Michael Artin

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28 June 1934
Hamburg, Germany

Michael Artin is an American mathematician known for his contributions to algebraic geometry.


Michael Artin's parents were Emil Artin, a famous mathematician with a biography in this archive, and Natalie Naumovna Jasny. Natalie, known as Natascha, had been born in St Petersburg, Russia, but her family had fled because of the Bolsheviks and, after many adventures, arrived in Europe after taking a boat to Constantinople. She attended the gymnasium in Hamburg and then Hamburg University where she took classes taught by Emil Artin. Emil Artin, born in Vienna, was descended from an Armenian carpet merchant who moved to Vienna in the 19th century. Emil and Natascha were married on 15 August 1929 and their first child, Karin, was born in January 1933. Michael was their second child. Because Natascha's father, the agronomist Naum Jasny, was Jewish, Emil Artin was in difficulties with the Nazi anti-Semitic legislation brought in in 1933. When Michael was three years old, in 1937, Emil lost his position at the University of Hamburg and decided to emigrate to the United States for the sake of his wife and children. They sailed on the steamship 'New York' on 21 October 1937, arriving in New York one week later where they were met by Richard Courant, Hermann Weyl and Naum Jasny who had escaped from Germany earlier. The family were supported at first from a fund set up to support refugees but, after spending the academic year 1937-38 at Notre Dame University, Emil and his family settled in Bloomington where he had a permanent position at Indiana University. Michael's young brother Thomas was born in the United States in November 1938.

