Pythagoras is most famous for the Pythagorean Theorem, which shows the relationship between the length of the two legs of a right triangle and the length of its hypotenuse. He is also famous for other aspects of his mathematical and philosophical insights. He was a mystic as well as a mathematician and founded a whole school of philosophy.
Pythagoras lived between approximately 560 and 480 B.C.E., and he had many insights about the natural world well ahead of his time. He came up with a relatively accurate theory of vision, theorized that the world was spherical in shape, and realized that both the morning and evening star were the planet Venus. The Pythagoreans also proved that the square root of two is an irrational number. Pythagoras investigated musical theory, particularly the lengths of lines corresponding to musical harmonies, always attempting to find meaningful patterns in the relationships between quantities.
Pythagoras and his followers held great reverence for math and numbers in general, believing them to be existent entities in and of themselves. Their group treated men and women as equals which was very radical for the time. They were rather famously vegetarian, to the point that, prior to about 1944, vegan diets were called "Pythagorean."