Artin was born in
Hamburg, Germany, and brought up in
Indiana. His parents were
Natalia Naumovna Jasny (Natascha) and
Emil Artin, preeminent algebraist of the 20th century of
Armenian descent. Artin's parents left Germany in 1937, because his mother's father was
Jewish. His elder sister is , who was married to mathematician
John Tate until the late 1980s. Artin did his undergraduate studies at
Princeton University, receiving an A.B. in 1955. He then moved to
Harvard University, where he received a Ph.D. in 1960 under the supervision of
Oscar Zariski, defending a thesis about
Enriques surfaces. In the early 1960s, Artin spent time at the
IHÉS in France, contributing to the
SGA4 volumes of the
Séminaire de géométrie algébrique, on
topos theory and
étale cohomology, jointly with
Alexander Grothendieck. He also collaborated with
Barry Mazur to define
étale homotopy theory which has become an important tool in algebraic geometry, and applied ideas from algebraic geometry (such as the
Nash equilibrium) to the study of
diffeomorphisms of
compact manifolds. His work on the problem of characterising the
representable functors in the
category of schemes has led to the
Artin approximation theorem in
local algebra as well as the "Existence theorem". This work also gave rise to the ideas of an
algebraic space and
algebraic stack, and has proved very influential in
moduli theory. He also has made important contributions to the
deformation theory of algebraic varieties, serving as the basis for all future work in this area of algebraic geometry. With
Peter Swinnerton-Dyer, he provided a resolution of the Shafarevich-Tate conjecture for elliptic
K3 surfaces and the pencil of elliptic curves over finite fields. He contributed to the theory of surface singularities which are both fundamental and seminal. The
rational singularity and fundamental cycles, which are used in matroid theory, are such examples of his sheer originality and thinking. He began to turn his interest from
algebraic geometry to
noncommutative algebra (
noncommutative ring theory), especially geometric aspects, after a talk by
Shimshon Amitsur and an encounter in
University of Chicago with
Claudio Procesi and Lance W. Small, "which prompted [his] first foray into ring theory". Today, he is a recognized world authority in
noncommutative algebraic geometry. == Awards ==