*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 GĂ¶del. 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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*God's Equation: Einstein, Relativity, and the Expanding Universe*

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