The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.

At some time in the history of the universe, there were no human minds, and at some time later, there were. Within the blink of a cosmic eye, a universe in which all was chaos and void came to include hunches, beliefs, sentiments, raw sensations, pains, emotions, wishes, ideas, images, inferences, the feel of rubber, Schadenfreude, and the taste of banana ice cream.

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.

More than sixty years ago, mathematical logicians, by defining precisely the concept of an algorithm, gave content to the ancient human idea of an effective calculation. Their definitions led to the creation of the digital computer, an interesting example of thought bending matter to its ends.

Every computer divides itself into its hardware and its software, the machine host to its algorithm, the human being to his mind. It is hardly surprising that men and women have done what computers now do long before computers could do anything at all. The dissociation between mind and matter in men and machines is very striking; it suggests that almost any stable and reliable organization of material objects can execute an algorithm and so come to command some form of intelligence.

Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake-there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?