Felix Christian Klein

Felix Christian Klein was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. He also contributed to the fields of function theory, differential equations, calculus of variations, mechanics, physics, and astronomy. He studied at the University of Bonn under Julius Plücker and Alfred Clebsch, and obtained his doctorate in 1868 with a thesis on the classification of line complexes using Plücker coordinates. He then became a lecturer at the University of Göttingen, where he collaborated with Bernhard Riemann and Peter Gustav Lejeune Dirichlet. In 1872, he moved to the University of Erlangen as a professor, where he initiated his famous Erlangen Program, a systematic study of geometries based on their underlying symmetry groups. In 1875, he married Anna Hegel, the granddaughter of the philosopher Georg Wilhelm Friedrich Hegel. They had six children, five of whom survived to adulthood. One of his sons, Felix Klein Jr., also became a mathematician. In 1877, Klein moved to the Technical University of Munich, where he worked on the mathematical theory of the conservation of energy and the foundations of mechanics. He also became interested in non-Euclidean geometry and discovered the Klein bottle, a surface with only one side and no boundary. He also developed the idea of a complex projective line as a model for elliptic geometry. In 1880, he moved to the University of Leipzig, where he continued his research on geometry and function theory. He also became involved in the development of mathematical physics and applied mathematics. He worked on the theory of automorphic functions, modular functions, elliptic functions, hypergeometric functions, and theta functions. He also studied the relation between algebraic equations and modular forms. In 1886, he returned to Göttingen as the successor of Riemann. There he established Göttingen as a leading center of mathematics research and education. He attracted many talented students and collaborators, such as David Hilbert, Hermann Minkowski, Carl Runge, Ludwig Bieberbach, Emmy Noether, and Richard Courant. He also founded several mathematical journals and societies. In his later years, Klein suffered from poor health and nervous breakdowns. He also became interested in mathematics education and reform. He wrote several textbooks and popular books on mathematics and its history. He also advocated for the internationalization of mathematics and science. He died on June 22, 1925 in Göttingen from heart failure.