My PhD thesis investigates a delicate problem in the history of ancient philosophy and science, the relationship between Pythagorean philosophy and the history of Greek mathematics. The names of Pythagoras and the Pythagoreans are immediately associated with mathematics; nevertheless, modern scholars mostly agree that the Master and his first disciples played at best a minor role in the development of what Archytas called the “sister disciplines” which form the core of ancient “scientific” knowledge, namely arithmetic, geometry, music, and astronomy. Between the tragic end of the Pythagorean school and the extinguishing of its last sparkles in the 4th century BC, on one hand, and the full Neopythagorean rebirth of the 1st century CE with fi...