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53 of 55 people found the following review helpful:
1.0 out of 5 stars
A massively wasted opportunity, December 13, 2006
Amir Aczel is as frustrating an author as you will find anywhere. The man is bright, no question about it. He also has impeccable taste when it comes to interesting subjects to investiagte. He has written books on various mathematical subjects: Fermat's Last Theorem, Descarte, and now Nicolas Bourbaki. Yet his followthrough and his writing habits are infuriatingly inconsistent and shows signs of discordant chaos in his reasoning. He also has a disconcerting proclivity towards doing a hack job on a subject to get paid and then moving on to better things.
The story of Bourbaki is a fascinating one, so I was eager to read this book. The miniscule size of this book should have been a red flag, Aczel's reputation, at least in my head, should have been another, but I proceeded to buy it because I am an eternal optimist and I believe that people can and will surprise me and change my preconceived notions.
It didn't work this time, nor any other times when I placed my faith in Aczel. So where to begin?
1) As the previous reviewers had stated, there are no math in this book. No explanation of what Bourbaki was up to. How do you write a book on mathematicians without writing about mathematics? I understand that one does not wish to populate the book with excesive mathematical details but the power of math is in its compact notations. He does try to explain things in general terms, but a few figures and a few lines of math would have done wonders to his narrative.
2) Not enough back ground material was covered. When Aczel is trying to explain the application of structuralism in linguistics and in psychology, he was doing some extremely fine narration of extremely dense and abstract ideas and putting them into the context of what Levi-Strauss and others are trying to do, but he was not consistent in narrating the other parts of the book, he did a lot of hand waving and hot air generating.
3) As an author writing about people, one can definitely become enamoured with certain people and grow to dislike certain others. Aczel definitely fell in love with Alexander Grothendieck's story and disliked Andre and Simohne Weil. It is irresponsible, however, for Aczel come out and say that the reason for the demise of Bourbaki is because Grothendieck left the group without explaining fully WHY category theory is a more reasonable foundation. It is equally irresponsible for the ad hominem attacks on Andre Weil's character without citing specific instances of his behavior.
4) The book reads like a very bad draft, there is no continuity to the history and the book is not built around mathematical logic nor is it based on chronological order, it is as if Aczel decided to put all these bits of stories and mathematics together haphazardously. The writing is very jagged. Reading and making sense of the story is extremely fatiguing because the author made every effort to confuse the reader. Many anecdotes are repeated for no apparent reason and they are repeated without qualifiers or additional information.
5) There does not seem to be any care taken to build a case for or against anything. The author just scattered facts and his own opinions out and it was up to the readers to figure out a logic for themselves.
6) As in his previous books, the author seem to be building toward a conclusion, a crescendo in the narrative, yet after the build up, there is no crescendo, nor a diminuendo, there is just a monotone white noise in the background.
Like I said, this is a massively wasted effort towards a very interesting subject. The only thing that I have gotten from this book is the germination of various subjects that the author mentioned in passing, so thank you Amir Aczel for your bibliography and a desultory book report.
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16 of 19 people found the following review helpful:
1.0 out of 5 stars
Poorly titled, poorly written!, December 21, 2006
Unlike the other reviewers, I was not interested in detailed discussions of the mathematics that the Bourbaki group wrote. I heard the author plugging his book on the radio and the topic sounded interesting. However, when I started reading the book it did not cover what he was talking about in much detail. The first half of the book is a poorly conveyed life history of the various mathematicians in the group. The book lacks cohesion and continuity. The book is not very long, but the author repeats material in later chapters that was covered in earlier chapters. I can not believe that any publisher would publish such a poorly written book.
I am a Physics instructor that emphasizes the importance of good writing even in technical fields. This is a perfect example that I often cite to my students of someone in a technical field that does not know how to convey his thoughts because he failed his English course.
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10 of 11 people found the following review helpful:
1.0 out of 5 stars
fluff & fuss, but where's the math?, October 15, 2007
This book is disappointing on a number of levels. I'll mention just a few. First, it is peppered with overstated superlatives. Every mathematician seems to be extremely important and every theorem is extremely important and every text is extremely important and we are rarely shown what is so important about anything. After awhile, the sensationalism looses its impact.
In stressing the importance of Nicholas Bourbaki, the book often ignores the contributions of others. So while Bourbaki contributed to the notion of building mathematics on the foundation of set theory, this misses the previous work of others such as Giuseppe Peano. Also, others deserve some credit for the level of precision mathematics now enjoys--David Hilbert and Alfred Tarski, to name just two.
At times it seems poorly edited. For example on page 101 we find "if we look at the set of numbers 123, the various possible orders form a group." Now, if you already know some group theory you can figure out what he meant to say. But the newcomer is more likely to say, "set of numbers???? I see only one number and it is one hundred and twenty three." As another example, we are given an illustration on page 104. We see a collection of spheres and a collection of arrows. It is supposed to illustrate how a topological space can be associated with a vector space. How the picture is meant to illustrate anything is puzzling.
One page 117 we are told "Algebraic geometry is an area in which the geometry of numbers is studied." In fact, algebraic geometry is a wide field connected to many branches of math including number theory and topology. It uses mostly commutative algebras to attack problems in geometry. So when I find a mistake like this, it calls into question remarks made in the rest of the text on topics that I'm unfamiliar with. I have to wonder if the author knows what he's talking about.
The book tends to repeat stories. It reminds me of visiting a nursing home where a resident with a memory problem keeps telling the same stories over and over. So for example, on three occasions in the book we're told that wedding invitations were printed for Bourbaki's imaginary daughter. And the fact is indirectly referenced at a fourth point. The first time it was interesting. On pages 69 and 119 we're told that Henri Poincare was called "the last universalist" and in both places we're told why. One page 125 we read, "As we shall see, the modern idea of structure originated in linguistics..." But we already saw this on page 102. My guess is the author didn't have enough to fill a book, so rather than doing a good job of explaining some of the mathematical ideas, he fluffed it out by repeating things.
Indeed, many interesting ideas are presented in the book but nothing seems well developed. So one last example, from page 197. Here we're told, "And then, of course, there are the great paradoxes in set theory, which make the discipline full of theoretical holes." What are these paradoxes? How do they poke holes in set theory? If Aczel has answers, he doesn't explain them. I only know of Russel's Paradox and the Cantor Paradox. The first has been taken care of and the second isn't really a paradox in the classical sense, but only used in a reductio ad absurdum argument.
Having said all these horrible things I'll acknowledge I did read the book to the end. It has some colorful characters and anecdotes that were new. I just wish the story was better told.
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