My mother says that I was a big baby and it was a difficult birth, although I don't know what I weighed. The conversion from German to English pounds adds ten percent, and I suspect that my mother added another ten percent every few years. She denies this, of course. Anyway, I'm convinced that a birth injury caused my left-handedness and some seizures, which, fortunately, are under control.

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.

When I was a child my father spent a fair amount of time teaching me about things. It wasn't primarily mathematics but other sciences, chemistry especially because his father had wanted him to be a chemist and that hadn't worked out, and it didn't work for me. He outfitted me with fairly elaborate chemistry outfit which he had got partly through a student who had transferred into mathematics from chemistry - a graduate student who became a mathematician.

I went to college and in college I couldn't stand physics after a year - there was an optic lab and I couldn't see anything. Then in chemistry that I started out with, I broke too many pieces of glass into my hands, then I guess I just lost interest. That left mathematics and biology and I never really made a decision. I decided to major in mathematics because I figured that it was at the theoretical end of the science spectrum so it would be easier to change out of - which is a stupid thing.

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.

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.

For her marriage the bride chose a street-length gown of silk with a short veil, and carried freesias and roses. ... Best man was Thomas Artin [Michael Artin's younger brother].

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.

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.

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'.

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.

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.

I cannot imagine bothering to search a book so deliberately and thoroughly written to make the reader ask and answer their own questions.

It's not easy for the traditional algebraists to use it as a textbook, because it has other stuff in it.

... 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.

Mike was president of the American Mathematical Society in 1991 and 1992. During his term, he established oversight committees for important AMS activities such as meetings and publications.

... an architect of the modern approach to algebraic geometry.

... for his fundamental contributions to algebraic geometry, both commutative and noncommutative.

Michael Artin is one of the main architects of modern algebraic geometry. His fundamental contributions encompass a bewildering number of areas in this field. To begin with, the theory of étale cohomology was introduced by Michael Artin jointly with Alexander Grothendieck. ... He also collaborated with Barry Mazur to define étale homotopy, another important tool in algebraic geometry, and more generally to apply ideas from algebraic geometry to the study of diffeomorphisms of compact manifolds. We owe to Michael Artin, in large part, also the introduction of algebraic spaces and algebraic stacks. These objects form the correct category in which to perform most algebro-geometrical constructions, and this category is ubiquitous in the theory of moduli and in modern intersection theory. ... In yet another example of the sheer originality of his thinking, Artin broadened his reach to lay rigorous foundations to deformation theory. This is one of the main tools of classical algebraic geometry, which is the basis of the local theory of moduli of algebraic varieties. Finally, his contribution to noncommutative algebra has been enormous. The entire subject changed after Artin's introduction of algebro-geometrical methods in this field.

For his leadership in modern algebraic geometry, including three major bodies of work: étale cohomology; algebraic approximation of formal solutions of equations; and non-commutative algebraic geometry.

Michael Artin is one of the founders of modern algebraic geometry, developing, together with Grothendieck, the notions of Grothendieck topology and étale cohomology, which were later key to the proofs of the Weil conjectures and many other developments. By introducing the notions of algebraic spaces and algebraic stacks, he created a context that permitted algebraic geometers to go beyond the limitations of schemes. Combined with his approximation and algebraisation theorems, this led to representability results for algebraic spaces and to existence theorems for moduli spaces of algebraic and geometric objects. These developments provided foundations for a more modern deformation theory, including the important notion of versal deformation in the study of local moduli.

These are notes that have been used for an algebraic geometry course at MIT. I had thought about teaching such a course for quite a while, motivated partly by the fact that MIT didn't have very many courses suitable for students who had taken the standard theoretical math classes. I got around to thinking about this seriously twelve years ago and have now taught the subject seven times. I wanted to get to cohomology of -modules (aka quasicoherent sheaves) in one semester, without presupposing a knowledge of sheaf theory or of much commutative algebra, so it has been a challenge. Fortunately, MIT has many outstanding students who are interested in mathematics. The students and I have made some progress, but much remains to be done. Ideally, one would like the development to be so natural as to seem obvious. Though I haven't tried to put in anything unusual, this has yet to be achieved. And there are too many pages for my taste. To paraphrase Pascal, we haven't had the time to make it shorter.

Before describing some of Mike Artin's mathematical work we would like to say a few words about our experiences with Mike as students, collaborators, colleagues and friends. Mike has broad interests, a great sense of humour and no need to follow convention. These qualities are illustrated in the gorilla suit stories. On his 40th birthday his wife, Jean, gave Mike a gift he had wanted, a gorilla suit. In experiments with the pets of family and friends, he found his wearing it did not disturb cats, but made dogs extremely agitated. Testing this theory on after-dinner walks, he found dogs crossed the street to avoid him. Experimenting once, Mike had gone ahead of his wife and friends to hide in a neighbour's bushes when a squad car stopped. As an officer got out of the car, Jean called out "He's with me." After a closer look the officer turned back, telling his buddy "It's OK - just a guy in a gorilla suit."

Once Mike wore the suit to class and, saying nothing, slowly and meticulously drew a very good likeness of a banana on the board. He then turned to the class, expecting some expression of appreciation, perhaps even applause, for a gorilla with such artistic talent, but was met with stunned silence.

Mike is a fine musician. As a youngster he played the lute and assembled a remarkable collection of Elizabethan lute music, but his principal instrument is the violin, which he practices and plays regularly. One of a group with whom he regularly plays quartets tells us, "Mike is a wonderful violinist, just a notch below professional. He is so good that he can pull the rest of us through Ravel and Schoenberg."

The MIT undergraduates in Mike's year-long algebra classes adore him, in spite of it being a challenging course. Mike is both demanding and supportive, and his students respond to him with loyalty, gratitude, and dedication. Indeed, during a typical week one can find Mike in his office talking to his students for hours on end. Mike also takes a very personal approach with his graduate students. As a student, Eric Friedlander would knock on Mike's door, and Mike would boom out "Who is it?" On hearing a loud "Eric Friedlander," Mike's response, still through the closed door, was almost invariably either "Let's go swimming" or "Go Away." Actually, Mike's relationship with graduate students is kind and caring, and he is sensitive enough to work in different modes appropriate to different students. In a mixed gathering, Mike tends to seek out young people to talk with, as well as visiting with his peers.

To learn a new topic with Mike is to do research on that topic. For example, asking Mike for a mathematical reference is not always very effective - he'll often respond "go and figure it out for yourself!" For those unfamiliar with Mike's approach to mathematics, keep this in mind: Mike sometimes makes statements that are at first difficult to understand, almost as if he is evoking an image or an idea through poetry. It is a very beautiful thing to witness, albeit sometimes flabbergasting. One sure-fire way to get to the bottom of things is to whip out an example, and see the poem transformed into concrete reality.