The calculus is the story this [the Western] world first told itself as it became the modern world.

Darwin's theory of evolution is the last of the great nineteenth-century mystery religions. And as we speak it is now following Freudians and Marxism into the Nether regions, and I'm quite sure that Freud, Marx and Darwin are commiserating one with the other in the dark dungeon where discarded gods gather.

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.

In the end, every scheme and every science is justified by itself or it is not justified at all.

Just who has imposed on the suffering human race poison gas, barbed wire, high explosives, experiments in eugenics, the formula for zyklon b, heavy artillery, pseudo-scientific justifications for mass murder, cluster bombs, attack submarines, napalm, intercontinental missiles , military space platforms and nuclear weapons? If memory serves it was not the Vatican.

Bystanders wandered in and out of the merchant's stall, passing the time, talking of dreams they might purchase. Workers and slaves stooped from labor asked timidly for dreams of wine and ease. Women asked for dreams of love, and men for dreams of women.

At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.