No doubt you have been wondering all these years what the fuss was all about when they made you prove the Pythagoras theorem in high school. No doubt you and your math teacher thought that it was merely an exercise to test or sharpen your mathematical skills. It certainly was that. You may still be able to demonstrate that in any right triangle the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose side are the two sides that meet at a right angle.
Your math teacher was not expected to spell out to you that Pythagoras (560–495 BC), to whom the theorem was attributed, was a gigantic figure in early Greek philosophy and that this theorem was of immense practical importance to navigators in the ancient world.
He lived on the Greek island of Samos, near the Turkish coast, then the Persian coast, at the crossroads between east and west. He may have visited Egypt whose scholars used sophisticated mathematics to build the pyramids. He may also have inherited some of his knowledge from the Babylonians. He taught that in nature truth can be found in numbers, a belief shared, in various ways, by thinkers up to and including Kepler, Copernicus and even Isaac Newton. His belief in the transmigration of the soul after death greatly influenced Plato and his studies of the physics of harmony secured him a prominent place in the history of music in antiquity.
You may ignore the unconfirmed report that Pythagoras visited not only Egypt but also the underworld.
Eric Koch’s new book, The Weimar Triangle, is available at Indigo-Chapters and in your local bookstore. 
Amazing coincidence. The Jan-Feb issue of the LRC has an article by David Orrell (a review of a book by Florin Diacu called Megadisasters), who talks about how western numerical traditions began with Pythagoras and — you’ll like this bit — mentions the relationship between math and music. His father was a gem engraver.
I have heard lots about Pythagoras who was not only a mathematician but also a mystic. He had quite a few disciples. I remember Dr. Wirtz (Die Wutz) talking about him. Actually, I know little about him and music. Mathematics, yes. RK
I don’t know how much Pythagoras’ philosophy remains relevant, but his math definitely still is. He defined the concept of math proof – it cannot be based on intuition or experiment/observation, but it must consist of deductive chains of reasoning.
He claimed that “numbers and their ratios rule the universe.” Alas, by proving his famous theorem, he stumbled into irrationals (and, in a way, discovered the real numbers on which much of the modern math is based). The discovery if irrational numbers – those who are not ratios of integers – proved very disturbing to him and his followers. They called the irrationals alogon, which in Greek had a double meaning – “not a ratio” and also “not to be spoken.” It seems that when Hippasus, a Pythagoras’ follower, spoke about the difficulties these numbers brought about, he was assassinated. It’s probably the only known case in the history of math when talk about an intractable math problem led to murder.