How did Pythagorean political influence grow in southern Italy?

Pythagorean political influence in southern Italy grew primarily through the activities of the school's "exoteric" associates—sympathizers who were not bound by the strict, secretive ritual requirements of the inner brotherhood. These associates became politically active and successfully established a Crotonian hegemony in the region. During the early 5th century BCE, these Pythagorean groups were deeply involved in government, even ruling the city of Croton for a period.12

The influence of these parties eventually became decidedly antidemocratic, which ultimately led to their decline. Around the middle of the 5th century BCE, a violent democratic revolution swept through southern Italy, resulting in the death of many Pythagoreans and the collapse of their political power in the region. While the school later saw a resurgence in the 4th century BCE under the leadership of Archytas in Tarentum, this later movement was characterized more by scientific and philosophical pursuits than the direct political dominance seen in the earlier Crotonian period.13