Born in Cnidus, which is now in Turkey, Eudoxus is reported as having studied mathematics under Archytas, a Pythagorean. He also studied under Plato and in Egypt. Although none of his works have survived they are quoted extensively by Hipparchus. Eudoxus was the first astronomer who had a complete understanding of the celestial sphere. It is only this understanding that reveals the irregularities of the movements of the planets that must be taken into account in giving an accurate description of the heavens. For Eudoxus the Earth was at rest and around this center 27 concentric spheres rotated. The outermost sphere carried the fixed stars, each of the planets required four spheres, and the Sun and the Moon three each. All these spheres were necessary to account for the daily and annual relative motions of the heavenly bodies. He also described the constellations and the changes in the rising and setting of the fixed stars in the course of a year.

In mathematics, Eudoxus is thought to have contributed the theory of proportion to be found in Book V of Euclid – the importance of this being its applicability to irrational as well as rational numbers. The method of exhaustion in Book XII is also attributed to Eudoxus. This tackled in a mathematical way for the first time the difficult problem of calculating an area bounded by a curve.