Mathematics and mysticism

"Throughout mans history there has been a close connection between the natural numbers and the activities of the divine Creator. The natural numbers have always been seen by some at least in every civilization to be symbolic of deep esoteric religious beliefs. The Babylonians had a hierarchy of sixty gods each of which was associated with one of the first sixty natural numbers. ...In ancient India, we find religious significance assigned to each of the first 101 numbers, and the Mayan civilization the first thirteen numbers all represented gods. There is something of a parallel in other sciences. Astronomy grew from astrology and chemistry from alchemy. It is therefore not surprising that number theory, first developed by the Pythagoreans, was associated with their religious beliefs and practices."

"A fifteenth century trend toward Platonic and Pythagorean mysticism, accompanying the growth of humanism over... earlier Scholastic philosophy, encouraged the previously denied use of the infinite and infinitesimal in geometry. As a result... mathematics was viewed as independent of the senses, not bound by empirical investigations, and thus free to use the infinitite and infinitesimal, provided that no inconsistencies resulted. By the early seventeenth century this view opened up bold new approaches."

"The word witr literally means "odd number," and tradition says: "God is odd, He loves the odd" Musalmaans pay the greatest respect to an odd number It is considered unlucky to begin any work, or to commence a journey on a day, the date of which is an odd number"

"Only a fool would try to compress several millennias blending of mathematics and religion. We proceed."

"It seems necessary to say something at the outset in justification of the scientific as against the mystical attitude. Metaphysics, from the first, has been developed by the union or the conflict of these two attitudes. Among the earliest Greek philosophers, the Ionians were more scientific and the Sicilians more mystical. But among the latter, Pythagoras, for example, was in himself a curious mixture of the two tendencies: the scientific attitude led him to his proposition on right-angled triangles, while his mystic insight showed him that it is wicked to eat beans. Naturally enough, his followers divided into two sects, the lovers of right-angled triangles and the abhorrers of beans; but the former sect died out, leaving, however, a haunting flavour of mysticism over much Greek mathematical speculation, and in particular over Platos views on mathematics. Plato, of course, embodies both the scientific and the mystical attitudes in a higher form than his predecessors, but the mystical attitude is distinctly the stronger of the two, and secures ultimate victory whenever the conflict is sharp. Plato, moreover, adopted from the the device of using logic to defeat common sense, and thus to leave the field clear for mysticism—a device still employed in our own day by the adherents of the classical tradition. The logic used in defence of mysticism seems to me faulty as logic..."

"A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow."