**Dusa McDuff** was christened Margaret Dusa Waddington. Her father, Conrad Hal Waddington, was appointed Professor of Genetics at the University of Edinburgh in Scotland while her mother, Margaret Justin Blanco White, was an architect who had a Civil Service post in Edinburgh. Dusa was educated at a girls school in Edinburgh and, although the standard was less good than at the boys school, nevertheless she had an exceptionally good mathematics teacher. She wrote:-

I always wanted to be a mathematician(apart from a time when I was eleven when I wanted to be a farmer's wife), and assumed that I would have a career, but I had no idea how to go about it: I didn't realise that the choices which one made about education were important and I had no idea that I might experience real difficulties and conflicts in reconciling the demands of a career with life as a woman.

By the time that Dusa completed her secondary schooling in Edinburgh she had a boyfriend. This led to her choosing the University of Edinburgh for her undergraduate studies, turning down a scholarship which she had won to go to Cambridge University. During her undergraduate years at Edinburgh Dusa married her boyfriend and took his name becoming Dusa McDuff. Awarded a B.Sc. from Edinburgh in 1967, Dusa went to Girton College, Cambridge for her doctoral studies.

At Cambridge McDuff was supervised by G A Reid and she worked on problems in functional analysis. This time her husband followed her to Cambridge. She solved a difficult problem on von Neumann algebras, constructing infinitely many different factors of type II_{1}, and published the work in the *Annals of Mathematics*.

After completing her doctorate in 1971 McDuff was appointed to a two-year Science Research Council Postdoctoral Fellowship at Cambridge. Then McDuff followed her husband again, this time with a six month visit to Moscow. He was studying the Russian Symbolist poet Innokenty Annensky and Dusa had no specific plans, yet it would turn out a very profitable visit for her mathematically. She met Israil Gelfand in Moscow and he gave her a deeper appreciation of mathematics. McDuff wrote:-

Gelfand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which he could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gelfand found hedgehogs lurking in the rows of his spectral sequences!

After the Moscow visit, where she studied Gelfand-Fuchs cohomology, McDuff returned to Cambridge. There she attended Frank Adams' topology lectures and around this time her first child was born. However her research at this time was not well focused and she began to lose her way a little. Appointed to a position as a lecturer at the University of York in 1973 she began to work with Graeme Segal on classifying spaces of categories. To a certain extent she considered this as a second doctorate to regain direction for her research.

Perhaps 1974 was a turning point for McDuff. She was invited to spend a year at Massachusetts Institute of Technology. She wrote:-

This was a turning point. While there I realised how far away I was from being the mathematician I felt that I could be, but also realised that I could do something about it. For the first time, I met some other women whom I could relate to and who also were trying to become mathematicians. I became much less passive: I applied to the Institute for Advanced Study and got in, and even had a mathematical idea again, which grew into a joint paper with Segal on the group-completion theorem.

Back in England, McDuff separated from her husband and, soon afterwards, she was appointed to a post at the University of Warwick in 1976. McDuff had a friend, the mathematician Jack Milnor who worked in Princeton. After two years at Warwick, McDuff resigned her tenured post there and accepted an untenured post at the State University of New York at Stony Brook so that she could be close to Milnor. McDuff wrote:-

I still worked very much in isolation and there are only a few people who are interested in what I did, but it was a necessary apprenticeship. I had some ideas, and gained confidence in my technical abilities. Of course, I was influenced by the clarity of Jack Milnor's ideas and approach to mathematics, and was helped by his encouragement. I kept my job in Stony Brook, even though it meant a long commute to Princeton and a weekend relationship, since it was very important to me not to compromise on my job as my mother had done. After several years, I married Jack and had a second child.

From the early 1980s McDuff worked on symplectic topology. During a sabbatical term at the Institut des Hautes Études Scientifique in Paris in 1985 she studied Gromov's work on elliptic methods which became the basis for much of her later work. In 1984 she was promoted to full professor at Stony Brook, being Chair of the Mathematics Department there from 1991 to 93.

McDuff has received many honours for her remarkable mathematical achievements. In 1991 she was awarded the Ruth Lyttle Satter Prize of the American Mathematical Society. The quotations we have given in this article are taken from the acceptance speech she gave on the occasion of the presentation of the Prize. Many other honours have come her way, perhaps the most prestigious of which is her election as a Fellow of the Royal Society of London in 1994. The citation for her election to the Fellowship read:-

McDuff is best known for her work in the geometry of multi-dimensional structures. Her work in symplectic geometry, functional analysis and diffeomorphism groups has provided understanding and unexpected results in a whole range of areas of great importance. Her work is based on a deep and wide mathematical understanding, and has opened an extraordinarily fertile new branch of mathematics.

In 1995 she was elected a Fellow of the American Academy of Arts and Science.

In addition to these honours McDuff has been invited to give many prestigious lectures. She gave the Invited Address at the American Mathematical Society Winter meeting in Atlanta in 1988, the first Progress in Mathematics lecture at the American Mathematical Society Summer meeting in Boulder in 1989, an Invited Address at the International Congress of Mathematicians in Kyoto in 1990, and a Plenary Address at the Second European Congress in Budapest in 1996.

Although her research contributions to mathematics have been truly outstanding, McDuff has given service to mathematics in many other ways. She has been involved in reform of undergraduate teaching at Stony Brook, is on the editorial board of Notices of the American Mathematical Society, and has been an active member of Women in Science and Engineering. We give one further quote from her acceptance speech of the Ruth Lyttle Satter Prize concerning women in mathematics:-

I think that there is quite an element of luck in the fact that I have survived as a mathematician. I also got real help from the feminist movement, both emotionally and practically. I think things are somewhat easier now: there is at least a little more institutional support of the needs of women and families, and there are more women in mathematics so that one need not be so isolated. But I don't think that all the problems are solved.

In 1998 McDuff was named Distinguished Professor at SUNY at Stony Brook. She is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College where she teaches "Introduction to Higher Mathematics" and courses in geometry and topology. She has continued to receive prestigious awards such as honorary degrees from the University of Edinburgh (1997) and the University of York (2000). In 2007 the London Mathematical Society elected her to Honorary Membership of the Society:-

... in recognition of her research in many areas of mathematics and in particular in symplectic topology.

In the *Bulletin* of the London Mathematical Society McDuff's important contributions which led to her honorary membership are described:-

In the early eighties, shortly before Gromov's work on pseudo-holomorphic curves began to move the subject in new directions, McDuff began her study of symplectic topology and geometry. Among her early contributions to the field is a paper on the flux homomorphism and a celebrated theorem on the classification of rational and ruled symplectic4-manifolds. Her work includes fundamental theorems on the symplectic blowup construction, a theorem on the symplectic packing problem(joint with Leonid Polterovich), and a series of seminal joint papers with François Lalonde on the symplectic energy and the stability of Hamiltonian flows. Among the many applications of this work is an important extension of Gromov's non-squeezing theorem. This work also introduced a technique called symplectic inflation, an application of which is a theorem of McDuff on the existence of two symplectic structures in the same cohomology class that can be connected by a path of symplectic forms, but not by a path representing the same cohomology class. This is a remarkable result(and so far the only known phenomenon of its kind)as the two symplectic forms cannot be distinguished by their Gromov-Witten invariants. Among her many other contributions, old and new, are fundamental results on symplectic fibrations, the Hofer metric, Hamiltonian circle actions, and the cohomology of symplectomorphism groups.

Throughout her distinguished career Dusa McDuff has received various awards, including invitations to address the International and European Congresses of Mathematics, several honorary degrees, a Fellowship of the Royal Society, and a Membership of the National Academy of Sciences. These reflect the inspiration she has been and is to a generation of mathematicians.

Outside mathematics McDuff says that her interests are reading, chamber music, playing the cello, gardening, walking, and talking to friends.

**Article by:** *J J O'Connor* and *E F Robertson*

**September 2009**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/McDuff.html]