Archytas (early to mid 4th century BC)

Archytas of Tarentum (modern Taranto in southern Italy) was a contemporary and personal acquaintance of Plato, and the last of the famous Pythagoreans in antiquity. An ancient source (Proclus) chytas with those mathematicians ‘who increased the number of theorems and progressed towards a more scientific arrangement of them’ and ranks him among the predecessors of Euclid. His chief contribution in mathematics was to find a solution for the doubling of the cube. As a Pythagorean philosopher, Archytas gave mathematics universal scope: he viewed the four cardinal branches of Greek scientific knowledge – arithmetic, geometry, astronomy and music – as ‘sister sciences’ since they could be formulated mathematically. In both mathematics and music he emphasized the study of mean proportionals. He also conducted empirical investigations in acoustics and invented simple technical devices by which to illustrate the application of mathematical principles to mechanics. Archytas was able to combine his philosophical-scientific interests with an active political career; he was a leading statesman of Tarentum and served as a successful general.