Joan Sylvia Lyttle Birman (born May 30, 1927, in New York City^{[1]}) is an American mathematician, specializing in lowdimensional topology. She has made contributions to the study of knots, 3manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University,^{[2]} where she has been since 1973.
Joan Sylvia Lyttle Birman  

Born  
Nationality  American 
Alma mater  B.A., Barnard College, 1948 Ph.D., Courant Institute (NYU), 1968 
Known for  Braid theory, knot theory 
Awards 

Scientific career  
Fields  Mathematics 
Institutions  Barnard College, Columbia University 
Doctoral advisor  Wilhelm Magnus 
Doctoral students  
Website  http://www.math.columbia.edu/~jb/ 
Her parents were George and Lillian Lyttle, both Jewish immigrants.^{[3]} Her father was from Russia but grew up in Liverpool, England. Her mother was born in New York and her parents were RussianPolish immigrants. At age 17, George emigrated to the US and became a successful dress manufacturer. He appreciated the opportunities from having a business but he wanted his daughters to focus on education. She has three children, Kenneth P. Birman, Deborah Birman Shlider, and Carl David Birman. Her late husband, Joseph Birman, was a physicist and a leading advocate for human rights for scientists. Her 5 Grandchildren includes Jared Birman who is an up and coming teacher and Joan Birman is a mentor towards his. ^{[4]}
After high school, Birman entered Swarthmore College, a coeducational institution in Swarthmore, Pennsylvania, and majored in mathematics. However, she disliked living in the dorms so she transferred to Barnard College, a women's only college affiliated to Columbia University, to live at home.^{[3]}
Birman received her B.A. (1948) in mathematics from Barnard College and an M.A. (1950) in physics from Columbia University. After working in the industry from 1950 to 1960, she did a PhD in mathematics at the Courant Institute (NYU) under the supervision of Wilhelm Magnus, graduating in 1968. Her dissertation was titled Braid groups and their relationship to mapping class groups.^{[5]}
After she earned her bachelor's degree from Barnard, Birman accepted a position at the Polytechnic Research and Development Co., which was affiliated with Brooklyn Polytechnic University. She later worked from the Technical Research Group and the W. L. Maxson Corporation.^{[6]}
Birman's first academic position was at the Stevens Institute of Technology (1968–1973). In 1969 she published "On Braid Groups", which introduced the Birman Exact Sequence which became one of the most important tools in the study of braids and surfaces.^{[7]} During the later part of this period she published a monograph, 'Braids, links, and mapping class groups' based on a graduate course she taught as a visiting professor at Princeton University in 1971–72. This book is considered the first comprehensive treatment of braid theory, introducing the modern theory to the field, and contains the first complete proof of Markov's theorem.^{[7]}
In 1973, she joined the faculty at Barnard College. She was a visiting scholar at the Institute for Advanced Study in the summer of 1988.^{[8]}
She supervised 21 doctoral students, and has a total of 50 academic descendants. Her doctoral students include Józef Przytycki.^{[5]}
Birman was a founding editor of the journals Geometry and Topology and Algebraic and Geometric Topology. ^{[9]}
Birman was a cofounder of Mathematical Sciences Publishing, a nonprofit publishing house. She was a member of the New York Academy of Sciences Human Rights of Scientists Committee.^{[10]}
in 1990, Birman donated funds to the American Mathematical Society to establish the Ruth Lyttle Satter Prize in Mathematics in honor of her sister, Ruth Lyttle Satter, who was a plant physiologist.^{[9]}
In 2017, she endowed the Joan and Joseph Birman Fellowship for Women Scholars at the American Mathematical Society to support mathematical research by midcareer women.^{[11]}
According to her MathSciNet author profile, Birman's scientific work includes 106 research publications and over 300 published reviews in Math Reviews. She is the author of the research monograph Braids, Links, and Mapping Class Groups.
In 1974, Birman was selected as a Sloan Research Fellow by the Alfred P. Sloan Foundation.^{[12]} In 1987, she was selected by the Association for Women in Mathematics to be a Noether Lecturer; this lecture honors women who have made fundamental and sustained contributions to the mathematical sciences.^{[13]} In 1994, she was selected as a Guggenheim Foundation Fellow by the John Simon Guggenheim Memorial Foundation.^{[14]} In 1996, the Mathematical Association of America awarded Birman the Chauvenet Prize, "the highest award for mathematical expository writing .^{[15]}
In 2003, Birman was elected to the European Academy of Sciences.^{[16]} In 2005, she won the New York City Mayor's Award for Excellence in Science and Technology.^{[1]}
Birman received a honorary doctorate from the Technion Israel Institute of Technology.^{[9]}
In 2012, Birman was elected to the American Academy of Arts and Sciences^{[17]}^{[18]} In 2013, she became a fellow of the American Mathematical Society in the inaugural class.^{[19]}
In 2015, Birman was named an honorary member of the London Mathematical Society.^{[20]}
The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for "her groundbreaking research connecting diverse fields, and for her awardwinning expository writing; for continuously supporting women in mathematics as an active mentor and a research role model; and for sponsoring multiple prize initiatives for women".^{[21]}
In 2021, Birman was elected to the National Academy of Sciences.^{[22]}