Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

by Simon Singh

book data

788 ratings, 4.08 average rating, 111 reviews (more data...)

rating	frequency	%
5		32%
4		47%
3		17%
2		2%
1		0%

edit

published

September 8th 1998 (first published 1997) by Anchor

binding

Paperback, 336 pages

isbn

0385493622 (isbn13: 9780385493628)

description

When Andrew Wiles of Princeton University announced a solution of Fermat's last theorem in 1993, it electrified the world of mathematics. After a flaw...more

find at: Amazon | Half.com | Barnes & Noble | Abebooks | compare prices…

new topic
discuss this book

topics	posts	views	last activity
College Students! : Verity's Challenge	5	75	8 hours, 19 min ago

friend reviews

To see what your friends thought of this book, please sign up.

lists with this book

Favorite Books

999 books | 1028 voters

Science books you loved

84 books | 106 voters

More lists...

other reviews (showing 1-20 of 1,130)

sort: default (?) | date
filters: all | text-only

06/18/08

Bruce rated it:

Read in April, 2009

recommends it for: everyone from high schoolers on up

What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the...more What a fun book this was (thanks, Trevor, for the recommendation)! There are many reasons I think I like (good) nonfiction -- a sense of direct relevance, gravitas, frequent insights into the workings of the universe (and people), but mostly for knowledge narcs -- high levels of information density served up into an intriguing package by someone else who has undertaken the heavy lifting (research, organization, thinking). So, here in Singh's work I get a solid lay understanding not only of the proof to Fermat's Last Theorem, but of much of mathematics (and the lives of mathematicians) since the seventeenth century.

I've been thinking also about what attracts me to books on mathematical topics -- the works by Martin Gardner, William Poundstone, and the various other authors in the company of whose thoughts I've had pleasure to spend a week or more. What I've come away with, is that the best of them feed off surprises, those bits of counterintuitive anecdotes that leave you blurting out, "Huh. How about that," and then looking madly around for someone to tell. Like a book of jokes, riddles, or puzzles that provides immediate gratification in the back of the book, Fermat's Enigma plugs at least ten conundrums (and their easy-to-understand, logical solutions) into its appendices. For example -- say you're unlucky enough to be forced into a three-way duel. If everyone gets to take turns in order of their skill such that worst shoots first, what should the worst do? Aim at the best in the hopes of getting lucky and eliminating the most dangerous gunsel? Nope, the correct answer is to pass up the turn in the hopes that your first shot will get to be expended against only one remaining combatant. That way, even if you miss, you at least had a chance to take aim at the only person able to shoot back.

Pierre Fermat turns out to have been quite the prankster, often tweaking professional mathematicians and academics by mailing them problems they knew full well he had already solved. For those who don't keep this type of trivia at the forefront of their brains, Fermat's the French recluse (and hanging circuit jurist) who once famously scribbled in a copy of Diophantus' Arithmetica that x^n + y^n ≠ z^n for any number n greater than 2, a propostion for which he had "a truly marvelous demonstration… which this margin is too narrow to contain." This gets to be Fermat's Last Theorem, simply because it ends up being the last of his conundrums to be proven (not necessarily the last one he wrote). Just think, were it not for the scrupulous care taken by Fermat's son to go through and publish all of Fermat, Sr.'s writings, the world would not have been tantalized by this particular gem for over 350 YEARS.

Andrew Wiles published the first (and only?) proof in 1994, and Enigma does a tremendous job of walking the reader through not only the stunning depth of his intellectual achievement, but its significance as well. Suffice it to say that I was happy here to read that Taniyama-Shimura get their well-earned due and that modular and elliptical equations can finally be understood to be mathematically analogous (whether or not I have any idea what modular equations actually are). Still, all of this leads to what I think is an even more tantalizing problem. We now know that all of Fermat's conjectures ultimately proved to be solvable and that Fermat's own notes would seem to indicate that he had indeed apparently found ways to solve each of them. But there is no doubt that Fermat's solution could not have relied on the up-to-the-minute maths Wiles employs over 200 pages. So if it was really the limitations of the margin and not of Fermat that inhibited publication… what was Fermat's proof?
(less)

Like this review? yes (2 people liked it)

2 comments

12/10/07

fbuser852655723 rated it:

Read in January, 2006

If you don't think math can be sexy and exciting, then you ought to give Singh's book a read.

