I feel my impression of this book is different enough to warrant writing a review. I actually quite enjoyed this book. Many of the other reviewers areI feel my impression of this book is different enough to warrant writing a review. I actually quite enjoyed this book. Many of the other reviewers are certainly on point with saying this book is poorly organized. I feel that is very true, I also feel that Aczel attempts to cram too many topics into a single book to its detriment.
If you work in the Mathematical field at all, it's likely you've come across the name Bourbaki at some point, even if you're a more modern mathematician. Famous for being the name of a group that wrote as a single individual, they are considered one of Mathematics' power house groups. I think Aczel did a good job in giving us a sort of inside look into the group for the lay reader. I found the story of Alexandre Grothendiek absolutely enthralling and I probably could have just read a biography on him. I had heard of him before this book, naturally, but I didn't realize he had such an incredible background story. I truly enjoyed reading about the mathematicians prior to World War II, which prompted the creation of the group and their struggles through the war. I feel like that's one of the more overarching points behind the book, to give Bourbaki's story and relay it's overarching goals in mathematics. I really liked reading about the interrelations of the Artists, Philosophers, and Mathematicians involved in Paris' Café scene and I felt that, very much, worked into the spirit of Bourbaki. I loved seeing how the Art and Philosophy influenced the mathematics and vice versa.
Unfortunately, I feel like the book gets pretty side tracked when it starts talking about Linguistics and Anthropology with Levi-Strauss. I feel like that sort of got forced into the narrative and broke the story up a bit too much for me. At a certain level I understand why it was inserted before Grothendiek's chapter covering his post-Bourbaki narrative and Bourbaki's demise, but I felt like it was too much to me and I didn't find the topic as interesting.
I realize some of the narrative is written for "dramatic effect", which is usually okay, but when it covers Weil's story at the beginning and ends with a cliff hanger... then doesn't continue until more than halfway through the book is kind of a bit much. This made it feel even more erratic and I can understand why some readers would mark this down.
Amidst this disorganization is a really good story about the famous mathematician Alexandre Grothendiek and the super group Bourbaki. I found both of these aspects very memorable and if you can focus on that excellent material, it really makes this book worthwhile....more
When I first read the description of this book on the dust jacket in the bookstore I realized I needed to buy the book immediately. When I got home, IWhen I first read the description of this book on the dust jacket in the bookstore I realized I needed to buy the book immediately. When I got home, I started reading right away. I tore through the first parts of this book as the real stories of Galois and the authors premise came to light... but then my interest sort of stalled out after a while.
I think it had to do with the fact that this book wound up coming off as very repetitive. This book is extremely well researched and I loved finding out Galois' story in this new light which challenges a lot of typically told stories. However, I can only take the reiteration of Galois' and Cauchy's interactions so many times. Amidst the repetitions there might be a slight smattering of new detail, which was all the more frustrating to read about, because I'd wished it was in the section covering that topic. This happened with other mathematicians Amir covered as well.
I really thought the premise of this book was very interesting. It sets out to get an idea of mathematical tropes throughout history. Such as how would a mathematician be cast in a story in the 1700's, vs. 1800's and so on. He finds very different approaches to mathematics over the years and sees the great innovators of the 1800's and modern times more akin to artists, poets, and musicians than men of science, which is how it was previously looked upon in the 1700's. The book mostly looks at the giants of the field over the centuries, but with the shift of the 1700's "grand géometrès" being aligned with the doers of science, I wonder if the Applied Mathematician has simply transitioned into this role. Whereas the Purist stays rooted in the beauty and truth of mathematics as an artist would in approaching their craft. This question is never really addressed in the context of 20th century mathematicians and instead reference is only given to the tragic and misunderstood purists like Nash and Grothendiek. However, no mention is made of Erdös, who was no doubt an immense purist and giant of his field, yet he was never shunned in tragedy as the author tries to argue with his other examples. Erdös never really got disillusioned with the field even though his peculiarities easily could have led him in that direction. Instead the mathematical community seems to have embraced him and perhaps he is an example of the mathematical community learning from history, however, it seems the treatment of Perelman may have been a step backwards in some peoples opinion.
The other, far more minor, gripe I had with the book was the technical section in Chapter 7. Now, to Amir's credit he does point out that this section can be skipped for those not wishing to engage the technical work without any loss to the overall story. Now, I like doing and reading about mathematics as much as any mathematician, but I sort of felt that the amount of time spent discussing Euclid's 5th postulate was a bit overly verbose. I feel like the purpose was to show readers how rooted in reality mathematics had been for centuries. Then with the invention of Non-Euclidean geometries mathematicians were free of the shackles of reality and were able to consider all kinds of lofty worlds, whether they had any merit in reality or not. I am not sure this section was successful at this... while I was reading it, I never got this impression, but after considering it more, I feel that was the spirit of wanting to include the details. Unfortunately, in order to write it in a way that wouldn't lose the original thesis, the section is left dry, even though attempts are made to tie it into the overall story. This section just came off as forced in there, rather than enlightening.
In the end, I am glad I read this book. Very glad actually, for it has given me new insights into the history I cherish. It just wasn't executed in a flawless way. I feel like this book is about fifty pages too long and I do recommend future readers skip Chapter 7 as the author suggests and just focus on the story. I almost wish he had developed the conclusion's artistic criticism of portraits more. Rather than discussing that for a few pages then switching back to repeating most of the stories again for six pages more than was necessary. I think the book could have been easily fleshed out with other examples rather than only focusing on giants. The absence of female mathematicians is rather striking, and I can only imagine one can easily find tragic tales there.
In the conclusion he also touches on the possible new ways of approaching purists interests of proof. Now there are computers that can literally test all possible cases of a situation. I believe the 4-Color Theorem was found in this way. Much of the mathematical community shuns this "proof by computer" method, for the reasons he lists as its lack of elegance etc. But there is another major reason this is sort of shunned. In developing groundbreaking work, often times connections between fields of mathematics are made in the proof process that were previously unheard of. This gives us very deep insight into the structure of mathematics and brings us in whole new and creative directions. Andrew Wiles' proof of "Fermat's Last Theorem" brought together many fields of mathematics. So, personally, I don't think its just lack of elegance that we lose when a computer brute forces a proof for us... its those subtle connections between other branches of the discipline that are also lost.
I do agree with his ultimate thesis when it comes to the modern representation of mathematicians. They are often cast as misunderstood geniuses that just can't overcome the trappings of real world. Hence movies like "Proof" and "Goodwill Hunting" emphasize these kinds of tragic traits in some ways. I suppose this is a more favorable approach versus the misunderstood scientist whose only course of action seems to commit evil acts in todays typical stories. A very sad misrepresentation of science in the end......more