A surprising number of mathematicians, even quite prominent ones, believe in a realm of perfect mathematical entities hovering over the empirical world - a sort of Platonic heaven. Alain Connes of the Collège de France once declared that 'there exists, independently of the human mind, a raw and immutable mathematical reality,' one that is 'far more permanent than the physical reality that surrounds us'. Roger Penrose, another unabashed Platonist, holds that the natural world is only a 'shadow' of a realm of eternal mathematical forms.

LRB 27 August 2009 | PDF Download