On October 28^th, 1945 Cathleen Synge married Herbert Morawetz, a chemist, and the two moved to Massachusetts where Cathleen attended the Massachusetts Institute of Technology for her Master’s Degree, which was awarded to her in 1946. Morawetz was granted U.S. Citizenship in 1950.

Cathleen became fascinated by transonic flow and associated phenomena as she was editing Courant and Friedrich’s "Supersonic Flow and Shock Waves" while working at the Courant Institute of Mathematical Sciences at New York University, and decided to write her thesis on the stability of a spherical implosion. In 1951, Cathleen received her Ph.D.. In the early 1950's, she started looking at the mathematics of transonic flow, and made many discoveries which opened the problem of developing a theory for transonic flow with shocks. Towards the end of that decade Morawetz used functional analysis along with ingenious new estimates for an equation of a mixed type to prove an innovative new principle for boundary value problems for partial differential equations. From then on, much of Cathleen’s work focused on the wave equation.

In the 1960's, Cathleen worked on the scattering of sound waves and electromagnetic waves striking objects. She extended this work in the 1970's to examine other solutions to the wave equation. Morawetz has proved many important results relating to the non-linear wave equation and has won countless awards for her research. From 1984 to 1988, she held the position of Director of the Courant Institute. With this, Cathleen became the first woman to hold that position or any comparable directorship within mathematical sciences in the United States. Morawetz was elected President of the American Mathematical Society for 1995-1996. Cathleen was honored by the National Organization for Women for successfully combining career and family. She is a mother of four and has six children.

In 1998 Cathleen Morawetz was awarded the National Medal of Science, which is the highest scientific honor that the United States can give, for "pioneering advances in partial differential equations and wave propagation resulting in applications to aerodynamics, acoustics, and optics". She was the first woman to receive this medal and hoped that by her winning it, she could help move more women forward in mathematics, be it grade school or graduate school.