Pythagorean philosopher, mathematician and politician, Archytas of Tarentum was a contemporary and a friend of Plato. He made a significant contribution to mathematics, and to the theory of music of the 4th c. B.C. Furthermore, he is thought to have influenced Plato's views on the relation between philosophy, politics and mathematics.
Arhytas was born, and became active, in Tarentum in south Italy. The exact dates of his birth and death are not available, but they seem to match with His philosophy is appraised as , but he was acclaimed primarily for his mathematical discoveries..
Archytas was a dominant political figure in Tarentum - one of the most powerful cities of Magna Graecia. His comparison with Pericles lies in the fact that he was elected a general seven consecutive times by the (democratic) political system of his homeland; let alone that he is reputed not to have ever been defeated in a battle. As it is suggested in Plato's,Archytas repeatedly rescued Plato from his .
Archytas' prominence, already established in the 4th c. B.C., resulted in the spurious attribution of a big amount of works and fragments to him. However, current research has securely attributed to him only four fragments written in Doric dialect. Genuine works of him are the Harmonics, On Sciences, and Discourses (Diatribai) .
The greatest achievement that Archytas accomplished, which elicited admiration in antiquity, was the solution he devised for the 'Delian Problem', that is, the problem of doubling the cube. Diogenes Laertius reports that Archytas "was the first to bring mechanics to a system by applying mathematical principles" (Lives of Eminent Philosophers VIII, 83); but we are in the dark as to the meaning of the term "mechanics". Archytas must have had an interest in fields of applied mathematics as it is evinced by his work in the theory of optics, in music theory (where he introduced a new system of musical scales), and by his explanation on how sound travels.
Taking into consideration that Archytas was the only friend of Plato to have wielded power, and also that he was an important mathematician and philosopher, it is not implausible to assume that he might had been the model for the philosopher-king of the platonic Republic. This assumption is upheld by the designation of five "akin sciences" as the curriculum for the propaedeutic education of the city's guards: arithmetic, geometry, stereometry, astronomy and harmonics. Both the list of the acknowledged sciences, and the term "akin sciences" must be drawn from Archytas himself, for in his 1st fragment he states that "indeed concerning the speed of the stars and their risings and settings as well as concerning geometry and numbers and not least concerning music, they [mathematicians] handed down to us a clear set of distinctions. For these sciences seem to be akin". Plato revised the Pythagorean quadrivium by ushering a fifth science -stereometry- which was a branch of mathematics that people like Archytas developed at that time. At any rate, the criticism lurking in the context is much more of the essence: true science is purely intelligible, and does not depend upon the sensible diagrams of the geometers, neither on the visible "ornaments" of the astronomers, nor on the sounds of the musicians. It is not improbable that Plato's criticism was assaulted against mathematicians such as Archytas, who (being a Pythagorean) could not make the distinction between a realm of sensible and a realm of intelligible beings. On the other hand, Archytas' thesis that arithmetic (which he names "logistic") is the principle mathematical science (Fr. 4) would be consistent with Plato's own views.
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