The greatest of the mathematics and astronomers of the time of Plato, Eudoxos of Knidos (400-350 BC approximately). He broadened the theory of numbers beyond the Pythagorean tradition by proving the existence of irregular substances, and inventing methods of calculating curved surfaces. Moreover, with the homocentric sphere system he invented, he gave the first well documented explanation of the planets movement, and presenting yet once more the persistence of ancient Greek to the perfection of the sphere. He was the one applying geometry to the science of astronomy, and the one to outline the fact that there should be interaction between theory and observation, a basic principle to astronomy ever since.
He studies mathematics and medicine to a school with a reputation similar to that of Hippocrates (the greatest doctor of ancient Greece). A rich doctor, impressed by his abilities, sponsored him to go to Athens and study at Plato’s academy. He lived in Egypt for 18 months, during the reign of Nectanevo the First. In Heliopolis (nowadays a suburb of Cairo) he was initiated into the Egyptian wisdom, including astronomy. It was there that he wrote “8 years”, his first important work, probably after studying Venus. Later on he travelled to Propontis Sea teaching, and then returned to Athens where he became a well known legislator.
Eudoxos made two important contributions to mathematics, one being the theory of analogy, and the other the theory of depletion, both attributed to Eudoxos by Proklos and Archimedes. It might be that the theory of axioms of Eukleides was first induced by Eudoxos.
It is often said that it was Aristarchos of Samos who first calculated the distance between Earth from the Moon and the Sun, but there is a possibility that it was Eudoxos who found it. He gave a solution to another astronomical problem, explaining mathematically the phenomenal movement of the Sun, Moon, and the five known planets, by defining each one’s distance from Earth, order being Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn.
He created a model of 27 spheres, placing on the external sphere every stable star so as to consider their daily movement, and building a model of connected spheres for each one of the celestial bodies, 3 for the sun, 3 for the moon, 4 for each of the remaining planets, each sphere with the desired pitch and velocity.
After his death, at around 350 BC, mathematic science was led to new frontiers due to his contribution, His idea that a normal circular movement can explain all celestial movement survived until the 17th century AD.