Heinrich Weber (1842—1913) was born in 1842, in Heidelberg, Germany. His main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.
In 1860, he studied mathematics and physics at the University of Heidelberg. He received his Ph.D. in 1863. He was appointed as extraordinary professor at the University of Heidelberg in 1869 and also taught at Edgenössische Polytechnikum in Zurich, the University of Königsberg, the Technische Hochschule in Charlottenburg, and the universities of Marburg, Göttingen, and Strasbourg.
Weber was a friend of Richard Dedekind and they often collaborated. Together they edited the work of Riemann in 1876. Herman Minkowski and David Hilbert were among Weber’s students.
Weber’s main research interests were in analysis and its applications to mathematical physics and number theory. He was encouraged by von Neumann to investigate physical problems and by Richelot to study algebraic functions. Along the lines of Jacobi, he worked on the theory of differential equations. He proved Abel’s theorem in its most general form. He also worked on physical problems concerning heat, static and current electricity, the motion of rigid bodies in liquids, and electrolytic displacement.
Weber’s most profound and penetrating work is in algebra and number theory. He, jointly with Dedekind, did work of fundamental importance on algebraic functions.
In 1891, Weber gave the “modern” definition of an abstract finite group. One of his outstanding accomplishments was the proof of Kronecker’s theorem, which states that absolute Abelian fields are cyclotomic.
Weber was an enthusiastic and inspiring teacher who took great interest in educational questions. He died in 1913.