Women’s Week #2: Joan Birman

Joan Birman was born in New York City in 1927, and received her B.A. from Barnard College of Columbia University in 1948. She then went on to earn a M.S. in physics from Columbia in 1950. After working in the aircraft industry as a systems analyst for several years, she returned to education to pursue graduate studies in the Courant Institute of Mathematical Sciences at the New York University. In 1968, under the supervision of Wilhelm Magnus, she received her Ph.D. in mathematics on her dissertation entitled ‘Braid groups and their relationship to mapping class groups‘. She is currently Research Professor Emeritus at Barnard.

Birman has specialised in the fields of braid theory and knot theory.

“I had an instant love affair with knot theory. The moment I heard about the braid group I knew that’s what I wanted to study, and twenty-six years later, I am still fascinated by its intricacies and beauty.”

She has made numerous publications, including her influential book ‘Braids, Links, and Mapping Class Groups’, which has become a standard introduction, with many of today’s researchers having learned the subject through it.

Birman also conducted a Noether lecture in which she discussed the classification of knots and links in the three-sphere – a fundamental problem in topology. Birman suggested an approach to this problem: Study links via the nested sequence of braid groups. Since each link can be represented as a closed braid, and since braids form a group, this would allow mathematicians to use familiar group invariants. This approach led to the discovery by Vaughan Jones of vast new families of polynomial invariants of links in 1984. Jones’ knot invariants have had applications to the work of molecular biologists who have been studying the knotted shapes of DNA.

“So they came to mathematicians and we said, ‘Oh, we’ve been working on that for years.’ I’m pleased when my work is useful, but I’m more pleased by the beauty of it. It’s a bit like art, and art is not necessarily useful.”

Sources: 1 | 2

Hope you enjoyed today’s post. M x


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