Eudoxus was born in 400 B.C. in Cnidos. He studied mathematics with Archytus in Tarentum. Later he studies medicine with Philistium on Sicily. At 23 years he went to Plato’s academy in Athens to study philosophy and rhetoric. He then went to Egypt to learn astronomy at Helopolis. Later he established a school in Asia Minor. In 365 B.C. he returned to Athens with his pupils. He became a colleague of Plato. At the age of 53 he died in Cnidos, highly honored as a lawgiver. He was the leading mathematician and astronomer of his day.

In astronomy, Eudoxus divised an ingenious planetary system based on spheres. In his system the spherical earth is at rest at the center. 27 concentric spheres rotate around the center. The exterior one carries the fixed stars. The others account for the sun, moon, and five planets. Each planet requires four spheres, the sun and moon, three each. He described the constellations as the rising and setting of the fixed stars.

Eudoxus also made several contributions to mathematics. He made the theory of proportion which allowed the study of irrational numbers. He developed the concept of magnitude and the method of exhaustion. He also established rigorous methods for finding areas and volumes of curvilinear figures. He had a profound influence in the establishment of deductive organization of proof on the basis of explicit axioms.

All information taken from: http://www.math.tamu.edu/~don.allen/history/eudoxus/eudoxus.html