Cristian Felix Klein. Photograph of the German mathematician Christian Felix Klein (1849-1925). Klein studied at Bonn, Gottingen, Berlin and Paris and began research in geometry, becoming professor of mathematics at Erlangen at 23. He himself, and through his influence many of his colleagues, worked on the unification of geometry. Klein developed projective geometry, taking it from 3 to n dimensions, and applied group theory widely, for example to the symmetries of regular solids. He invented the Klein bottle in topology, which is a one-sided closed surface with no boundaries (it has no 'inside'). He also worked on number theory, and on the theory of the gyroscope.