Mary Claire Pugh is an applied mathematician known for her research on thin films, including the thin-film equation and Hele-Shaw flow. She is a professor of mathematics at the University of Toronto.
Pugh completed her Ph.D. in 1993 at the University of Chicago. Her dissertation, Dynamics of Interfaces of Incompressible Fluids: The Hele-Shaw Problem, was supervised by .Before moving to Toronto, she worked at the Courant Institute of Mathematical Sciences at New York University and then as a faculty member at the University of Pennsylvania, where she won a Sloan Research Fellowship in 1999.