The Artist and the Mathematician (ISBN 1568583591)

fluff & fuss, but where's the math?:
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.

Maddening:
Brief review for a brief book: Very disappointing. My expectation had been something similar to 'The Professor and the Madman' which is an excellent non-fiction account of dictionary writing. This book was maddening in that it read as a listing of names and simply lacked any cohesion or narrative arc. The author seemed to be simply spilling his research - formidable, yes - on the pages. I was looking for some basic explanations of mathematics wound into a narrative. Even the 'mystery' behind the Bourbaki group was revealed blandly. I wound up skimming the last hundred pages and feel no loss that the book will be quickly discarded.

Does a decent job for a 240 pages mass-market book:
I was expecting something bad after reading the customer reviews (many 1 star). But no, I am satisfied so 4 stars. You have to consider that this book is a short, mass-market book. You can't expect to cover the intellectual/political/economical/cultural/... situation of the Bourbaki period and the biographies of all the great mathematicians of the group and the MATH in 214 pages of text. Aczel does a good job of presenting all the elements necessary to understand Bourbaki. I have the impression that the bads reviews resulted from the deception that it was not THE FINAL BEST BOOK that it could have been; maybe this book is still to be written but it's probably not for general public.

At least one other criticism false:
I am writing this review, simply because I am a great fan of Aczel's other books -- fermat's last theory, entanglement, and his book on the discovery of the compass, and for another reason. Firstly, All of these were excellent!! Secondly, The criticism leveled against him by some writer who did a review for the post, reflects more on the sloppy style of that reviewer than it does on Aczel's scientific writing. The Post really should retract their review and get a proper review for his book. They owe him that much. It really is a sign of the dumbing down of our society that the Post can let stand this kind of mindless review. I am not associated with Amir Aczel in any way, and his current book might not be cracked out to be what the others have been. We all have off days, but I do know he deserves a better review than the Post gave him. -- as well as one GREAT BIG apology!! Sometimes reviewers try to elevate themselves, like fleas, by biting the backs of other people. I think this is what is going on here. Good luck . I, for one, shall buy this book!

A good solid biography of a collective individual:
The idea of a collective individual named Nicolas Bourbaki seems to be a communism ( small C) of mathematics. The idea came from Andrew Wiles originally it seems as way to produce needed new mathematics texts as a joint venture of elite French mathematicians. In many case the result tends to generalizations, axiomatics approaches and texts that are hard to read and understand, if superior to the French texts that existed before 1933. The world war scattered the people involved and delayed publications until the 1950's of the most representative texts. The collective seems to have declined after the hey days of the '60's as a result of Bourbaki liberal political activity. Alexandre Grothendieck seems to have been associated also with the decline as he wanted to rewrite the basic foundation from set theory to category theory. There is no doubt of the influence of this era of mathematics, but the "structualism" philosophy the text reports is less important maybe that the author gives credit? I liked this book better than Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem as is is clearly just biography and history of mathematics and pretty much leaves the mathematics alone. Radical claims about Grothendieck's extreme genius seem to be belied by the lack of concrete everyday results: that he thought 57 was prime seems to show he was a generalizer/ abstractor but not someone who left a lot of concrete examples like his dessins l'infant which the author never mentions ( but where I first ran into Grothendieck in mathematics). The great French mathematician Benoit Mandelbrot who had a history of a Jew in France very much parallel to Grothendieck is not mentioned, but his uncle is twice. Rene Thom gets one mention near the end. Yet it is chaos theory and fractals that brought down the structualist approach to mathematics? Mathematics is moving on from Nicolas Bourbaki, but it appears he has left us some classic mathematical texts that are very hard to find in English translations?