Pythagorean mathematics

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism. Pythagorean ideas exercised a marked influence on Aristotle, and Plato, and through them, all of Western philosophy.

Later revivals of Pythagorean doctrines led to Neopythagoreanism.

Pythagoras’ was already in ancient times well known for the mathematical achievement of the Pythagorean theorem. Although the Babylonians had used this formula for centuries, Pythagoras had discovered that "in a right-angled triangle the square of the hypotenuse is equal to the squares of the other two sides". In ancient times Pythagoras was also noted for his discovery that music had mathematical foundations. Antique sources that credit Pythagoras as the philosopher who first discovered music intervals also credit him as the inventor of the monochord, a straight rod on which a string and a movable bridge could be used to demonstrate the relationship of musical intervals.

Much of the surviving sources on Pythagoras originate with Aristotle and the philosophers of the Peripatetic school, which founded histographical academic traditions such as biography, doxography and the history of science. The surviving 5th century BC sources on Pythagoras and early Pythagoreanism are void of supernatural elements. While surviving 4th century sources on Pythagoreas' teachings introduced legend and fable. Philosophers who discussed Pythagoreanism, such as Anaximander, Andron of Ephesus, Heraclides and Neanthes had access to historical written sources as well as the oral tradition about Pythagoreanism, which by the 4th century BC was in decline. Neopyhagorean philosophers, who authored many of the surviving sources on Pythagoreanism, continued the tradition of legend and fantasy.

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