The Artin home was always filled with music. Emil played the piano and the Hammond organ, while Karin played the cello and piano. Michael played the violin, and later at college played classical guitar and the lute. Although he gave up the lute after college, he has continued to enjoy playing the violin. Michael explained in [2] how his father's love of learning and teaching came across when he was a child:-
My father loved teaching as much as I do, and he taught me many things: sometimes mathematics, but also the names of wild flowers. We played music and examined pond water. If there was a direction in which he pointed me, it was toward chemistry. He never suggested that I should follow in his footsteps, and I never made a conscious decision to become a mathematician.
The family grew up to be bilingual. Michael's father used to read to him in German when he was a child and then later they had a rule that only German was spoken at the dinner table. At other times they alternated between English and German. In April 1946 Emil Artin was appointed as a professor at Princeton and he was joined in Princeton by the rest of his family in the autumn of 1946. Michael was an undergraduate at Princeton where, because his father was on the faculty, he received free education. He said [3]:-
I originally thought I might do topology. When I was an undergraduate, my advisor was Ralph Fox, who was a topologist, and he got me doing things. In Princeton - in those days, at least - you had to write a junior paper, and a senior paper. I did what was thought to be original research in my senior thesis, but I never published it. I think Ralph mentions the result in one of his books, but I didn't think it was good enough. Biology was my other field when I was an undergraduate. But in those days, mathematical biology was zero. ... But now its a fascinating subject. Maybe I chose the wrong field.
Artin graduated with an A.B. from Princeton in 1955 and, later that year, went to Harvard for graduate studies. His first year was not, by his own account, too successful although he was awarded a Master's Degree by Harvard in 1956. It was in the following year that the passion for mathematics really gripped him and he was became Oscar Zariski's student [2]:-
Those were exciting times for algebraic geometry. The crowning achievement of the Italian school, the classification of algebraic surfaces, was just entering the mainstream of mathematics. The sheaf theoretic methods introduced by Jean-Pierre Serre were being absorbed, and Grothendieck's language of schemes was being developed. Zariski's dynamic personality, and the explosion of activity in the field, persuaded me to work there. I became his student along with Peter Falb, Heisuke Hironaka, and David Mumford.
Artin was awarded a Ph.D. by Harvard in 1960 for his thesis On Enriques' Surfaces. He did not publish his thesis because he did not think it good enough for publication. As he often related, his parents had very high standards and he accepted these high standards as the norm. In fact his first paper was Some numerical criteria for contractability of curves on algebraic surfaces (1962). After the award of his doctorate in 1960, Artin was appointed as a Benjamin Peirce Lecturer at Harvard. He held this position until 1963 when he was appointed to the Massachusetts Institute of Technology. However, he arranged leave for his first year at MIT to enable him to spend it in France at the Institut des Hautes Études Scientifiques (IHES). At IHES, Artin attended Alexander Grothendieck's seminars which had a major influence on the direction of his research in algebraic geometry at this time. He made several other visits to IHES during the 1960s. His contributions to algebraic geometry are beautifully summarised in the citation for the Lifetime Achievement Steele prize he received from the American Mathematical Society in 2002:-
Michael Artin has helped to weave the fabric of modern algebraic geometry. His notion of an algebraic space extends Grothendieck's notion of scheme. The point of the extension is that Artin's theorem on approximating formal power series solutions allows one to show that many moduli spaces are actually algebraic spaces and so can be studied by the methods of algebraic geometry. He showed also how to apply the same ideas to the algebraic stacks of Deligne and Mumford. Algebraic stacks and algebraic spaces appear everywhere in modern algebraic geometry, and Artin's methods are used constantly in studying them. He has contributed spectacular results in classical algebraic geometry, such as his resolution (with Swinnerton-Dyer in 1973) of the Shafarevich-Tate conjecture for elliptic K3 surfaces. With Mazur, he applied ideas from algebraic geometry (and the Nash approximation theorem) to the study of diffeomorphisms of compact manifolds having periodic points of a specified behaviour.
At MIT, Artin was promoted to professor in 1966 and, in August of the same year, was given the honour of being a plenary speaker at the International Congress of Mathematicians held in Moscow. He gave the lecture The Etale Topology of Schemes. He began his lecture with the following introduction:-
Since André Weil pointed out the need for invariants, analogous to topological ones, of varieties over fields of characteristic p, several proposals to define such invariants have been made, notably by Jean-Pierre Serre, Alexander Grothendieck, and Paul Monsky and Gerard Washnitzer. I would like to describe some of the recent work on one of these approaches, that of the 'etale cohomology' of Grothendieck.
He served as chairman of Pure Mathematics at MIT in 1983-84 and was named Norbert Wiener Professor there in 1988. His main research area changed from algebraic geometry to noncommutative ring theory as he explained in his response to receiving the Steele Prize [2]:-
My interest in noncommutative algebra began with a talk by Shimshon Amitsur and a visit to Chicago, where I met Claudio Procesi and Lance Small. They prompted my first foray into ring theory, and in subsequent years noncommutative algebra gradually attracted more of my attention. I changed fields for good in the mid-1980s, when Bill Schelter and I did experimental work on quantum planes using his algebra package, 'Affine'.
Artin has written several outstanding books. These include the monograph (with Barry Mazur) Étale homotopy (1969) and Algebraic spaces (1971) which is a printed version of the James K Whittemore Lecture in Mathematics given by Artin at Yale University in 1969. His most famous book, however, is Algebra (1991). In [3] he describes how this book developed from a year-long undergraduate course he taught for thirty years:-
I didn't start out to write a textbook at all. I just wanted to teach a class, and to do some topics that weren't traditional. So I handed out notes for those, and eventually I started using them instead of the textbook. And then I revised them every year.
Gerald Janusz begins a review as follows:-
This is a remarkable text designed for highly motivated undergraduates having some preparation in linear algebra and some other post-calculus mathematics. It is noteworthy for its contents and the style of presentation. In the preface, the author lists three principles that he followed (briefly: examples should motivate definitions, technical points are presented only if needed later in the book, topics should be important for the average mathematician) and takes pains to point out that "Do it the way you were taught'' is not one of them. The style throughout the text is to present basic concepts, give many nontrivial examples and present brief and understandable discussions of advanced material.
It is interesting to look at reviews by students who have used the book. They are sharply divided into those who find the book outstandingly good at teaching and making them think about algebra, and those who criticise it because it is not encyclopaedic. As one puts it:-
I cannot imagine bothering to search a book so deliberately and thoroughly written to make the reader ask and answer their own questions.
Artin acknowledges this problem himself [3]:-
It's not easy for the traditional algebraists to use it as a textbook, because it has other stuff in it.
Artin has been closely connected with the American Mathematical Society over a long period. He was the first editor-in-chief of the Journal of the American Mathematical Society, served on the Council, was elected Vice-President, and served as 51st President of the Society during 1991-92. He spoke in [3] of the range of activities that the President has to undertake:-
... there's the volunteer side, the president and the council and committees; and the executive director's side, which runs the Providence and Washington offices and does things like arrange meetings and publish journals. They're both very complicated. And often at the council meeting, there are political issues brought up, which concern the Mathematical Society only very peripherally, and which are very divisive.
We have already mentioned above that Artin was awarded the American Mathematical Society's Steele Prize for Lifetime Achievement in 2002. In 2005 he was awarded the MIT Graduate School of Arts & Sciences Centennial Medal for being:-
... an architect of the modern approach to algebraic geometry.
He also received the Undergraduate Teaching Prize and the Educational and Graduate Advising Award from MIT University. His outstanding contributions have been recognised with election to the National Academy of Sciences in 1977, and to a fellowship of the American Academy of Arts and Sciences in 1969. He is a member of the American Association for the Advancement of Science, and of the Society for Industrial and Applied Mathematics. He has also been honoured with election as a Foreign Member of the Royal Holland Society of Sciences and Humanities, and as an Honorary Member of the Moscow Mathematical Society. He has received honorary doctorates from the University of Antwerp and from the University of Hamburg.

Michael Artin is married to Jean. They have a daughter Wendy S Artin, a talented painter who lives and paints in Rome in Italy and a second daughter Caroline who works as an editor.

References (show)

  1. M Cook, Mathematicians : an outer view of an inner world (Princeton University Press, Princeton-Oxford, 2009).
  2. 2002 Steele Prizes, Notices Amer. Math. Soc. 49 (4) (2002), 466-471.
  3. J Segel, Michael Artin, in Recountings: conversations with MIT mathematicians (A K Peters, 2009), 351-373.

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Written by J J O'Connor and E F Robertson
Last Update July 2011