Cathleen S. Morawetz with Harold Grad, a New York University colleague, in 1964. (New York University)

Cathleen S. Morawetz, whose achievements in mathematics found widespread practical use, helped open her profession to other women and made her the first female mathematician to receive the National Medal of Science, died Aug. 8 at her home in New York. She was 94.

Her death was announced by New York University, where she spent nearly her entire career, and where she was a former director of the Courant Institute of Mathematical Sciences. The cause was pneumonia and renal failure, said a daughter, Nancy Morawetz.

Dr. Morawetz rose to the top of her profession at a time when few women received the encouragement or opportunity to pursue mathematical studies or work. She gravitated to questions with immediate and useful applications, once describing herself as “an applied mathematician who proves theorems to solve problems.”

After establishing herself in the 1950s, she quickly became known for her study of transonic flow, or the behavior of air when an object such as a plane approaches the speed of sound.

It was a matter of vital importance for military aeronautical engineers, who sought to design airplane wings capable of blunting the shock waves that are produced when air around the plane passes the sound barrier.

Dr. Morawetz’s theorem showed that, contrary to the hopes of the engineers, a shockless design was “theoretically maybe possible but practically not possible,” Robert V. Kohn, a professor of mathematics at NYU, said in an interview. Engineers, therefore, focused on reducing rather than averting shock waves.

Speaking to the journal Science in 1979, Dr. Morawetz remarked that her work on transonic flow presented the unusual example of engineers calling upon a mathematician for a proof, rather than engineers bellyaching about mathematicians who explain problems the engineers have already solved.

Dr. Morawetz also was noted for her work explaining the scattering of sound, light, water and gravitational waves off obstacles. The concept of a “Morawetz inequality,” as her formulation was known, “continues to be used in a very broad range of applications,” said Deane Yang, also a mathematics professor at NYU.

The citation for Dr. Morawetz’s National Medal of Science, awarded in 1998, credited her with academic achievements that were “matched by her leadership and inspiration, judgment and vision, and knowledge and generosity to colleagues and collaborators.”

She often was cited as a trailblazing influence for women in mathematics. In 2014, the Iranian mathematician Maryam Mirzakhani became the first woman to win the prestigious Fields Medal. She died in July at age 40 of breast cancer.

Cathleen Synge — her maiden name was pronounced “sing” — was born on May 5, 1923, in Toronto, where her father, the noted Irish mathematician John Lighton Synge, held an academic appointment at the University of Toronto. His students over the years included John F. Nash Jr., the Nobel Prize-winning game theorist whose life was dramatized in the 2001 film “A Beautiful Mind.”

Her mother, Elizabeth Allen, who also was from Ireland, had studied mathematics as well. Dr. Morawetz credited both parents with encouraging her intellectual and professional ambitions — traits that she once joked were “at the time very unladylike.”

She received a bachelor’s degree from the University of Toronto in 1945, a master’s degree from the Massachusetts Institute of Technology in 1946 and a PhD from NYU in 1951, all in mathematics.

Looking for work, she “just wanted what a man could get,” she once told USA Today. She said the Courant Institute supported her career by giving her a raise when she had her first child, so that she could pay for child care when she returned to work.

Asked if she fretted about her children when she was at the office, she quipped to Science that she was “much more likely to worry about a theorem” when she was with her children. A paid death notice in the New York Times described her as equally “at home proving a complex theorem as getting down on the floor to play with her grandchildren.”

Survivors include her husband of 71 years, Herbert Morawetz, a chemist, of New York; four children, Pegeen Rubinstein of Westport, Conn., John Morawetz of Erlanger, Ky., Lida Jeck of Chapel Hill, N.C., and Nancy Morawetz of New York; a sister; 10 grandchildren; and three great-grandchildren.

Dr. Morawetz served as a trustee of Princeton University and of the Alfred P. Sloan Foundation, as well as president of the American Mathematical Society, which honored her with a lifetime achievement award.

When she received the National Medal of Science, she told USA Today that she hoped the honor would “draw attention to the idea that women can do math and will have some influence on women all the way from grade school to graduate school and beyond.”

An earlier version of this article misstated the surname of a colleague of Dr. Morawetz’s at New York University. He is Deane Yang, not Deane Young. Also, her mother was known as Elizabeth Allen, not Eleanor Allen. The article has been updated.