Mathematician, political leader, and Pythagorean philosopher from *Tarentum. He was elected general seven times and sent a ship to rescue *Plato (1) from *Dionysius (2) II of Syracuse in 361. He figures prominently in several Platonic letters whose authenticity is controversial, but he is never mentioned by name in the dialogues. Many works were forged in his name in later antiquity. Only Fragments 1–4 are generally accepted as authentic, although these are supplemented by extensive testimonia. He was famous for his technical work in mathematics, providing the earliest solution to the celebrated problem of the duplication of the cube. He was the most accomplished music theorist in the Pythagorean tradition. His proof that numbers in superparticular ratio (n+1/n) have no mean proportional has relevance for music theory as does his work with the arithmetic, geometric, and harmonic means (fr. 2). He gave mathematical accounts of the diatonic, enharmonic, and chromatic scales and developed an influential theory of acoustics. His primary philosophical principles may have been inherited from his predecessor, *Philolaus.