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German mathematician Ferdinand Georg Frobenius was a number theorist who made critical contributions to the study of group theory.
Frobenius lived most of his life in and around Berlin. He was born in Berlin-Charlottenburg, Prussia in 1849, and after seven years in the Joachimsthal Gymnasium, or secondary school, he embarked on an academic career at the University of Göttingen at age 18. Frobenius only spent a semester at Göttingen before moving to the University of Berlin. He studied under the respected mathematician Karl Weierstrass in Berlin, and was awarded his doctorate in 1870. Four years later, he was awarded a professorship in mathematics at the University of Berlin. Frobenius only remained in the position for a year when he decided to relocate to Zürich, Switzerland to teach mathematics at the Eidgenössische Polytechnikum (Federal Polytechnic) there. Frobenius remained in Zürich until 1892, when he returned home to Berlin to resume his position at the University as mathematics professor.
While in Zürich, Frobenius began to publish his pivotal papers on group theory. In 1879, Frobenius and colleague Ludwig Stickelberger published "Über Gruppen von vertauschbaren Elementen" ("Concerning Groups of Permutable Elements"), which explained the mathematicians' work on abstract group theory. Several other important papers followed, including important work on group characters (1896) and group representations (1897-1899) that laid the foundation for future work on representation theory.
Frobenius also served as mentor and teacher, overseeing the doctoral studies of such promising mathematicians as Edmund Landau and Issai Schur. He died at the age of 67 in Berlin.