 Archytas, son of Hestiaeus (see Aristoxenus in Diels-Kranz 1952, chap. 47, passage A1; abbreviated as DK47 A1), lived in the Greek city of Tarentum, on the heel of the boot of Italy. The later tradition almost universally identifies him as a Pythagorean (e.g., A1, A2, A7, A16). Aristotle and his pupil Eudemus do not explicitly call Archytas a Pythagorean and appear to treat him as an important independent thinker. Plato never refers to Archytas by name except in the Seventh Letter, if that is by Plato, and he is not called a Pythagorean there. In the Republic, however, when Plato quotes a sentence which appears in Fr. 1 of Archytas (DK47 B1), he explicitly labels it as part of Pythagorean harmonics (530d). Cicero (de Orat. III 34. 139) reports that Archytas was the pupil of Philolaus, and this is not improbable. Philolaus was the most prominent Pythagorean of the preceding generation (ca. 470–390) and may have taught in Tarentum. Archytas’ achievements in mathematics depend on the work of Hippocrates of Chios, but we have no evidence that he studied with Hippocrates. The only pupil of Archytas who is more than a name, is Eudoxus (ca. 390–340), the prominent mathematician. Eudoxus presumably did not learn his famous hedonism from Archytas (see DK47 A9), and it is specifically geometry that he is said to have studied with Archytas (Diogenes Laertius VIII 86).