## Democritus of Abdera (c460BC - c370BC)

Sometimes known as the ‘laughing philosopher’, Democritus is probably better called the ‘lost philosopher’. All his works have disappeared and the brief glimpses we get of his thinking come mainly from Aristotle and Epicurus.

He was born in Northern Greece to a wealthy family that allowed him to travel abroad. He certainly went to Athens and probably to Egypt, Persia and even further afield to Babylon, Ethiopia and India.

He was taught by Leucippus and it was building on his work that his atomic theory was conceived.

This materialist idea argued that the world could be reduced to atoms (unbreakable and unperishable elements) and the void in which they existed. He argued that this state had always existed and would always exist.

Changes in the world, rather than the act of a supernatural force were caused by interaction between atoms. Qualitative ideas like taste and colour were the result of atoms moving and interchanging not actual facts. His outlook, which has influenced scientists throughout the ages, was of a mechanised world obeying fixed laws.

## Democritus’ mathematics

We know Democritus wrote extensively on mathematics, particularly geometry. *On Numbers*, *On Geometries*, *On Tangencies*, *On Mapping* and *On Irrationals* are all lost books of his.

We also are told in the method of Archimedes that Democritus enunciated the proposition that the volume of a cone is one third of that of a cylinder with the same base and height.

He also argued that the volume of any pyramid can be calculated in a corresponding way - as one third of the product of the area of its base and its height.

He gave this result 50 years before it was proved by Eudoxus.

While acknowledging his mathematical contribution, it is argued that his reliance on atomic theory stopped him developing more mathematical ideas.