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Title: Georg Cantor by Joseph Warren Dauben ISBN: 0-691-02447-2 Publisher: Princeton Univ Pr Pub. Date: 20 September, 1990 Format: Paperback Volumes: 1 List Price(USD): $37.50 |
Average Customer Rating: 4 (2 reviews)
Rating: 4
Summary: Philosophy that can be mathematically proven
Comment: Some areas of mathematics can be described as philosophy that can be proven, and that certainly applies to the transfinite arithmetic created by Georg Cantor. When his results were first published, they were met with a great deal of opposition by many established and influential mathematicians. Considering the revolutionary aspects of his work, the fact that there was opposition was not surprising and indeed necessary for mathematics to properly advance. However, the opposition to Cantor's main results was so strong that the story that it drove him mad has become a part of the mathematical folklore. As Dauben is careful to point out, his research indicates that Cantor would have suffered from the bouts of depression independent of the degree of opposition to his work and most likely independent of what kind of work he did. In fact, Cantor himself is quoted as stating that his time spent in institutions was some of the most restful and productive of his life.
Cantor was in fact a very strong personality, he stood up well against the opposition and ultimately was proven to be correct. Dauben not only explains the sources of that strength, from his supportive, yet not domineering father to his wife and children. His religious beliefs were also very strong, to the point where he firmly believed that his work was part of God's structure of the universe and he was nothing more than a messenger.
However, it is the mathematics that really matters and Dauben does an excellent job in describing the essence of Cantor's discoveries. These are complex topics, and yet he does a good job in explaining the fundamentals of the mathematics and why it was so difficult for other mathematicians to accept. This is the best description of Cantor's work at a general level that I have ever read.
Published in Journal of Recreational Mathematics, reprinted with permission.
Rating: 4
Summary: Hard core and worth it
Comment: I found this was an excellent memoir of Cantor and his ideas. It goes far more deeply into the mathematics than other discussions of Cantor, and makes you want to read more about both set theory and about the development of topology in the early twentieth century. It also attempts to place Cantor's philosophy and mathematical ideas into a psychological context as well, which is probably appropriate - even essential - in the case of Cantor. Though, in twenty years, this aspect of the book may not wear well. All in all, it is a refreshingly strong and insightful treatment of one of the major historical figures in nineteenth century mathematics.
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Title: Contributions to the Founding of the Theory of Transfinite Numbers by Georg Cantor ISBN: 0486600459 Publisher: Dover Pubns Pub. Date: 01 June, 1955 List Price(USD): $9.95 |
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Title: Essays on the Theory of Numbers by Richard Dedekind ISBN: 0486210103 Publisher: Dover Pubns Pub. Date: 01 June, 1963 List Price(USD): $8.95 |
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Title: Understanding the Infinite by Shaughan Lavine ISBN: 0674921178 Publisher: Harvard Univ Pr Pub. Date: March, 1998 List Price(USD): $22.95 |
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Title: Uses of Infinity by Leo Zippin ISBN: 0486411788 Publisher: Dover Pubns Pub. Date: 20 February, 2000 List Price(USD): $6.95 |
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Title: Axiomatic Set Theory by Patrick Suppes ISBN: 0486616304 Publisher: Dover Pubns Pub. Date: 01 June, 1972 List Price(USD): $11.95 |
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