Pythagoreanism is a modern term referring to a multifaceted phenomenon that covered different aspects of the ancient world such as political life, religion, philosophy, and science and existed in only partly overlapping forms. Its originator, Pythagoras of Samos, moved c. 530 bce to Italian Croton, where his followers, the Pythagoreans, organized a political society, whose participants were at the same time encouraged to undertake various intellectual pursuits. Pythagoras’s best attested doctrine is transmigration of the soul, whereas philosophical theories and scientific discoveries ascribed to him are highly disputed. Often he is regarded as a purely religious thinker, though not a single religious figure is known of among his followers. All known ancient Pythagoreans belong to five overlapping categories: politicians, athletes, doctors, natural philosophers, and mathematical scientists. After Pythagoras’s death the Pythagorean societies politically dominated in Croton, Metapontum, Tarentum, and other cities of Southern Italy until the anti-Pythagorean uprising (c. 450), when many Pythagoreans were killed or forced to flee to mainland Greece. The last center of Pythagoreanism in Italy remained in Tarentum, led in 367–361 by Archytas, a successful general and brilliant mathematician. The Pythagorean school created theoretical arithmetic and mathematical harmonics and greatly contributed to natural philosophy, geometry, and astronomy. Its disappearance after 350 bce marked the end of ancient Pythagoreanism. A new form of Pythagoreanism without the Pythagoreans were the pseudo-Pythagorean writings ascribed to Pythagoras and his fictitious family members. The first wave of Pseudo-Pythagorica (late 4th to late 2nd centuries bce) was neither numerous nor popular but since the early 1st century bce it was superseded by the second, more successful wave that was part of the emerging Neopythagoreanism. These treatises written under the names of historical and fictional Pythagoreans and containing Stoic, Platonic, and Aristotelian doctrines aimed to present Pythagoras and his followers as the precursors of Plato and Aristotle. The first Neopythagoreans writing under their own names appeared in the mid-1st century ce and doctrinally belonged to Middle Platonism. The most important representatives of late antique Pythagoreanism were the Neoplatonists Porphyry and especially Iamblichus, who secured its existence until the end of Antiquity.