SOME OF THE PEOPLE MAKING CONTRIBTIONS TO MATH DURING THIS TIME:

ARCHYTAS THE TARANTINEAN , born in southern Italy, was the last of the Pythagoreans.  Besides being a mathmatition, Archytas was an astronimer and engineer.  He worked on the problem of doubleing a cube and solved it with a geometric solution.  He was the first to apply motion the solution of geometric problems; he was the first to study mechanical problems based on
mathmatics.  He built a mechanical pigeon propelled by a stream jet.  He came up with the theory for the pulley.  He worked on the harmonic mean and named it. Plato would use Archytas' math skills.  Depending on the source, his life span is said to be 440-360 BC,  420-350 BC, 428-350 BC, or somewhere along those lines. He died in a ship wreck on the Adriatic Sea.

ANAXAGORAS OF CLAZOMENAE, was Greek.  He formulated the correct theory for the eclipses.

ARISTOTLE, among other things, he showed that free fall was an accelerated form of motion.

EUDOXUS OF CNIDUS was a Greek astronomer and mathmatician, of the school of Plato.  He formed a theory of proponents and methods of exhaustion.

PLAT0, of Athens, felt that math was an important part of education.

DEMOCRITUS OF ABDERA wrote On Numbers, On Geometrics, On Tangencies, On Mapping, and On Irrationals. He felt the universe was mechanical and simply obeying fixed laws.

Author: Maggie Cooper

References:
Eves, Howard, An Introduction to the History of  Mathematics, 6th ed, Saunders College Publishing,  Maine,1990, pg676.

http://www.brown.edu/students/Hellenic_Students_Association/math/archytas.html
http://www.csd.uch.gr/~usiris/ancient_greeks.html
http://www.groups.xs.st.and.ac.uk/~history/mathematicias/Archytas.html
http://www.groups.cs.st.and.ac.uk/~history/chronology/Chronologyl.html