E. Artin

E. Artin
Konrad Jacobs, Erlangen · CC BY-SA 2.0 de · source
Name	Emil Artin
Birth date	March 3, 1898
Birth place	Vienna, Austria-Hungary
Death date	December 20, 1962
Death place	Hamburg, West Germany
Fields	Mathematics
Alma mater	University of Vienna, University of Leipzig
Doctoral advisor	Helmut Hasse
Known for	Class field theory, Artin reciprocity, noncommutative ring theory, braid groups

E. Artin was an Austrian-American mathematician renowned for foundational work in algebraic number theory, class field theory, and algebra. He transformed reciprocity laws and promoted structural approaches that influenced Emmy Noether, Helmut Hasse, Max Noether, Richard Dedekind, David Hilbert, Évariste Galois, Niels Henrik Abel, Leopold Kronecker, Carl Friedrich Gauss, Srinivasa Ramanujan, Bernhard Riemann, Felix Klein, Hermann Weyl, Ernst Witt, Norbert Wiener, John von Neumann, Paul Erdős, André Weil, and generations of algebraists.

Early life and education

Artin was born in Vienna into a family with connections to Armenia and Greece and moved in youth to Graz and Leoben. He studied at the University of Vienna where he encountered instructors influenced by Felix Klein and David Hilbert. He completed doctoral work under Helmut Hasse at the University of Hamburg and engaged with research communities around Leipzig and Göttingen, interacting with scholars like Emmy Noether, Richard Courant, and Max Dehn.

Academic career and positions

After his doctorate Artin held positions at the University of Hamburg, the University of Göttingen, and the University of Halle. In the 1930s he accepted a chair at the University of Hamburg before emigrating to the United States, where he joined the faculty of Indiana University Bloomington, later moving to Princeton University and then to Columbia University. Postwar he returned to Europe and served at the University of Hamburg and participated in collaborations with institutions including Institute for Advanced Study and visiting posts at Harvard University and University of Chicago.

Contributions to mathematics

Artin restructured parts of algebraic number theory and class field theory by formulating reciprocity via group-theoretic maps, influencing Helmut Hasse and Claude Chevalley. He developed concepts in noncommutative algebra and advanced the study of Brauer groups, central simple algebras, and Galois theory with links to work by Emmy Noether, Richard Dedekind, and Évariste Galois. His investigations into braid groups and knot theory connected with ideas later used by Vladimir Arnold and Michael Atiyah. Artin's emphasis on structural clarity affected pedagogy at Princeton University and textbooks used at Harvard University and Columbia University.

Major theorems and concepts

Artin formulated the Artin reciprocity law, a cornerstone tying ideal class groups and Galois groups in abelian extensions by explicit reciprocity maps; this work interlaces with the achievements of Carl Friedrich Gauss and David Hilbert. He introduced notions in noncommutative ring theory and criteria for the simplicity of algebras that relate to the Brauer group and results of Richard Brauer and Jacobson. The concept of the Artin L-series generalized Dirichlet L-series and echoed methods from Bernhard Riemann and Ernst Kummer. His articulation of the Artin conjecture on nonabelian L-functions stimulated later research by Andrew Wiles, Pierre Deligne, Robert Langlands, Gérard Laumon, and John Tate.

Publications and selected works

Artin authored influential papers and texts, including expositions on reciprocity and algebraic structures that were used across departments at Princeton University, Indiana University Bloomington, and Columbia University. Key works connected to his correspondence with Helmut Hasse and collaborations with Emmy Noether shaped modern treatments found alongside writings by Claude Chevalley, André Weil, and Pierre Samuel.

Awards, honors, and legacy

Artin received recognition from academic bodies such as the National Academy of Sciences and was honored through lectureships and memorials at institutions like Princeton University and the Institute for Advanced Study. His legacy endures in eponymous concepts—Artin reciprocity, Artin L-series, and the Artin map—and in the influence on successors including Emil Artin Jr. (students and relatives not to be linked) and prominent students who became faculties at Harvard University, University of Chicago, University of California, Berkeley, and Massachusetts Institute of Technology.

Personal life and students

Artin's personal circle included collaborations and mentorships with figures such as Emmy Noether, Helmut Hasse, Claude Chevalley, John Tate, André Weil, and Paul Erdős. His students went on to appointments at Princeton University, Harvard University, University of Chicago, and Columbia University, contributing to algebra, number theory, and topology in the traditions of David Hilbert and Carl Friedrich Gauss.

Category:Mathematicians Category:Austrian mathematicians Category:20th-century mathematicians