Archytas of Tarentumwas a Greek mathematician of the Pythagorean school who formulated the harmonic mean and was the first to integrate mathematics and mechanics. He also developed an ingenious geometric solution for the ancient Greek problem of doubling the cube. A contemporary of the famous Greek philosopher Plato, Archytas was also famous in his own time as a philosopher, statesman, and military leader.

Only a few fragments identified as the work of Archytas have survived. As a result, most of what we know about his life and work comes from ancient Greek writers, such as Aristotleand Proclus. Archytas was probably born in Tarentum (now Taranto, Italy) around 428 B.C., possibly into an aristocratic family. Nothing else is known about his early life.

In the beginning of the fourth century B.C., Dionysius the Elder, a tyrant of Syracuse, had driven the Pythagoreansout of most southern Italy's cities. Tarentum...