Meta Maths: The Quest for Omega, by Gregory Chaitin (Atlantic, Ł17.99)
Imagine The Fast Show's Swiss Toni explaining number theory to a child by saying "Searching for prime numbers is like making love to a beautiful woman", and you have something of the rampantly idiosyncratic flavour of Chaitin's strange and marvellous book. From Euclid's proof that there are infinitely many primes, we are ushered through Gödel's Incompleteness Theorem and Turing's Halting Problem, so as to understand the author's own arcane but major contribution to the fields of mathematics and computing, an infinitely long and completely incalculable number called Omega. Apart from constantly comparing maths to sex, Chaitin also has an irrepressible way with bold type and exclamation marks (he loves to interject "Contradiction!", like a TV lawyer shouting "Objection!"). Disarmingly funny, but also thrillingly clear, as when he persuades the reader of the baffling arguments to the effect that real numbers do not actually exist. He has a taste, too, for the pregnant aphorism: "Software is frozen thought." Nice.
The Calculus Wars, by Jason Bardi (High Stakes, Ł16.99)
The feud between Leibniz and Newton over who invented the calculus is here narrated once again. Chaitin has strong views on the matter in Meta Maths: "Leibniz was such an elevated soul that he found good in all philosophies: Catholic, Protestant, Cabala, medieval scholastics, the ancients, the Chinese . . . It pains me to say that Newton enjoyed witnessing the executions of counterfeiters he pursued as Master of the Mint." This book reminds us that Leibniz was not above publishing anonymous attacks on his rival, but Newton's initial allegation that Leibniz stole his ideas was vicious and malign. Current scholars agree that the two discovered calculus independently: Newton wrote it down first, but Leibniz published it first. Bardi's workmanlike account spends a lot of time on scene-setting and evinces a slightly frustrating preference for précis over extensive citation and analysis of the voluminous correspondence that flew about on all sides. Readers of Neal Stephenson's superb Baroque Cycle trilogy need not trouble themselves further here.