[2] Her thesis research concerned Lie groups, but subsequently her interests broadened to include also polynomial factorization, partial differential equations, harmonic analysis, and the theory of several complex variables.

[3] The daughter of Philadelphia fur merchants, she was unable to attend the best high school of the city, which were then restricted to boys.

[2][3] Rejected from graduate study at Princeton University because it was also male-only,[3][4] she earned her Ph.D. in 1970 from the Massachusetts Institute of Technology under the supervision of Isadore Singer.

[2][4] The mother of two sons by her first marriage, her second husband, M. Salah Baouendi, was a distinguished professor of mathematics at UC San Diego; he died in 2011.

[2][3] In 1997, Rothschild gave the Noether Lecture of the Association for Women in Mathematics, on the subject "How do Real Manifolds live in Complex Space?