By the time Pierre de Fermat - sometime civil servant and occasional brilliant mathematician - left this earth, he'd left an indelible mark on the 17th century. His work with Pascal on "laws of chance" (considered by some an oxymoron) was groundbreaking and enduring, as was his contribution to proto-calculus.

Fermat, though, was very often remembered for something he wro...more

Like this review? yes (2 people liked it)

add a comment

03/10/09

Manny rated it:

bookshelves: science

Read in January, 1999

I guess the author does a reasonable job. But when I reached the end, I still didn't feel I understood at all how the proof worked. Probably that's just because it's so bloody hard. I got a lot more though out of Prime Obsession, Derbyshire's book on the Riemann Hypothesis, where the author opens up the box and shows you some of the actual math...

Like this review? yes (1 person liked it)

add a comment

08/08/07

Anna rated it:

bookshelves: 2008, history, re-read, science-popular

Read in March, 2008

recommends it for: all who're interested in maths but not necessarily experts at it

Finished. I have to admit I got completely lost in the last fourth of the book, where he discussed the modular somethings (equations, perhaps). It still is s really great book though.

**re-reading**

After 'White Dog', I strongly felt the need for something neat. Re-reading this is like plunging into a cool ocean.

______original review: ______
After I had finished his Code Book, I picked this one up. I always loved maths in school...trying to find a pat...more

Like this review? yes (1 person liked it)

2 comments

06/07/09

Kururu rated it:

(review of isbn 1841157910)

bookshelves: history, math, non-fiction

Read in May, 2009

This book is meant for the latter half of the bell curve. If you're mathematical experience stopped at high school, this book will still disappoint you. I don't understand how you can write about math without writing some math. The equations given weren't pertinent to Fermat's Last Theorem, most were digressions that were meant to prove an already obvious point, an explanation of the Pythagorean theorem?, thank you but my elementary school teacher did plenty enough. The book skimps over the hard...more

Like this review? yes

add a comment

06/27/09

Bob rated it:

Read in February, 2009

It was as exciting as fiction to follow not only the history of Fermat's conjecture and the effort it has evoked for 3 centuries but also the personal quest of Andrew Wiles, who embraced this quest as a boy and fortuitously was equipped with appropriate math skills to mount a mighty effort in pursuit thereof. The twists and turns the tale takes on are intriguing.

Among the insights shared is the metaphorical description by Wiles of the process of entering a room in total darkness, di...more

Like this review? yes

add a comment

05/18/09

Lamont rated it:

This review has been hidden because it contains spoilers. To view it, click here.

Like this review? yes

add a comment

06/27/09

Suzanne rated it:

Read in June, 2009

i thought this book would be boring because it was about math. hmm. in fact, it wasn't just good for a math book, but was genuinely compelling storytelling in its own right. it's not solely about fermat & crazy man wiles, which was my main concern, but instead covers hundreds of years of math and research and mathematicians, and makes the whole researching business seem far more exciting than, in my experience, it actually is. it was neat to have some context for all the names that pop up ov...more

Like this review? yes

add a comment

01/05/09

Brian rated it:

Be careful with this one. This is the one that will get you interested in mathematics, but it's sneaky. All the numbers are stuffed into appendices -- you don't have to touch the stinky stuff. Each chapter is a mini biography, starting in ancient Greece and ending now-ish. If you think rock stars have crazy lives, then check out the men and women in here. Not for the faint of heart: one has meat stripped from bone with sharpened clam shells and another lies bleeding to death in a field aft...more

Like this review? yes (1 person liked it)

add a comment

01/03/09

fbuser675532321 rated it:

What an amazing story! I am not a mathematician, so the math discussions were often over my head, although the author does his best to make the subject matter accessible. The most interesting part was the history of the quest to solve the problem and of mathematics in general. I skimmed some so that I would not get bogged down in the minutiae, but really enjoyed the book. It was fascinating to be drawn into the secretive, elite world of high-end mathematicians. It's great to know that there...more

Like this review? yes

add a comment

02/13/09

Davis rated it:

