Mathematics and mysticism

“Of the perfection of the number six, which it the first of the numbers which is composed of its aliquot parts.These works are recorded to have been completed in six days... because six is a ,—not because God required a protracted time... but because the perfection of the works was signified by the number six.”

“If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.”

“When a man counts one, two, three, he is not only doing mathematics, he is on the path to the mysticism of numbers in Pythagoras and Vitruvius and Kepler, to the Trinity and the signs of the Zodiac.”

“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.”

“The word witr literally means "odd number," and tradition says: "God is odd, He loves the odd."Musalmāns 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.”

“Hardy had a] profound conviction that the truths of mathematics described a bright and clear universe, exquisite and beautiful in its structure, in comparison with which the physical world was turbid and confused. It was this that made his friends... think that in his attitude to mathematics there was something which, being essentially spiritual, was near to religion.”

“Only a fool would try to compress several millennia's blending of mathematics and religion. We proceed.”

“An equation for me has no meaning unless it expresses a thought of God.”

“: Prithee, no more prattling; go; I'll hold. This is the third time; I hope good luck lies in odd numbers. Away, go! They say there is divinity in odd numbers, either in nativity, chance, or death. Away!”

“The development of the theory of numbers had its root in the number mysticism of Pythagoras, attained a strictly scientific character in the theory of the even and the odd, and led finally to the systematic establishment of the theory of the divisibility and the proportion of numbers as found in Book VII of the Elements.”

“The necessity of ratiocination by symbols does carry in its train a tendency to mysticism from which even the keenest intellects cannot always free themselves. ...[footnote:] Some thinkers have spoken of, or alluded to, a certain 'reaction of language upon thought' which results in error or confusion... It is to this kind of illusion or, to... the mental attitude which makes it possible, that I refer when I speak of mysticism, the mystical tendency or bias.”

“Even in pure mathematics, conspicuously the domain of definite and stable conceptions, careful investigation might be found to reveal evidence of an infiltration of the mystical. ...this fact, if so it be, in some measure accounts for the almost insuperable difficulty which many strenuous minds find in mastering even the first principles of the subject, as well as for the purely intellectual repugnance with which they regard it.”

“Everyone knows that to read an author simply in order to refute him is not the way to understand him; and to read the book of Nature with a conviction that it is all illusion is just as unlikely to lead to understanding. If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians.”

“Several interesting peculiarities should not be omitted, as for instance, that Leibniz, about 1667, was secretary of an alchemist's society (of so called rosicrucians) in Nuremberg. Leibniz describes alchemy as an "introduction to mystic theology" and identifies the concepts of "Arcana Naturae" and "Chymica."”