Rating: 
Summary: On the Right Track but Flawed
Review: Amir D. Aczel's _Fermat's Last Theorem_ starts with great promise. Aczel begins by describing Andrew Wiles' initial, although flawed, surprise presentation of a proof of Fermat's Last Theorem--one of the "Holy Grails" of mathematics--at a 1993 conference. Here, Aczel writes with gripping suspense. You can't wait to read on and find out all the details--a summary of the solution unfolding like a mystery novel as Wiles spells out the proof on the blackboard, an account of the reaction of Wiles' colleagues, an explanation of the hole in the proof that was soon after discovered, and the tale of how Wiles plugged the hole. But after only a few pages, Aczel takes a sidestep to tell a bit of the history of Pierre de Fermat and the origin of the theorem. This is understandable, since the reader needs some background information on the nature of the problem, its difficulty, and its importance before we get back to the proof. However, the Fermat detour is only the first of many, and the next 100 pages (in a book only 136 pages long) amount to one long alternate route explaining the mathematics that led to Fermat's conjecture and the mathematics that grew out of attempts to prove it. Unfortunately, there are some serious flaws with the approach and the overall conception of the book. _Fermat's Last Theorem_ is written for interested laypersons. That idea in itself is problematic in that the mathematics behind the proof encompasses a huge swath of the entire field, including many complex graduate-level topics. It is still possible to tackle the job, but Aczel, or his publisher, further compounded the problem by limiting the book to 136 relatively scant pages. Aczel's solution is to handle the book as a cursory survey of the personalities and ideas that contribute to the problem and solution. Each personality receives only a few pages, and the ideas are presented in a way that they'll probably further confuse a novice yet frustrate a more serious student or amateur who would like to really _understand_ some of the mathematics--not just know the names of some of the ideas. Worse, Aczel never bothers to really tie the ideas together and relate them all to solving Fermat's Last Theorem--in retrospect many just hang like forgotten laundry. Additionally, Aczel loses his intriguing, suspenseful voice soon after the material on Fermat begins and barely recovers it near the end. The final result is a very shallow history of mathematics where novices will forget 80% of what they read by the next day and serious students and amateurs will feel that they don't know much more than when they began. It would have been wiser to expand the book to at least four times its current size, spend more time on each topic, and present more serious mathematical material in a large number of sidebars, which novices could skip. It would have also been wiser to maintain the Wiles story and lay out a simplified version of the proof step-by-step, delving into background material as necessary. As written, the best we can hope for is that Fermat's Last Theorem might whet your appetite for a more in-depth study. Aczel's writing is not bad, and I'm confident he knows his subject--if he'd only tell us about it. It's a shame that such interesting material is given such a light treatment.
Rating: 
Summary: Well Done
Review: An ancient mathematical problem, claimed to be solved by a French mathematician, Fermat, over 300 years ago, but no proof survived. This problem known as Fermat's last theorem still stymied modern mathematicians until Andrew Wiles armed with modern mathematical techniques and theory demonstrated a proof in 1994.
This is one of Amir Aczel's better books. A balanced book that succeeds in giving the reader a general idea of the mathematics involved. Mr. Aczel's explanation of a difficult field of math are very good, and keeps the reader's interest. This author in many of his other works usually expands his text to the point where the story does not agree with the title or purpose of the book, This time he got it right. A short book, fast paced, occasional tidbits of interesting facts to setup a historical background of the problem and its solution. It finishes with the trials and tribulations and eventual success of Andrew Wiles, a mathematician turned into a recluse being consumed and driven to solve this secret.
Rating: 
Summary: Tries hard to capture the excitement
Review: At the time, proof of Fermat's Last Theorem really was exciting, at least to mathematicians. The story of the theorem starts out with all the right pieces for a tale that would really hold the general reader's attention. Fermat - a brilliant but reclusive mathematician - left a tantalizing clue in the margin of a book "... a truly remarkable proof which this margin is too small to contain." It was a hint at a map to a wonderful treasure of number theory.
More than 300 yeears later, Andrew Weil did in fact excavate that treasure by creating a proof of the theorem. It took him more than seven years of lonely dedication, and built on seemingly every mathematical innovation between Fermat's time and his own. Unfortunately, Aczel got carried away in tracing those innovations. Aczel traced many of those historical strands, from Archimedes and the ancient Phoenecians, through the 18th and 19th centuries, and into the present. I'm afraid he didn't tie those strands together as tightly as I could have hoped. I came away form the book remembering vingettes, but no real historical plot. Maybe the real continuity, through the mathematical developments, would have been to technical to follow.
The book is brief enough, however, that it was still easy to read. That famous theorem, so called long before it was proved, has been a part of mathematical culture for centuries. Its conquest really is a good story, but I'm still looking for a good telling of it.
//wiredweird
Rating:
Summary: one star for the argument and one for the effort, but...
Review: For those who read Italian: questo libro e' un'accozzaglia di brevi excursus senza legami fra loro. Quando avrete finito di leggerlo ne saprete come prima, al massimo avra' stimolato la vostra curiosita'.
A collection of small notes disconnected from each other. Quite a pity.
Rating:
Summary: Some of us actually liked it!
Review: From about 2/3's of the reveiws, one would presume this to be the worst history of mathematics ever written however, I found it completely enjoyable. I have avoided math all my life, and learned more from this book that I did in high school and college combined. The style is simple enough for me to tie mathematics in with the real world, and fun enough for me to persue other books on mathematical history, as well as venture back to math class to learn more. I do question the validity of some of the historical statements: beans and testicles aside, (editing could have been a little tighter,) this book has started me on a wonderful journey. I am no mathematician, but at least I have a fighting chance at comming to grips with it due to this light introduction.
Rating:
Summary: A quick read mathematical history of Fermat's Last Theorem
Review: I had this book sitting around the house for more than a year before picking it up yesterday. Once started, I could hardly put it down and finished it today. This is an entertaining read for the person more interested in mathematical history than a true mathematician (but what mathematician reads or writes about the history of mathematics anyway?) I might challenge one or two historical references, but the anecdotes about ancient mathematicians represent the true charm of this book. A quick, easy, enjoyable read.
Rating: 
Summary: A very enjoyable, light read for amateur mathematicians.
Review: I very much enjoyed the way that the author brought details of the history of mathematics into the story of the final proving of Fermat's Last Theorem. I enjoyed the intrigue and the suspense. I especially enjoyed the little tidbits, such as the story of happenings when the Pythagoreans discovered irrational numbers. If my teachers back in junior high school had shared such interesting sidelights of history, I am sure that I would have come to appreciate math at a much earlier age. I bought copies of this book as Christmas presents for those of my friends who enjoy trivia of the world of mathematics.
Rating:
Summary: What, an interesting Math book!?
Review: I would have thought the only way to make a Math book interesting would be to have it be a pop up book where the Numbers would start attacking you or something. Let's face it, math blows bit time. This makes Aczel's work even more amazing. This relatively small book reads even quicker than its size. I completed it in one day - a weekday, with a full day of work no less. Akzel's turns the proof of a 300-year-old equation into a great work of literature. He goes through the proof in a unique way, by describing the history of each part of the proof chronologically. He give mathematical history lessons stretching from Babylonian times to the present day in a way that any layman can understand. Even if you have no interest in numbers or equations, this book will fascinate you. It helps me understand why professors devote their whole lives to mathematics. Heck, it even got me a little interested in Math as well (of course I snapped out of once the Simpsons came on). I would highly recommend this book to anyone.
Rating:
Summary: Misses the target
Review: Someone who wants to report events in a complex technical field to laypersons has two choices. First, attempt to explain the content in nontechnical language. Second, concentrate on the personages involved and help us relate to them as human beings. Aczel fails on both counts. He barely even attempts to cover the technical issues involved. Readers will come away from this book knowing virtually nothing about the mathematics entailed in the proof of Fermat's Last Theorem, other than that it builds on topics developed over thousands of years by many contributors. He can hardly be faulted for this, since the math required for understanding the proof is extremely dense and well beyond the capacity of any but graduate-level mathematicians. It is on the personal level that Aczel really fails. His descriptions of most of the mathematicians covered read as if they had been lifted from a poorly-written encyclopedia. He glosses over them and their work so lightly that we are left completely unsatisfied. The question is, "Why?" He could have extended the book beyond its scant 137 pages and given us more detail about the players and explained some of the simpler mathematics. This would have produced a much better book. The reason why this book gets three stars, instead of one, is its coverage of the Taniyama-Shimura-Weil-Serre controversy. This is actually interesting and reasonably well-written. If this had been excerpted and placed in a Sunday supplement, it would have been an admirable effort. The net is that if you want to know anything about the mathematics, or details about the people, look elsewhere. If you only want to know the barest outline of what all the fuss is about, this will suffice.
Rating:
Summary: Very good history of Fermat's Last Theorem.
Review: This book described the history of Fermat's last theorem. It also described the history of some of the theories that Andrew Wiles built upon to solve Fermat's last theorem. For example, it gives an in-depth account of how Wiles proved that all elliptic curves are modular, thus drawing the world closer to solving Fermat's last theorem. It is a must-read for anyone interested in high-level mathematics.
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