Pythagoras:

A Universe made of Numbers

PART 1 Pythagoras & His Philosophy Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet there is relatively little known about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, there is nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. This does not mean that we cannot gain some incite on who he was or what he taught or believed, because there are details of Pythagoras's life from
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Everything somehow can be explained in mathematical terms. It is the archas, or principle, of mathematics that make things what they are, that give to everything its distinctiveness. To use later terminology, it seems that the Pythagoreans view the principles of mathematics as providing structure or form to Being. Even though they are immaterial, the principles of mathematics, nevertheless, are more "real," as it were, than that to which they give structure or form: that which is an archê is more real in the sense that without it other things would not be what they are; their greater reality consists in their logical priority. In the above quotation, Aristotle adds that the Pythagoreans hold that in fact it is the elements of numbers that are the elements of all things; this makes their teaching more difficult to understand. It seems they reasoned that, since numbers were by nature "first" with respect to mathematicsin other words, since mathematics is impossible without numberseverything must somehow be numbers. Aristotle explains how impressed the Pythagoreans were to discover that musical scales could be expressed as ratios (using numbers); from this discovery they may have sought to ascribe numbers to all things. Indeed, they conclude that the whole heaven to be a musical scale and a number. This part of Pythagoreanism has perplexed scholars, however, since it is not obvious how numbers