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" "In comparison with the wise man, the saint is perhaps just a specialist - a specialist in holiness; whereas the wise man has no specialty. This is not to say, far from it, that Dehn was not a mathematician of great talent; he left behind a body of work of very high quality. But for such a man, truth is all one, and mathematics is but one of the mirrors in which it is reflected - perhaps more purely than it is elsewhere.
André Weil (6 May 1906 – 6 August 1998) was one of the greatest mathematicians of the 20th century, whether measured by his research work, its influence on future work, exposition or breadth. He is known for his foundational work in number theory and algebraic geometry. He was a founding member, and de facto the early leader, of the influential Bourbaki group. The philosopher Simone Weil was his sister.
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I had also, unsuccessfully, looked for the works of Saint John of the Cross. The flashing beauty of his poems would probably have moved me more than did Saint Theresa, but it was not until much later that I came to know his work. I read a little of Saint Theresa and became quickly convinced that mystic thought is at bottom the same in all times and places: reading Suzuki's popular works on Zen was soon to confirm this conclusion. ... Speaking of a saint whose behavior was somewhat eccentric, one of the monks remarked gently: "But Christianity is madness" ("el cristianismo es una locum"). This perfectly orthodox statement often comes to mind when I think about my sister's life.
Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously, and in which the unconscious (however one interprets this word) seems to play a role. In a famous passage, Poincaré describes how he discovered Fuchsian functions in such a moment. About such states, Gauss is said to have remarked as follows: "Procreare jucundum (to conceive is a pleasure)"; he added, however, "sed parturire molestum (but to give birth is painful)." Unlike sexual pleasure, this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do so at will, unless perhaps by dogged work which it seems to reward with its appearance. It is true that the pleasure experienced is not necessarily in proportion with the value of the discoveries with which it is associated.
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Mozart's music, even at its most beautiful, often gives an impression of some being who, though very far above us in his incomprehensible serenity, nevertheless stops to remember us for a brief instant and comes within our reach, with gentle mockery and tender pity, to transcribe a fleeting message for us. But sometimes, in certain quartets and quintets, and in certain parts of The Magic Flute, this same being, without a thought for us, communicates with his fellow beings, and what we hear then is a world unknown to us, a world of which we are allowed only a furtive glimpse.