...this refinement and delicacy were what Cale adored; but Cale had been beaten into shape, hammered in dreadful fires of fear and pain. How could she be with him for long? A secret part of Arbell had been searching for some time for a way to leave her lover__lthough she was unaware of this, it is only fair to record. And so as Cale waited for her to save him while he worked out a way of saving her, she had already chosen the bitter but reasonable path of the good, of the many over the one...

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.

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing__ne great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.