Who they were
Pythagoras was a Greek philosopher and mathematician who settled at Croton in southern Italy, part of the Greek world known as Magna Graecia. Much about his life is legendary, and the work of his followers is hard to separate from his own.
What they did
At Croton he founded a religious and philosophical brotherhood, teaching the transmigration of souls and the idea that numbers underlie reality. The Pythagorean theorem bears his name, though the relationship it describes was already known earlier in Babylonia, and his personal authorship of specific results is uncertain — he cannot be flatly credited with proving it.
Legacy
Pythagorean ideas about number, harmony, and the cosmos deeply influenced Plato and later thought. Partly through him, southern Italy is remembered as one of the cradles of Greek philosophy.