Numerous mathematicians have studied geometry and made major contributions throughout history. Ancient geometers of importance include Pythagoras, Euclid, Hippocrates and Archimedes. More modern figures include Rene Descartes, Isaac Newton and Johann Bolyai.
According to GeomHistory.com, ancient Greece was home to some of the most important founders of geometry. Archimedes is considered the greatest of the Greek mathematicians. He proved fundamental theorems regarding the center of gravity of plane figures, made connections regarding the angles and radius lengths of spirals and discovered 13 semi-regular polyhedra.
Pythagoras discovered that the angles of a triangle add up to 180 degrees and developed the Pythagorean theorem for finding the lengths of the sides of a right triangle.
Hippocrates developed geometric solutions to quadratic equations, worked on duplicating the cube and was the first person to prove that the ratio of the areas of two circles is equal to the ratio of the squares of their radii.
Rice University describes the importance of modern geometer Rene Descartes. His enormous contribution consisted of uniting algebra and geometry through the creation of a coordinate plane. Isaac Newton, who lived a century after Descartes, created calculus.
Johann Bolyai and his contemporaries were responsible for finally establishing the impossibility of proving Euclid's fifth postulate and subsequently creating the field of non-Euclidian geometry.