Read in April, 2009

If you hated math in elementary/high school, you probably won't like this book. But for anyone that likes math, this is a very good book. The author does an excellent job of explaining some of the more challenging mathematical concepts. Though there are some that are just too complex that you have to take the author's word for it. As the title conveys, the book focuses on Fermat's last unresolved theorem which stood for over 350 years. Fermat stated that he was able to prove his theorem, but did...more

Like this review? yes

add a comment

11/13/08

melydia rated it:

(review of isbn 1857026691)

Read in February, 2009

Most people are familiar with the Pythagorean Theorem which describes a right triangle: a^2 + b^2 = c^2. However, what you may not know is that Pierre Fermat claimed back in the 1600s to be able to prove that a^n + b^n = c^n has no whole number solutions for n > 2. Trial and error suggests this to be true, but for over 350 years, no one could prove it. This is the story of the equation and those who worked towards the eventual solution in the early 1990s, from Pythagoras through Andrew Wil...more

Like this review? yes

add a comment

10/22/08

Tom rated it:

bookshelves: my-favorites

Read in November, 2008

recommends it for: Red Sox fans and people who love curiosity

There are going to be a certain number, most likely a fairly large number of people who would never consider reading "Fermat's Enigma," because it is about math. That's a shame. Yes, there is math in this book, but you don't have to be a mathematical genius to understand it. God knows I'm not one. What Singh's book actually reminded me of was being a Red Sox fan. (I'll explain.)In the late 18th century Pierre Fermat, an amateur French mathematician, proposed a fairly simple theory. Eve...more There are going to be a certain number, most likely a fairly large number of people who would never consider reading "Fermat's Enigma," because it is about math. That's a shame. Yes, there is math in this book, but you don't have to be a mathematical genius to understand it. God knows I'm not one. What Singh's book actually reminded me of was being a Red Sox fan. (I'll explain.)In the late 18th century Pierre Fermat, an amateur French mathematician, proposed a fairly simple theory. Everyone learns Pythagoras's theory about right triangles, a squared + b squared = c squared. For example, if one side of a right triangle is 3 feet, and the second side is 4 feet, then the hypotenuse must be 5 feet. 3 squared (9) + 4 squared (16) = 5 squared (25). Fermat took that theory which can be generalized as a to the nth power + b to the nth power = c to the nth power, and stated that it could never be true for any value of n higher than 2. He jotted in his notes that he had "a marvelous proof," of this fact, but these notes were only discovered after his death, and the proof was never discovered.

Over time it became more and more clear that there were no examples of numbers that disproved Fermat's theory, and that it was almost certainly true, but nobody could prove it. Proving the theory became the greatest prize in mathematics. People unsuccessfully devoted their lives to it. Advances were made towards solving it by some of the greatest mathematical minds of the 19th century, but it was a long way from being proven. In the 20th century many professional mathematicians weren't interested in working on it because they feared it was impossible to prove and they didn't want their careers to be spent working on a problem that couldn't be solved. However, mathematical ideas came about that were not intended to be used for Fermat, but eventually ended up being essential.

Andrew Wiles was 10 years old and living in Cambridge England when he first came across Fermat's theorem. It immediately captured his imagination, and with the attitude of a fearless child, he thought of how great it would be if he could prove it, when so many others had failed. This isn't quite as crazy as it sounds since many of the most important ideas in math history had been made by young adults in their twenties. He eventually came to be a PHD student at Cambridge, and while he toyed with Fermat's theory, he knew that too much interest would be discouraged, since it was considered a dead end. Luckily, his chosen field, elliptical curves, ended up being vital in finally proving Fermat's theory. Eventually he became a professor at Princeton, and as various, seemingly unrelated breakthroughs were made, he thought the time had come to take a serious crack at Fermat. Without telling anyone but his wife, he worked feverishly for seven years, constantly making progress on the proof. He used new breakthroughs, he used forgotten 19th century ideas, and when those didn't work he made his own techniques. Finally in June 1993, he was ready to share his proof with the world. He asked for, and was given 3 lectures at a conference in Cambridge. People suspected that he had something major to share, but didn't know what. Then rumors started flying that he had proved Fermat's theory, but Wiles wouldn't comment. His first lecture had to do with already understood math that laid the groundwork for his proof. During his second lecture he started to introduce new ideas that people saw might be leading toward Fermat. A buzz of excitement gripped the conference.When he presented his final lecture people who couldn't get into the auditorium were crammed into the halls. Wiles then presented his proof. Towards the end of the lecture, flashes started going off as people recorded the historic moments.

