They told of dripping stone walls in uninhabited castles and of ivy-clad monastery ruins by moonlight, of locked inner rooms and secret dungeons, dank charnel houses and overgrown graveyards, of footsteps creaking upon staircases and fingers tapping at casements, of howlings and shriekings, groanings and scuttlings and the clanking of chains, of hooded monks and headless horseman, swirling mists and sudden winds, insubstantial specters and sheeted creatures, vampires and bloodhounds, bats and rats and spiders, of men found at dawn and women turned white-haired and raving lunatic, and of vanished corpses and curses upon heirs.

Refusing the false securities of a stable and linear past, such an approach celebrates heterogeneous sensations and surprising associations, random connections, the ongoing construction of meaning and also admits into its orbit the mysterious agency of artifacts, space and non-humans from the past.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Heresy would like to think of itself as 'invented Truth'. But of course, all Reason and Logic would agree that no man can ever create Truth; he can only discover it. If heresy were ever at all beneficial, God would use it really to bring one right back to Truth, as countless 'inventions' have brought men to discovery.

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.