Klein, Christian Felix (krĭsˈtēän fāˈlĭks klĪn) [key], 1849–1925, German mathematician. He is noted for his work in geometry and on the theory of functions. His Erlangen program (1872) for unifying the diverse forms of geometry through the study of equivalence in transformation groups was influential, especially in the United States, for over 50 years. In his Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree (1884, tr. 1888) he showed how the rotation groups of regular solids could be applied to the solution of difficult algebraic problems. Klein was professor of mathematics successively at the Univ. of Erlangen, the Technical Institute, Munich, and the universities of Leipzig and Göttingen, and was a prolific writer and lecturer on the theory, history, and teaching of mathematics. His works include Famous Problems of Elementary Geometry (1895; tr., 2d ed. 1930) and Elementary Mathematics from an Advanced Standpoint (2 vol., 1907–8; tr. 1932–40).