Emil Artin

Emil Artin
source
Name	Emil Artin
Caption	Emil Artin, c. 1950s
Birth date	3 March 1898
Birth place	Vienna, Austria-Hungary
Death date	20 December 1962
Death place	Hamburg, West Germany
Fields	Mathematics
Alma mater	University of Leipzig
Doctoral advisor	Gustav Herglotz
Doctoral students	John Tate, Serge Lang, Max Zorn, Hans Zassenhaus
Known for	Artin reciprocity, Artin L-function, Artin–Schreier theory, Brauer–Artin theorem, Artin–Wedderburn theorem
Prizes	American Mathematical Society Cole Prize (1939)

Emil Artin was an Austrian mathematician of Armenian descent who made foundational contributions to algebraic number theory, class field theory, and abstract algebra. His work, characterized by profound depth and elegant clarity, reshaped modern mathematics and influenced generations of researchers. He spent significant portions of his career at the University of Hamburg and Princeton University, mentoring many prominent students.

Biography

Born in Vienna, he showed early mathematical talent and began his university studies at the University of Vienna before moving to the University of Leipzig. Under the supervision of Gustav Herglotz, he completed his doctorate on quadratic number fields in 1921. He then joined the faculty at the University of Hamburg, where he collaborated with colleagues like Otto Schreier and Helmut Hasse. With the rise of the Nazi Party, his wife's Jewish ancestry forced the family to emigrate in 1937, leading to a position at the University of Notre Dame and later at Indiana University. In 1946, he joined the Institute for Advanced Study and Princeton University, returning to a professorship at the University of Hamburg in 1958, where he remained until his death.

Mathematical contributions

Artin's contributions are central to several major areas of twentieth-century mathematics. In class field theory, he proved the general Artin reciprocity law, a monumental result that generalizes quadratic reciprocity and serves as the cornerstone of the abelian extension theory of number fields. He introduced the Artin L-function to incorporate non-abelian Galois group representations. In abstract algebra, his name is attached to the Artin–Wedderburn theorem on the structure of semisimple rings and the Artin–Schreier theory for real closed fields. His work with George Whaples established an axiomatic foundation for algebraic number fields, while his collaboration with John Tate led to a celebrated reformulation of class field theory. He also made significant advances in braid group theory, algebraic topology, and the theory of rings with minimum condition.

Influence and legacy

Artin's influence is profound and enduring, both through his written work and his exceptional teaching. His expository books, such as his volume on Galois theory and his influential lectures on algebraic number theory, are considered classics. As a thesis advisor at Princeton University and the University of Hamburg, he guided a remarkable group of students including John Tate, Serge Lang, and Hans Zassenhaus, who became leading figures in mathematics. His conceptual and structural approach to problems fundamentally shaped the development of modern algebra and number theory. The Artin conjecture on L-functions remains a major open problem, driving ongoing research in analytic number theory and the Langlands program.

Selected publications

* *Galois Theory* (Notre Dame Mathematical Lectures, 1942) * *Rings with Minimum Condition* (with Cecil J. Nesbitt and Robert M. Thrall, 1944) * *Theory of Algebraic Numbers* (Göttingen lecture notes, 1959) * *Class Field Theory* (with John Tate, 1961) * *The Gamma Function* (translated by Michael Butler) * *Algebraic Numbers and Algebraic Functions* (lecture notes from Princeton University) * *Geometric Algebra* (a seminal text intertwining linear algebra, group theory, and geometry)

Awards and honors

Artin received the prestigious American Mathematical Society Cole Prize in Number Theory in 1939 for his work on L-functions and class field theory. He was elected a member of the Academy of Sciences Leopoldina and the Göttingen Academy of Sciences and Humanities. He was also a plenary speaker at the International Congress of Mathematicians in 1932 in Zürich and in 1954 in Amsterdam. His legacy is honored through mathematical concepts bearing his name, such as the Artin conductor, Artin–Hasse exponential, and Artin–Tate lemma.

Category:20th-century mathematicians Category:Austrian mathematicians Category:Algebraic number theorists