Background
Ferdinand Frobenius was born on October 26, 1849, in Berlin, Germany. He was the son of Christian Ferdinand Frobenius, a parson, and Christiane Elisabeth Friedrich.
Prenzlauer Allee 28, Templin 17268, Berlin, Germany
Georg attended the Joachimsthal Gymnasium in Berlin.
Wilhelmsplatz 1, 37073 Göttingen, Germany
Georg began his mathematical studies at Göttingen in 1867, but later transferred to Berlin.
Unter den Linden 6, 10117 Berlin, Germany
Georg obtained his doctorate at the University of Berlin in 1870.
Germany
Ferdinand Georg Frobenius
Germany
Ferdinand Georg Frobenius
Germany
Ferdinand Georg Frobenius
educator mathematician scientist
Ferdinand Frobenius was born on October 26, 1849, in Berlin, Germany. He was the son of Christian Ferdinand Frobenius, a parson, and Christiane Elisabeth Friedrich.
Georg attended the Joachimsthal Gymnasium in Berlin and then began his mathematical studies at Göttingen in 1867, completing them with a doctorate at Berlin in 1870.
After graduating, Frobenius taught at the Joachimsthal Gymnasium and moved to the Sophienrealschule the following year. In 1874, on the basis of his mathematical papers, Frobenius was appointed assistant professor at the University of Berlin. The next year he was made a full professor at the Eidgenossische Polytechnikum in Zurich. Frobenius returned permanently to the University of Berlin in 1892, as professor of mathematics.
Frobenius wrote many papers, a number of them of decisive importance. Several were done with other prominent researchers, particularly with Ludwig Stickelberger and Issai Schur.
Frobenius’ major achievements were in group theory, which in the 1870’s and 1880’s, through the joining of its three historical roots - the theory of solutions of algebraic equations (Galois theory, permutation groups), geometry (finite and infinite transformation groups, Lie theory), and number theory (composition of quadratic forms, modules) - produced the concept of the abstract group, the first abstract mathematical structure in the modern sense.
Frobenius, who had become acquainted with the idea of abstract algebra in Berlin, through Leopold Kronecker and Ernst Kummer, made fundamental contributions to the concept of the abstract group in “Ueber Gruppen von vertauschbaren Elementen,” written with Stickelberger, and in “Über endliche Gruppen.” He exerted even greater influence on the development of group theory by means of the theory of finite groups of linear substitutions of n variables. This theory, which he and Schur completed in all its essential aspects, was conceived from the beginning as a representation theory of abstract groups. Its nucleus is the theory of group characters. Among the relevant works on this topic are “Über die Gruppencharaktere,” “Über die Darstellung der endlichen Gruppen durch lineare Substitutionen,” “Über die Komposition der Charaktere einer Gruppe,” and “Über die reellen Darstellungen der endlichen Gruppen,” written with Schur.
The representation theory of finite groups through linear substitutions was later to offer the possibility of surprising and important applications to difficult questions in the theory of finite groups, properly speaking, and, in the 1920’s and 1930’s, to grouptheory questions in quantum mechanics.
Frobenius was a member of the Prussian Academy of Sciences at Berlin.
Ferdinand married Auguste Lehmann in 1876.