The mathematikoi

As is well-known, Pythagoras founded a famous school of philosophy in the Italian city of Croton.  Interestingly, his school was open to both men and women.  It was stratified into two classes: the members of the outer circle were called the akousmatikoi, and those of the inner circle were called the mathematikoi.  The mathematikoi lived communally and observed a vegetarian diet.  Russell, in the History of Western Philosophy, summarizes the accomplishments of Pythagoras as follows:

He founded a religion, of which the main tenets were the transmigration of souls and the sinfulness of eating beans. His religion was embodied in a religious order, which, here and there, acquired control of the State and established a rule of the saints. But the unregenerate hankered after beans, and sooner or later rebelled.

(One wonders, by the way, how the mathematikoi, being vegetarians, were able to get enough protein if they were forbidden from eating beans.)  Russell also has something interesting to say regarding the original meaning of the word “theory”:

[N]ow I want to speak about the word “theory.” This was originally an Orphic word, which Cornford interprets as “passionate sympathetic contemplation.” In this state, he says, “The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.” For Pythagoras, the “passionate sympathetic contemplation” was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, “theory” gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue. It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.

Some further thoughts of Russell concerning mathematics from the chapter on Pythagoras:

Most sciences, at their inception, have been connected with some form of false belief, which gave them a fictitious value. Astronomy was connected with astrology, chemistry with alchemy. Mathematics was associated with a more refined type of error. Mathematical knowledge appeared to be certain, exact, and applicable to the real world; moreover it was obtained by mere thinking, without the need of observation. Consequently, it was thought to supply an ideal, from which every-day empirical knowledge fell short. It was supposed, on the basis of mathematics, that thought is superior to sense, intuition to observation. If the world of sense does not fit mathematics, so much the worse for the world of sense. In various ways, methods of approaching nearer to the mathematician’s ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge. This form of philosophy begins with Pythagoras.

[…]

Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as in a super-sensible intelligible world. Geometry deals with exact circles, but no sensible object is exactly circular; however carefully we may use our compasses, there will be some imperfections and irregularities. This suggests the view that all exact reasoning applies to ideal as opposed to sensible objects; it is natural to go further, and to argue that thought is nobler than sense, and the objects of thought more real than those of sense-perception. Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God’s thoughts. Hence Plato’s doctrine that God is a geometer, and Sir James Jeans’ belief that He is addicted to arithmetic. Rationalistic as opposed to apocalyptic religion has been, ever since Pythagoras, and notably ever since Plato, very completely dominated by mathematics and mathematical method.