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Emil Artin (March 3, 1898, in Vienna – December 20, 1962, in Hamburg) was an Austrian mathematician. His father, also Emil Artin, was an art-dealer, and his mother was the opera singer Emma Laura-Artin. He grew up in Reichenberg (today Liberec) in Bohemia, where German was the primary language. He left school in 1916, and one year later went to the University of Vienna.

Artin spent his career in Germany (mainly in Hamburg) until the Nazi threat when he emigrated to the USA in 1937. He was at Indiana University from 1938 to 1946, and at Princeton University from 1946 to 1958.

Contents 1 Influence and work 2 Conjectures 3 Supervision of research 4 Family 5 See also 6 Selected bibliography 7 External links

He was one of the leading algebraists of the century, with an influence larger than might be guessed from the one volume of his Collected Papers edited by Serge Lang and John Tate. He worked in algebraic number theory, contributing largely to class field theory and a new construction of L-function. He also contributed to the pure theories of rings, groups and fields. He developed the theory of braids as a branch of algebraic topology.

He was also an important expositor of Galois theory, and of the group cohomology approach to class ring theory (with John Tate), to mention two theories where his formulations became standard. The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as well as those of Emmy Noether. He wrote a book on geometric algebra that gave rise to the contemporary use of the term, reviving it from the work of W. K. Clifford.

He left two conjectures, both known as Artin's conjecture. The first concerns Artin L-functions for a linear representation of a Galois group; and the second the frequency with which a given integer a is a primitive root modulo primes p, when a is fixed and p varies. These are unproven; Hooley proved a result for the second conditional on the first.

Artin advised over thirty doctoral students, including Bernard Dwork, Serge Lang, Kollagunta Ramanathan, John Tate, Hans Zassenhaus and Max Zorn. He died in 1962, in Hamburg, Germany.

He married in 1932 Natascha Jasny, who was Jewish and born in Russia[1]. Artin himself was not Jewish, but was dismissed from his university position in 1937. They had three children, one of whom is Michael Artin, an American algebraist currently at MIT.

• Artin reciprocity
• Artin-Wedderburn theorem
• Artinian
• Artin L-function
• Artin's conjecture for conjectures by Artin. These include

• Artin's conjecture on primitive roots
• Artin conjecture on L-functions

• Artin-Schreier theory
• Artin group
• Ankeny-Artin-Chowla congruence
• Artin billiards
• Artin-Hasse exponential
• Artin-Rees lemma

• [2] Emil Artin, The theory of braids, Annals of Mathematics (2) 48 (1947), 101 – 126
• Emil Artin (1998). Galois Theory. Dover Publications, Inc.. ISBN 0-486-62342-4.  (Reprinting of second revised edition of 1944, The University of Notre Dame Press).

• O'Connor, John J., and Edmund F. Robertson. "Emil Artin". MacTutor History of Mathematics archive.
• Emil Artin at the Mathematics Genealogy Project
• [3] "Fine Hall in its golden age: Remembrances of Princeton in the early fifties", by Gian-Carlo Rota. Contains a section on Artin at Princeton.