In The Mystery of the Aleph Aczel sketches a history of the mathematics of infinity, focusing on key mathematicians. Around a third of it is devoted to Georg Cantor; before him Aczel touches on the Pythagoreans, the Kabbalah, Galileo and Bolzano, and Gauss, Riemann, and Weierstrass; and after him on Zermelo, Russell, Russell's Paradox and the Axiom of Choice, Cohen, and Gödel. This is fascinating material, and Aczel finds a good mix of mathematics (nothing technical) and biographical detail. Covering such a range it is necessarily superficial, but the account of Cantor's life had a fair bit of detail that was new to me: about his conflict with Kronecker, his illness, and his obsession with proving Francis Bacon wrote Shakespeare's plays.

The Mystery of the Aleph is awkwardly placed between a biography of Cantor and a more general history: the selection of mathematicians and topics covered seems driven as much by the popular appeal of their life stories as by any internal logic. More worrying are some simple mistakes, unnecessary exaggerations, and overblown rhetoric. Cantor Diagonalisation is not, for example, used to prove the enumerability of the rationals, but rather to prove the reals are uncountable. Aramaic was not "the lingua franca of the Near East at the dawn of civilization". And what on Earth does it mean to say "Galileo was the first person in history to have touched actual infinity and survived the ordeal"? The editing is also sloppy in places: a discussion of whether or to what extent Cantor was Jewish is awkwardly split up, sentences are attached to unconnected paragraphs, and there's at least one spelling mistake any automated spelling-checker should have picked up. The Mystery of the Aleph is not a bad book, but it would have been a much better book if it had had a clearer focus and more careful editing.

November 2000

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Related reviews:

- Amir D. Aczel - God's Equation: Einstein, Relativity, and the Expanding Universe
- more history of science
- books published by Four Walls Eight Windows