Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever [Hardcover]

Hal Hellman (Author)

Book Description

Publication Date: September 11, 2006 | Series: Great Feuds

Praise for Hal Hellman

Great Feuds in Mathematics

"Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments."
-Professor Dirk van Dalen, Philosophy Department, Utrecht University

Great Feuds in Technology

"There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master."
-New Scientist

Great Feuds in Science

"Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences."
-American Scientist

"Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time."
-Nature

Great Feuds in Medicine

"This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here."
-The New York Times

"Stimulating."
-Journal of the American Medical Association

Editorial Reviews

Review

"…genuinely insightful…accurate…rapid and fluent…" (London Mathematical Society, January 2007)

Review

"Those who think that mathematicians are cold, mechanic proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man, but Hellman's stories also show how scientific fights bring out sharper formulations and better arguments."
—Professor Dirk van Dalen, Philosophy Department, Utrecht University

"Hellman's fascinating book illustrates what can happen when great scholars employ weapons of math destruction."--William Dunham, Muhlenberg College, author of The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities

"A very engaging effort and a good introduction to the human side of mathematics."--Mathematics Association of America

See all Editorial Reviews

Product Details

• Hardcover: 256 pages
• Publisher: Wiley; 1 edition (September 11, 2006)
• Language: English
• ISBN-10: 0471648779
• ISBN-13: 978-0471648772
• Product Dimensions: 9.3 x 6.5 x 0.9 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #134,380 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

17 of 17 people found the following review helpful:

5.0 out of 5 stars Fascinating Disputes But Beware The Challenging Arguments, October 29, 2006

By 

G. Poirier (Orleans, ON, Canada) - See all my reviews
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This review is from: Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever (Hardcover)

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.

6 of 6 people found the following review helpful:

4.0 out of 5 stars David Foster Wallace's Righteous Twin, May 8, 2007

By 

Christopher Grant (Salem, UT USA) - See all my reviews
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This review is from: Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever (Hardcover)

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.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Readable Math, February 1, 2007

By 

F. Klein (NJ, USA) - See all my reviews
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This review is from: Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever (Hardcover)

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.