The Path Into Math

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When Dusa McDuff, the Joan Lyttle Birman ’48 Professor of Mathematics, entered the field of mathematics in the 1970s, it could be a lonely business for a woman.

“One real difficulty [with math] was that I didn’t have a strong cohort of friends, which left me feeling very isolated. I didn’t know any women trying to follow a path similar to mine, and the men I knew were not looking to be friends,” she says of former colleagues in the male-dominated discipline.

She says it took her a long time to find collaborators and friends who would encourage her to press on — but press on she did. McDuff, who has taught at Barnard since 2007, is now one of the leading figures in the field of symplectic geometry and topology. This abstract field of study on space examines interactions of pairs of quantities via the measurement of two-dimensional areas, instead of the measurements of a single quantity, like the length of an object.

If the profession is male dominated today, then it was even more so when she was coming of age in post-World War II Scotland. “When I was in school, I was considered to be very bright but very prosaic at the same time. As a teenager, I was looking for inspiration,” she says.

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Her sometimes lonely journey, however, led her to provide decades of mentorship for women at Barnard and with the Women+ and Mathematics program of the Institute for Advanced Study in Princeton, New Jersey. Never given to the false rhetoric that men are better at math, she advises mentees to pace themselves and stay focused: “Take things slow, try to find good help with understanding, and be patient with yourself.”

Noting that women’s talents are less often recognized — let alone celebrated — McDuff emphasizes the importance of community.

“Finding like-minded people — whether a fellow Barnard student or a mentor — can bolster one’s confidence and help one feel validated as a mathematician,” she says.

Though she didn’t find a role model in her exacting field, her family’s scholarly background did help prime her for a career in academia. Her mother was a trained architect and town planner; her father was a distinguished developmental biologist, geneticist, and philosopher of science.

During her first two years as a Ph.D. student at the University of Cambridge, she focused on functional analysis, which involves studying the behavior of collections of functions. 

A turning point came in 1970, after a six-month stint in Moscow working with renowned Ukrainian-born mathematician Israel Gelfand. McDuff returned to Cambridge and, following Gelfand’s advice, began studying topology, a branch of mathematics that looks at the geometric and spatial properties of objects.

“I was coming to the end of a particular line of inquiry about the properties of motions that preserve volume and started considering similar questions for symplectic motions. None of what I had done before worked in this situation,” she says.

At that time, amid new developments by Russian-French mathematician Mikhael Gromov, she planted herself in the field of symplectic geometry and topology, where she’s remained ever since.

“Gromov had a breakthrough idea in symplectic geometry that made many more questions in this area accessible,” she says. “I was fortunate enough to have a sabbatical that year, which I used to find applications of this idea.”

McDuff has since authored two seminal textbooks, been awarded several honorary degrees, and been elected to the National Academy of Sciences and the American Philosophical Society. In January, she was awarded the 2025 AMS Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society, which recognized McDuff for her “enormously influential” research and her “long-continued leadership and mentoring.”

No longer alone or lonely, McDuff espouses a liberal arts mindset fostered in part by mentors and family.

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“When I went to Moscow in 1969, my mentor Israel Gelfand, knowing of my love for music and poetry, played records to [me] and read me works from Pushkin,” she says. “He believed that was all part of the process of learning mathematics.”

She adds that her first husband, poet David McDuff, held a completely different mindset from herself.

“I remember in 1962, we were both in the [British] National Youth Orchestra, and he explained to me how Schubert felt as he was composing the symphony that we were playing,” she says.

The arts remain a huge part of her life, from reading novels and nonfiction to playing the cello and visiting art galleries. And while the arts inspire, even mundane tasks can provide inspiration for mathematical “aha” moments.

“Sometimes, ideas come to me after I have finished working directly on the problem — like when washing up or when I am walking. Often, the key idea comes in flash. And then, of course, you spend a lot of time working it out, making sure it is not a chimera.”