Pythagorean Quotes
It becomes you to be wise to smell, feel, and have in estimation these fair books, de haulte gresse, light in the pursuit, and bold at the encounter. Then you must, by a curious reading and frequent meditation, break the bone and suck out the substantific marrow, - that is what I mean by these Pythagorean symbols, - with assured hope of becoming well-advised and valiant by the said reading; for in it you shall find another kind of taste, and a doctrine more profound, which will disclose unto you deep doctrines and dreadful mysteries, as well in what concerneth our religion as matters of the public state and life economical.
François Rabelais
The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square which is incommensurable with the side, being in the ratio to it of √2 to 1. The Pythagorean proof of this particular case survives in Aristotle and in a proposition interpolated in Euclid's Book X.; it is by a reductio ad absurdum proving that, if the diagonal is commensurable with the side, the same number must be both odd and even. This discovery of the incommensurable... showed that the theory of proportion invented by Pythagoras was not of universal application and therefore that propositions proved by means of it were not really established.... The fatal flaw thus revealed in the body of geometry was not removed till Eudoxus discovered the great theory of proportion (expounded in Euclid's Book V.), which is applicable to incommensurable as well as to commensurable magnitudes.
Thomas Little Heath
There is no foundational mathematical or physical reason the relationship between Pythagorean and tempered western music should exist. It just does. The rich flexibility of the tempered scale and the ... bountiful archives of western music are a testimonial to this wonderful coincidence provided by nature.
Robert J. Marks II
After Aristotle and Ptolemy, the idea that the earth moves - that strange, ancient, and "entirely ridiculous", Pythagorean view was thrown on the rubbish heap of history, only to be revived by Copernicus and to be forged by him into a weapon for the defeat of its defeaters. The Hermetic writings played an important part in this revival, which is still not sufficiently understood, and they were studied with care by the great Newton himself.
Paul Karl Feyerabend
Koyré's exaltation of the "Platonic and Pythagorean" elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by mathematical reasoning. But later research has definitively established that Galileo's experiments preceded his attempts to give a mathematical account of their results.
Galileo Galilei