**Pythagoras** (*Πυθαγόρης* in ancient Ionian, *Πυθαγόρας* in modern Greek) of Samos was an ancient Greek philosopher, the founder of a religious and philosophic tradition that lasted for centuries, the **Pythagoreans** (*πυθαγόρειοι*).

Credited by his followers and later ancient historians with significant developments in mathematics, it seems likely that these were only done by his followers. Most famously, the Pythagorean Theorem was known to be true long before Pythagoras, while the earliest proofs in the western tradition (although one appears earlier in China) came after Pythagoras, but possibly by the Pythagoreans. More significantly, the idea that numerical and geometric theorems require proof at all (rather than merely empirical verification) is connected with the branch of Pythagoreans who called themselves *learners* (‘μαθηματικοί’, ‘mathematicians’).

Even if he did no true mathematics, Pythagoras himself seems to have had a mystical conception of number (meaning, more or less, natural number) as part of the order underlying the universe. This inspired the mathematical Pythagoreans to develop mathematical ideas to explain Pythagoras's moral precepts. The other branch of Pythagoreans, calling themselves *hearers* (‘ακουσματικοί’), concentrated on these precepts (‘ακούσματα’) and considered the mathematicians to be heretical. The mathematicians eventually joined the Platonists, and the acousmaticians (if we may call them that) joined the Cynics. There was a later revival of mathematical Pythagoreanism (the *Neopythagoreans*), influenced by Platonism and in turn influencing Neoplatonism, in the Hellenistic world. There was also a more typically religious group of Pythagoreans in Italy who influenced the Orphics.

- the Pythagorean theorem,
- Pythagorean triples,
- the Pythagorean temperament? (in music).

category: people

Last revised on January 3, 2021 at 08:28:05. See the history of this page for a list of all contributions to it.