This philosopher and mathematician, born about the year B.C. 570, is one of the great names of antiquity; but his life is shrouded in dim magnificence. The old historians paint him as "clothed in robes of white, his head covered with gold, his aspect grave and majestic, wrapt in the contemplation of the mysteries of existence, listening to the music of Homer and Hesiod, or to the harmony of the spheres." [Footnote: Lewes, _Biog. Hist. Phil._] To him is ascribed the use of the word _philosopher_ rather than _sophos_, a lover of wisdom, not wise man. He taught his doctrines to a select few, the members of which society lived in common, and venerated him as an oracle. His great doctrine is, that _number_ is the essence of things, by which is understood the _form_ and not the _matter_ of the sensible. The elements of numbers are the _odd_ and _even_, the former being regarded as limited, the latter unlimited. Diogenes Laertius thus sums up his doctrines, which were that "the _monad_ is--the beginning of every thing. From the monad proceeds an indefinite _duad_. From the monad and the duad proceed _numbers_, and from numbers _signs_, and from these _lines_, of which plain figures consist. And from plain figures are derived solid bodies, and from these sensible bodies, of which there are four elements, fire, water, earth, and air. The world results from a combination of these elements." [Footnote: Diog. Laert., _Lives of Phil._] All this is unintelligible or indefinite. We cannot comprehend how the number theory will account for the production of corporeal magnitude any easier than we can identify monads with mathematical points. But underlying this mysticism is the thought that there prevails in the phenomena of nature a rational _order, harmony_, and conformity to _law_, and that these laws can be represented by numbers. Number or harmony is the principle of the universe, and order holds together the world. Like Anaximander, he passes from the region of physics to metaphysics, and thus opens a new world of speculation. His method was purely deductive, and his science mathematical. "The _Infinite_ of Anaximander became the _One_ of Pythagoras." Assuming that number is the essence of the world, he deduced that the world is regulated by numerical proportions, in other words, by a system of laws, and these laws, regular and harmonious in their operation, _may_ have suggested to the great mind of Pythagoras, so religious and lofty, the necessity for an intelligent creator of the universe. It was in moral truth that he delighted as well as metaphysical, and his life and the lives of his disciples were disciplined to a severe virtue, as if he recognized in numbers or order the necessity of a conformity to all law, and saw in obedience to it both harmony and beauty. But we have no _direct_ and positive evidence of the kind or amount of knowledge which this great intellect acquired. All that can be affirmed is, that he was a man