This is the definitive book about George Cantor, the brilliant mathematician whose work includes the groundbreaking development of both set theory and transfinite numbers.



Interestingly, the author's preface says this is not a biography of Cantor, though it does include personal information, especially as it relates to Cantor's intellectual development and emotional issues. Rather, it's a thorough and rigorous exposition of his mathematical and philosopical ideas. Dauben says, "... this book represents a study of the pulse, metabolism, even in part the psychodynamics of an intellectual process: the emergence of a new mathematical theory".



But, a few warnings. While both the Amazon and jacket blurb claims this is for the "general reader", it is not. It is most definitely NOT a popularization, and I don't think the publisher tries to make that clear. It is a scholarly tract, an extension of Dauben's Harvard doctoral dissertation, and it seems he has not watered it down much. It is highly technical, with many equations, and is primarily written for academicians who are fluent in higher mathematics (clearly, not a large potential audience for the book!). Consistent with such a scholarly publication, it includes excellent index, bibliography, and notes sections, with many entries being technical, from obscure journals, and/or in foreign languages.



I found that my three semesters of college calculus (though no set theory) were inadequate preparation to follow many of the mathematical arguments. If you have an undergraduate or higher degree in pure mathematics, you should have no trouble.



Dauben also uses a fair amount of German, and a little French and Latin, all without translation -- you're expected to know these things.



It's possible to get a sense of Cantor's accomplishments by simply skipping over the math and foreign languages that are beyond you, although the more prepared you are in these areas, the more you'll get out of the book.



However, if you're interested in the history of math but want to avoid the naked technicalities, I instead recommend William Dunham's "Journey Through Genius", which uses nothing beyond high-school mathematics. Dunham's book has twelve readable chapters on significant mathematical discoveries, and as a measure of Cantor's importance, he, like Euclid and Euler, gets two chapters while Archimedes, Newton, and the rest get just one.

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