 There have been tendencies both to overvalue and to undervalue Archytas’ achievement as a mathematician. Van der Waerden went so far as to add to Archytas’ accomplishments both Book VIII of Euclid’s Elements and the treatise on the mathematics of music known as the Sectio Canonis, which is ascribed to Euclid in the ancient tradition (1962, 152–5). Although later scholars (e.g., Knorr 1975: 244) repeat these assertions, they are based in part on a very subjective analysis of Archytas’ style. Archytas influenced the Sectio Canonis, since Proposition 3 is based on a proof by Archytas (A19), but the treatise cannot be by Archytas, because its theory of pitch and its account of the diatonic and enharmonic tetrachords differ from those of Archytas. On the other hand, some scholars have cast doubt on Archytas’ prowess as a mathematician, arguing that some of his work looks like “mere arithmology” and “mathematical mystification” (Burkert 1972a, 386; Mueller 1997, 289). This judgment rests largely on a text (A17) that has been mistakenly interpreted as presenting Archytas’ own views, whereas, in fact, it presents Archytas’ report of his predecessors (Huffman 2005: 428–37; Barker 2007: 193–5). The duplication of the cube and Archytas’ contributions to the mathematics of music (Barker 2007: 287 calls him “a heroic figure in the early history of mathematical harmonics”) show that there can be no doubt that he was one of the leading mathematicians of the first part of the fourth century BC. This was certainly the judgment of antiquity. In his history of geometry, Eudemus identified Archytas along with Leodamas and Theaetetus as the three most prominent mathematicians of Plato’s generation (A6 = Proclus, in Eucl., prol. II 66, 14). Netz (2014) has recently argued that there were two networks that accounted for most of the progress in ancient Greek mathematics. The later used Archimedes as the paradigmatic figure, while the earlier used Archytas. Netz suggests that we should apply Bertrand Russell’s description of Pythagoras as “one of the most important men that ever lived” to Archytas instead both because of his mathematical genius and also because of his pivotal position in three different groups: (1) South Italian Pythagoreans, (2) Greek mathematicians, and (3) philosophers whose work was in dialogue with Plato (2014: 181–2). 