Joan Sylvia Birman née Lyttle (1927 - ) American mathematician and educator. Considered one of the pioneers of braid theory, she has published extensively on the topic. Now a professor emeritus at Columbia University, she has won several awards since 1974, such as the Chauvenet Prize in 1996. Birman currently has a National Science Foundation grant to further research braids.

Birman has Erdős number 3: she co-authored “Abelian and solvable subgroups of mapping class groups of surfaces” in Duke Math. J. 50 No. 4 with Alex Lubotzky, who co-authored “Discrete groups of slow subgroup growth” in Israel J. Math. 96 with László Pyber, who co-authored “Isomorphic subgraphs in a graph” in Colloquium Math. Soc. János Bolyai 52 with Erdős.