Peace came to an end in 431 B.C. with the start of the Peloponnesian War between Athens and Sparta. This proved to be a long-drawn-out con-flict. Athens, at first successful, later suffered a devastating plague which killed off a fourth of it's population, and finally, in 404 B.C., had to accept humiliating defeat. Sparta assumed political leadership only to lose it, in 371 B.C., by defeat at the hands of a league of rebellious city-states During these struggles little progress was made in geometry at Athens, and once again development came from the more peaceful regions of Magna Graecia. The Pythagoreans of southern Italy had been allowed to return, purified of political association, and a new Pythagorean school at Tarentum arose, under the influence of the gifted and much admired Archytas.