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-functions. 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.
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