Michael Artin (; born 28 June 1934) is a German-American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and a professor emeritus in the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

mathematics department, known for his contributions to algebraic geometry.Faculty profile
, MIT mathematics department, retrieved 2011-01-03

Life and career

Michael Artin or Artinian was born in

Hamburg (male), (female) en, Hamburger(s), Hamburgian(s) , timezone1 = Central (CET) , utc_offset1 = +1 , timezone1_DST = Central (CEST) , utc_offset1_DST = +2 , postal ...

, 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 Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

. His elder sister is Karin Tate, who was married to mathematician John Tate until the late 1980s. Artin did his undergraduate studies at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

, receiving an A.B. in 1955; he then moved to

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

, where he received a Ph.D. in 1960 under the supervision of

Oscar Zariski , birth_date = , birth_place = Kobrin, Russian Empire , death_date = , death_place = Brookline, Massachusetts, United States , nationality = American , field = Mathematics , work_institutions = ...

, defending a thesis about

Enriques surfaces In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity ''q'' = 0 and the canonical line bundle ''K'' is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex n ...

. 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 In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notio ...

and

étale cohomology In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectur ...

, 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 approximation) to the study of

diffeomorphism In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two ...

s of

compact manifold In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only ''non-compact'' components. Examples The only connected one-dimensional example is ...

s. His work on the problem of characterising the

representable functor In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an abstract category in terms of known structures (i.e. sets a ...

s in the category of schemes has led to the

Artin approximation theorem In mathematics, the Artin approximation theorem is a fundamental result of in deformation theory which implies that formal power series with coefficients in a field (mathematics), field ''k'' are well-approximated by the algebraic functions on ''k' ...

in local algebra as well as the "Existence theorem". This work also gave rise to the ideas of an

algebraic space In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, wh ...

and algebraic stack, and has proved very influential in

moduli theory In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme (mathematics), scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of suc ...

. 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 surface In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected al ...

s 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 In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist ''a'' and ''b'' in the ring such that ''ab'' and ''ba'' are different. Equivalently, a ''noncommutative ring'' is a ring that is not ...

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 isfirst foray into ring theory". Today, he is a recognized world authority in noncommutative algebraic geometry and his impact can be felt across many related areas. In 2002, Artin won the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

's annual Steele Prize for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal. In 2013, he won the Wolf Prize in Mathematics, and in 2015 was awarded the

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

from the President

Barack Obama Barack Hussein Obama II ( ; born August 4, 1961) is an American politician who served as the 44th president of the United States from 2009 to 2017. A member of the Democratic Party, Obama was the first African-American president of the ...

. He is also a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences (1969), the American Association for the Advancement of Science, the Society for Industrial and Applied Mathematics, and the

. He is a Foreign Member of the Royal Netherlands Academy of Arts and Sciences and Honorary Fellow of the Moscow Mathematical Society, and was awarded honorary doctorates from the universities of Hamburg and Antwerp,

Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...

. He was invited to give a talk on the topic "The Étale Topology of Schemes" at the International Congress of Mathematicians in 1966 in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...

, USSR.

Books

As author

*with Barry Mazur: * * *in collaboration with Alexandru Lascu & Jean-François Boutot: *with notes by C.S. Sephardi & Allen Tannenbaum: *

As editor

*with David Mumford: *with John Tate: *with Hanspeter Kraft & Reinhold Remmert:

References

External links