what sources the author refers to and if they work under the same mathematical system with us. The author even tries to claim that there is a 'possible fatal flaw' in Wile's proof by doubting 'whether the same basic arguments could be constructed to hold for all exponents', when the essence of the proof is that a^n + b^n = c^n only works for integers n > 2! This is as ridiculous as saying that 'there is a fatal flaw in the AM-GM inequalities as it can't be used for all real numbers, what if they are negative' according to my friend.

With the faulty logic, the author goes on to reject imaginary number by saying that 'how can we justify using them to prove a contradiction'. An imaginary number is defined but not 'proved'. This is the same as 1 = 1 is not 'proved' but defined in the Peano axioms. The writer disappointingly cannot discriminate definitions from proofs. Although it was found that there was truly a fallacy in Wile's proof in 1993 (the proof is corrected and republished in 1995) and the author's doubt is true, overall the text is misleading and messes up with the basics.

Due to the author's limitation she could not present the text in a more rigorous way. But please the publisher! Do not publish math as if it is a fantasy!

Some reviews by real mathematicians: https://dms.umontreal.ca/~andrew/PDF/...

[Ragini · Rating 3 out of 5]

A short, simple, easy-to-understand read about the fascinating Fermat's Last Theorem! Her own ideas are insightful but clouded by excessive news articles, books, etc. to which she referenced. I just wish she had used fewer outside quotes and presented more concrete information on the history and math behind the theorem. That being said, the ideas she brings up piqued my curiosity and inspired me to delve further into them.

[Brian Sison · Rating 4 out of 5]

Interesting quick read about the greatest math problem ever, written by the highest IQ ever. But surprisingly, the heart of the book was not mathematically complex at all. (The actual proof in the appendix was completely un-graspable to anyone but the higher echelons of math nerd-dom. of which I am not a part.) This book did a good job of summarizing the famous conjecture, its origin, its applications (or lack thereof), and the general sense of wonder surrounding it.

[Joe · Rating 2 out of 5]

So far, this book about math history is boring, confusing and completely devoid of math. Also, almost every paragraph cites a newspaper article, which just makes me want to read the originals. We'll see what happens.

[Frances Sawaya · Rating 4 out of 5]

A return to a good summary of this complex problem and Fermat's "tease" about his solution. Wanted to explain it to a teen-aged neighbour and needed a refresher. Sure wish I was one of the dozen or so who have the smarts to understand it in full.

[Mike R]

Fermat's Last Theorem

[Simon A. · Rating 3 out of 5]

Very nice and short book on that famous theorem.

[Michael · Rating 3 out of 5]

A quick little read on Fermat's Last Theorem.

[Gary Fixler · Rating 3 out of 5]

This is a short book of about 70 actual pages of text, put together under a 3-week deadline by the woman who spent 3 years as the Guinness World Record holder of the highest recorded IQ (before they retired the category as being too hard to measure properly). It's a speculative book that gives a bit of history, and ponders the likelihood that Andrew Wiles proof, itself published just months before this book, is correct. It's a good read for someone not in the maths world, but watching with curiosity from the sidelines. Though short, and summary in nature, there's quite a bit of interesting information throughout, on everything from the background of the proof, and how it was first shared, and the reaction to it, to the history of the mathematics involved, to the nature of proofs and how we can know things in the first place. It gave me a good dozen ponderous "Hmmm"s, with a 2-page listing of follow-up readings for those interested in diving deeper.