In the year 532 B.C. the most prominent mathematician was Pythagoras of Samos.  Pythagoras was in between his late thirties and late forties, depending on the source.  In this particular year Pythagoras moved from  Samos because Polycrates had taken control  his homeland.  It was in his new home, the seaport of Crotona in southern Italy, that Pythagoras founded the Pythagorean school.  It is from this school that the mathematical theories like the Pythagorean Theorem came.  The members of this school were very secretive and believed in  communalism.  Therefore they attributed all of their mathematical discoveries to the founder of the school, Pythagoras.  Although the Babylonians had been using the “Pythagorean” Theorem, Pythagoras was the first was probably the first to prove it.   Another major discovery of the school of Pythagoras was irrational numbers.   This came about from studying the diagonal of a square and realizing that it was not a rational multiple of its side.

Author: Tim Lucas

References:
Mac Tutor Hisotry of Mathematics Archive, http://www-groups.dcs.st-and.ac.uk/~history/index.html

History of Mathematics
 http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html

Eves, Howard.  An Introduction to the History of Mathematics,  Philadelphia:  Saunders College Publishing, 1990.