 (3) Many other sixth-, fifth- and fourth-century thinkers are labeled Pythagoreans in the Greek tradition after the fourth century BCE. By the late fourth century CE many of the most prominent Greek philosophers including Parmenides, Plato and Aristotle come to be called Pythagoreans, with no historical justification. There are nonetheless a number of thinkers of the fifth and fourth century BCE, who can legitimately be called Pythagoreans, although often little is known about them except their names. The most important of these figures is Hippasus. What criterion should be used to identify an early figure as a Pythagorean is controversial and there is debate about individual cases. Fourth-century evidence shows that Pythagoreanism gave an unusually large role to women for an ancient philosophhical school. It is likely that the Pythagorean communities that practiced a way of life that they traced back to Pythagoras died out in the middle of the fourth century BCE. 