Mathematical Fallacies and Paradoxes

Mathematics may seem to be the embodiment of certainty, but in Mathematical Fallacies and Paradoxes Brian Bunch shows that you sometimes have to watch your step.In the first chapter he demonstrates that the circumference of a circle doesn't always seem to be 2πr, as well as proving that 1=0. This is followed by a look at the paradoxical nature of infinity, and a chapter on arguing by contradiction. Bunch then gets on to self reference and the paradoxes of set theory, leading up to a well written explanation of Gödel's incompleteness theorem.

Gödel's incompleteness theorem would have made a good finale for the book, but Bunch then moves on to paradoxes of space and time, where he gets a bit lost - in particular his explanation of Schwarz paradox is wide of the mark, and his relativistic race between Achilles and the tortoise is very muddled. (There is also a flash of illogic earlier in the book concerning intuitionism and the contrapositive of Goldbach's conjecture). But if you don't mind the occasional lapse when Bunch is trying too hard to find a paradox where there isn't one, then you will find that most of the book provides and enjoyable and informative read.