What do You think about Fermat's Enigma: The Epic Quest To Solve The World's Greatest Mathematical Problem (1998)?
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?
—Bruce
This is the kind of book that we non mathematical minds can easily digest and love. It gives you an epic scope of the number of minds that it takes to build new ideas. I doubt if Fermat had actually solved this theorem correctly, but this is impossible to prove. Fermat's theorem however was not impossible to prove! It was solved! Thanks to the efforts of many men (and women!) over many lifetimes and one final man who had the determination and persistence to finish the unthinkable. This book has a lot of wonderful elements, and really exemplifies a love of mathematics. Although if you want to actually understand the theorem this book may not be for you! I can honestly say reading it did not put the theorem in any more digestible light than it started out with. Perhaps it was to the authors advantage to skip the technicalities and focus on the enjoyment of the journey. I personally loved this approach, but it may not be for everyone, especially if you are actually looking to understand the theorem (a massive undertaking that is really not in my repertoire to comment on).
—Cassandra Kay Silva
If you buy the latest Jilly Cooper instead of this you WILL go to hell!This one languished on my bookshelf for the best part of a year as I was too scared to pick it up & start it. What held me back is what will probably put a lot of other potential readers off trying it - the boring old "I'm no good at maths" argument. Although my maths education is probably little above average (a good O Level and a terrible A Level, after which I rallied somewhat to obtain a reasonable HNC maths module) it's //very// many years out of use and it's all I can do to add two numbers up in my head. Given that this book is about a problem that flummoxed the best mathematical minds in the world for over 350 years you'd be forgiven for putting this back on the shelf and choosing something a little simpler. Well, don't even try that... YOU DON'T NEED ANY MATHS TO READ THIS! What Singh has done here is to present a hugely complex subject in a hugely entertaining way. The search for the answer to Fermat's riddle reads like a detective story and not a matehematical treatise and it includes a truly absorbing potted history of the development of maths over the years and, from Pythagoras to Fermat to Godel to Wiles, each part has a fascinating human side to it. Budding mathematicians needn't feel left out as the mechanics of the maths is also included, but it's treated in a gentle way: each step of the problem (and it's solution) is described in a simplified (but certainly not dumbed down) manner and some simple exercises are included in several short appendices. However, take heart! There are several places where elements of the maths are obviously too complex for us mortals and Singh is not afraid to say soo and then gloss over them completely. That may be a disappointment to some, but it's not at all unreasonable in my opinion. All in all, the net result is a book that is sensitive to its readers, intelligent, interesting and important. It's literally unputdownable and it had the added bonus of tricking me into thinking that I'm a little cleverer than I really am. I notice there's an inevitable Wills and Kate bio on the bestseller list at the moment. Put your hard earned cash into Andrew Morton's pockets or read something that will make you feel like a genius. The choice is yours.
—Campbell Mcaulay