What I loved about this book, and why it reminded me of being a Red Sox fan, was the atmosphere of an accomplishment that had been so deeply desired for so long, that people had given up. When Wiles completed his proof he did so because of his own amazing imagination and dedication, but also because of the work of many who had gone before him, some famous, others tragic and almost anonymous. Nothing, no matter how great an accomplishment, has the explosive joy of something that has been prayed for and desired over a great period of time. When the Red Sox won the World Series in 2004, after an 86 year drought, I felt like a 16 year old girl at a Beatles concert. I'm sure that is how the most learned minds in math felt as Wiles completed his proof.(less)

Like this review? yes

add a comment

06/08/08

Hung added it

Pretty nice read, tells the history of Fermat's Last Theorem, the centuries of mathematicians who tried to solve it, and the one(s) who finally did. Singh writes a surprisingly compelling and human story. Lots of suicides and deaths, some romantic intrigue and twists of fate thrown in, too. But above all, there is a lot of struggle--of many sorts. If you like watching Nova and the Discovery Channel, you'd like this.

The funny thing to me is that I know some math zealots who point to t...more

Like this review? yes

add a comment

04/05/08

Taka rated it:

(review of isbn 000724181X)

bookshelves: japan_jul07-present, popular-science

Read in April, 2008

Great (4.5)--

Although I would've appreciated a little more concrete math, Simon Singh does another superb job at explaining in lay terms what Fermat's Last Theorem meant for mathematics at large and what Andrew Wiles achieved in proving it after 350 years of numerous failures by other greatest minds of their times. It's a fascinating history whose intensity and influence can't be gleaned from just reading the theorem, which states simply:

For n greater than 2, there is no ...more

Like this review? yes

add a comment

01/21/08

Bloodaxe rated it:

Read in May, 2003

The book "Fermat's Enigma" gives an account of the history of Fermat's Last Theorem and its proof. For those who are not familiar with the story, the theorem in question was stated, without proof, by the French mathematician Pierre de Fermat in the 17th Century. Fermat claimed to have a clever proof of his theorem, but the margin on the page was too narrow to contain it. Thus, after his death, many great mathematicians struggled to uncover the proof that Fermat never gave, and the prob...more

Like this review? yes

add a comment

12/08/07

Trevor rated it:

Read in January, 2000

This book is as interesting as a detective story while being about quite advanced mathematics - as such it is quite a book showing the remarkable skill of its writer to explain complex ideas in ways that are always readable and enjoyable.

A mathematician finds a simple proof to what seems like a deceptively simple problem of mathematics - that pythagoras's theorem only works if the terms are squared, and not if they are any other power up to infinity. Sounds dull. Except that the mat...more

Like this review? yes

add a comment

05/15/07

Raghu rated it:

Read in January, 2001

This book is about the history of mathematicians trying to find a proof for Fermat's theorem, formulated 350 years ago. Pierre de Fermat, the great French mathematician, postulates that

x^n + y^n = z^n

has no non-zero integer solutions for x, y and z when n > 2. Fermat also wrote that he has discovered a truly remarkable proof which his notebook margin was too small to contain.
That set the mathematical community to find the 'elegant' proof that Fermat talked ...more

Like this review? yes

add a comment

06/14/08

Rebecca rated it:

bookshelves: math-science-stats, non-fiction

A very good book, one of my favorites. It brings out the excitement of doing mathematics, makes it a human endeavor. It gets across to the reader some of the beauty of mathematics. It also describes how some areas of math relate to one another, and how many areas relate to Fermat's Last Theorem. It makes clear why the proof is important and gives the reader some basic understanding of the broadest possible outline of the proof (not that I remember it at all now, 8 years later).

I ...more

Like this review? yes

add a comment

04/06/09

Danny rated it:

A great history of number theory, starting with Pythagoras, heading to Euclid and the library of Alexandria, through the dark ages, then the modern era.

The importance of Fermat's last theorem seems a bit overstated to me, but I guess that's to be expected given the title. Nonetheless, the math parts are pretty accessible, and the history is story is very interesting.

Like this review? yes

add a comment