## The History of Mathematics## Greek and Roman Mathematics |

## What were Pythagoras’s other contributions? |

It is interesting that the Pythagorean theorem was not Pythagoras’s only contribution. He is considered the first pure mathematician. He also founded a school that stressed a fourfold division of knowledge, including number theory (deemed the most important of the pursuits at the school and using only the natural numbers), music, geometry, and astronomy (these subjects were called the *quadrivium* in the Middle Ages). Along with logic, grammar, and rhetoric, these studies collectively formed what was deemed the essential areas of knowledge for any well-rounded person.

Pythagoras not only taught these subjects, but also reincarnation and mysticism, establishing an order similar to, or perhaps influenced by, the earlier Orphic cult. The true lives of Pythagoras and his followers (who worshipped Pythagoras as a demigod) are a bit of a mystery, as they followed a strict code of secrecy and regarded their mathematical studies as something of a black art. The fundamental belief of the Pythagoreans was that “all is number,” or that the entire universe—even abstract ethical concepts like justice—could be explained in terms of numbers. But they also had some interesting non-mathematical beliefs, too, including an aversion to beans.

Although the Pythagoreans were influential in the fields of mathematics and geometry, they also made important contributions in astronomy and medicine, and were the first to teach that the Earth revolved around a fixed point (the Sun). This idea would be popularized centuries later by Polish astronomer Nicolaus Copernicus (1473–1543). By the end of the 5th century B.C.E., the Pythagoreans would become social outcasts; many of them were killed as people grew angry at the group’s interference with traditional religious customs.