Customer Reviews

Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

5 star:		(2)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

This is an excellent book. The prose is clear and engaging and, despite the title, there are very few equations such that those who are equation-phobic have little to fear. However, many of the disputes center on nineteenth to twentieth century front-line research in pure mathematics - areas such as set theory, concepts of infinity, etc. These early ideas were prone to heated discussion and, in many cases, led to feuds. In order to allow the reader to understand the basis for these feuds, the author has included the essence of some of the key contentious mathematical arguments, often directly quoting members of each camp. I found that carefully following these arguments in detail could be difficult at times, but I certainly agree that pondering them is important if one is to clearly understand the position of each side. The final chapter poses the fascinating question: Are mathematical advances discoveries or inventions?" And here again, there are avid supporters of each side. I gave the book five stars because of the interesting subject matter and because I feel that the author has done a truly excellent job in presenting such a potentially difficult subject to as broad an audience as possible. Nevertheless, I still believe that I would benefit from reading some chapters a second time. Although anyone reading this book could learn much from it, I believe that it would be most enjoyed by serious math buffs.

Wallace's seriously flawed Everything and More: A Compact History of Infinity (Great Discoveries) made me wary of buying another pop math book by a non-mathematician, so I put off buying _Great Feuds_ for some time, but eventually I gave in, and I'm glad I did. Hellman's cautious approach contrasts nicely with Wallace's bombast, and, unlike Wallace, Hellman gets almost all of the details right, with a notable exception being his claim that having a smallest element (rather than each of its nonempty subsets having smallest elements) is what makes a set well-ordered.

There's a lot of quoting of the opinions of professional historians, which is probably appropriate for a book written by an outsider, but I found it a bit tiresome after a while (just as I did when Peter Ackroyd took a similar approach in Albion: The Origins of the English Imagination). Also, I felt that Hellman didn't make it as clear as he could have who ended up winning the war of which these feuds were battles. 21st century mathematics is overwhelmingly Cantorian, Zermeloian, and Hilbertian, in the sense that the existence of actual infinities and the appropriateness of using the Law of the Excluded Middle and the Axiom of Choice are all taken for granted by mainstream practitioners. There are respected researchers probing the effects of rejecting these principles, but they are few in number and those who do reject them are definitely working in the margins.

Don't let these quibbles or my 4-star rating keep you from buying this book. Within its genre, it's about as good as they come.

After seeing Mr. Hellman on CBS Sunday Morning News recently, I picked up his newest book, Great Feuds in Mathematics. A most enjoyable book. Although I am not a mathematician I was able to read "around" the few equations and enjoy the insight he brought to the math and its place in history. A good read.

This book would be of most interest to advanced mathematicians and some philosophy initiates. I am a lay person with a large curiosity, however not being a math college major, limited my enjoyment of the "feuds."
Antonio Gonzalez