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Review - The Mystery of the Aleph - Amir Aczel
Georg Cantor was a man who suffered for his maths - arguably it drove him mad. To be more precise, the opposition Cantor faced, particularly from one mathematical authority figure, was certainly enough to drive this unstable character over the edge.
Aczel's book is a well-balanced mixed of life story and life's work. There is plenty of information on Cantor himself, and a good explanation of his contribution to the mathematics of set theory and the infinite.
It's arguable that Aczel is just a little too determined to find links between Cantor, infinity and the Jewish mystical secret writings, the Kabbalah, which at best have a tangential importance, but as long as you don't give that too much weight, the book is very good.
We see how Cantor moved the university of Halle as stepping stone to greater things, only to be stuck there for the rest of his life, in part because of the horrendous intervention of Leopold Kronecker, at one point Cantor's sponsor, but a man who could not tolerate the sophistry of working with infinite sets and made every effort to stop Cantor being published or progressing in his career.
We also get to see how Cantor pulled together the various contributory parts that would make up set theory, and how he extended this to take in infinite sets. Best of all there are Cantor's beautifully simple and elegant proofs without a single equation that show the relationship between the infinity of the integers and that of rational fractions, and all the fractions between 0 and 1.
It's a story you will come across in any book on infinity - you can't do infinity without taking on Cantor - but by dedicating a book to Cantor, Aczel has the space to really explore this strange man.
Also in hardback:
Reviewed by Peter Spitz
See more about the author in the Amir Aczel biography
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