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Eudoxus, born in the city of Cnidus in southern Asia Minor, in the last years of the Vth century B. C., is one of the great mathematicians of all times, and probably the greatest of ancient Greece's mathematicians. He may have belonged to a family of physicians, because, at the time, Cnidus was famous for its school of medicine, and started his carrier travelling with fellow-physicians. When he was 23, he stayed for two months in Piræus, going each day to Athens to listen to Plato and other Socratics. Later he went to Egypt, where he learned astronomy from priests of Heliopolis. Back from Egypt, he went to Halicarnassus and then settled for a while in Cyzicus, where he founded a school of astronomy that remained famous long after his death. Then, he came to Athens where he probably worked with Plato at the Academy. Toward the end of his life, he returned to his native city of Cnidus where he was involved in lawmaking.
Most of his works, which covered many areas including, aside from mathematics, astronomy, geography, music, philosophy and more, are lost and known only through mentions in other works. His works in mathematics are better known and it is likely they were at the root of a large part of Euclid' Elements. This is sure, based on the testimony of Archimedes (IIIrd century B. C.), for book XII, but may be true also for other books. Indeed, Proclus, the Neoplatonist philosopher (Vth century A. D.), in his Commentary on Euclid, book I, introduces Euclid as the one "who put together the elements, arranging in order many things from Eudoxus..." Eudoxus, with the method of exhaustion he developed in geometry, is one of the fathers of integral calculus. He is also the inventor in astronomy of a scheme to account for the mouvement of planets based on concentric spheres turning within one another, a method that was to be complexified later by Aristotle, and he can thus be viewed as the father of scientific astromony. This should give a feel for how developed mathematics, and especially geometry, were in the time of Plato, showing that a large part of what ended up in Euclid's Elements was already known.