# Cathleen Morawetz

### NY Times Obituary

Mathematician with real-world impact, dies at 94

Cathleen S. Morawetz, a mathematician whose theorems often found use in solving real-world engineering problems, has died at her home in New York City. She was 94. One of her notable papers helped explain the flow of air around airplanes flying close to the speed of sound.

Her death was reported by New York University, where she had been a professor.

Much of Morawetz's research centered on equations that describe the motion of fluids and waves --in water, sound, light and vibrating solids. One of her first notable papers helped explain the flow of air around airplanes flying close to the speed of sound.

Although the aircraft itself does not break the sound barrier, she found, some of the air rushing around the curves of its wings goes supersonic. Below the speed of sound, air flows in a fundamentally different manner than at supersonic speeds, and the mix of the two speeds -- called transonic flight -- produces shock waves that slow the aircraft.

Wings can be designed so that transonic airflow remains smooth at certain speeds without generating shock waves. But Morawetz's work demonstrated that such shock-free wings do not work in the real world. The slightest perturbation --an imperfection in the shape, a tilt in the angle of the wing, a gust of wind -- disrupts the smooth flow.

"The search for shock-free airfoils is sort of futile,"said Jonathan Goodman, a math professor and one of Morawetz's colleagues at New York University at the Courant Institute for Mathematical Sciences. Morawetz's paper on the subject, he said, was "a beautiful proof."

With that insight, aerospace engineers now design wings to minimize shocks rather than trying to eliminate them.

In later work, Morawetz studied the scattering of waves off objects. She invented a method to prove what is known as the Morawetz inequality, which describes the maximum amount of wave energy near an object at a given time. It proves that wave energy scatters rather than lingering near the object indefinitely.

"She did some very nice things that are still quoted today,"said Louis Nirenberg, a New York University mathematician who first met Morawetz as a graduate student.

He said he attended a general relativity conference a few weeks ago. "People there were using her inequalities,"he said.

Cathleen Synge was born May 5, 1923, in Toronto, the daughter of Irish immigrants. Her father, John Lighton Synge, was a physicist and mathematician known for research that used a geometric approach to study Einstein's theory of general relativity. Her mother, the former Elizabeth Eleanor Mabel Allen, had been a math major in college but dropped out when she married. Morawetz credited her mother with encouraging her to have a career.

She earned a bachelor's degree in mathematics at the University of Toronto in 1945, the same year she married Herbert Morawetz, a polymer chemist.

She toyed with the idea of going to India as a teacher, but a Toronto math professor who was a family friend persuaded her to go to graduate school instead. She received a master's degree in mathematics at the Massachusetts Institute of Technology the next year and a doctorate at New York University in 1951. She wrote her thesis about imploding shock waves.

After a postdoctoral fellowship at MIT, she returned to New York University. She worked part time, supported by Navy contracts, before she was offered an assistant professorship in 1957. She spent the rest of her career at the university, including serving as the director of the Courant Institute from 1984 to 1988.

Morawetz was a member of the National Academy of Sciences and a fellow of the American Academy of Arts and Sciences. In 1995 she became president of the American Mathematical Society, and in 1998 she became the first female mathematician to receive a National Medal of Science.

In addition to her husband, Morawetz is survived by three daughters, Pegeen Rubinstein, Lida Jeck and Nancy Morawetz; a son, John; a sister, Isabel Seddon; six grandchildren; three great-grandchildren; and four step-grandchildren.

In an interview with the journal Science in 1979, Morawetz recalled that when her children were young --a time when few women pursued professional careers -- people often asked whether she worried about them while she was at work.

Her reply: "No, I'm much more likely to worry about a theorem when I'm with my children."

KENNETH CHANG

Published: August 15, 2017 © New York Times

Her death was reported by New York University, where she had been a professor.

Much of Morawetz's research centered on equations that describe the motion of fluids and waves --in water, sound, light and vibrating solids. One of her first notable papers helped explain the flow of air around airplanes flying close to the speed of sound.

Although the aircraft itself does not break the sound barrier, she found, some of the air rushing around the curves of its wings goes supersonic. Below the speed of sound, air flows in a fundamentally different manner than at supersonic speeds, and the mix of the two speeds -- called transonic flight -- produces shock waves that slow the aircraft.

Wings can be designed so that transonic airflow remains smooth at certain speeds without generating shock waves. But Morawetz's work demonstrated that such shock-free wings do not work in the real world. The slightest perturbation --an imperfection in the shape, a tilt in the angle of the wing, a gust of wind -- disrupts the smooth flow.

"The search for shock-free airfoils is sort of futile,"said Jonathan Goodman, a math professor and one of Morawetz's colleagues at New York University at the Courant Institute for Mathematical Sciences. Morawetz's paper on the subject, he said, was "a beautiful proof."

With that insight, aerospace engineers now design wings to minimize shocks rather than trying to eliminate them.

In later work, Morawetz studied the scattering of waves off objects. She invented a method to prove what is known as the Morawetz inequality, which describes the maximum amount of wave energy near an object at a given time. It proves that wave energy scatters rather than lingering near the object indefinitely.

"She did some very nice things that are still quoted today,"said Louis Nirenberg, a New York University mathematician who first met Morawetz as a graduate student.

He said he attended a general relativity conference a few weeks ago. "People there were using her inequalities,"he said.

Cathleen Synge was born May 5, 1923, in Toronto, the daughter of Irish immigrants. Her father, John Lighton Synge, was a physicist and mathematician known for research that used a geometric approach to study Einstein's theory of general relativity. Her mother, the former Elizabeth Eleanor Mabel Allen, had been a math major in college but dropped out when she married. Morawetz credited her mother with encouraging her to have a career.

She earned a bachelor's degree in mathematics at the University of Toronto in 1945, the same year she married Herbert Morawetz, a polymer chemist.

She toyed with the idea of going to India as a teacher, but a Toronto math professor who was a family friend persuaded her to go to graduate school instead. She received a master's degree in mathematics at the Massachusetts Institute of Technology the next year and a doctorate at New York University in 1951. She wrote her thesis about imploding shock waves.

After a postdoctoral fellowship at MIT, she returned to New York University. She worked part time, supported by Navy contracts, before she was offered an assistant professorship in 1957. She spent the rest of her career at the university, including serving as the director of the Courant Institute from 1984 to 1988.

Morawetz was a member of the National Academy of Sciences and a fellow of the American Academy of Arts and Sciences. In 1995 she became president of the American Mathematical Society, and in 1998 she became the first female mathematician to receive a National Medal of Science.

In addition to her husband, Morawetz is survived by three daughters, Pegeen Rubinstein, Lida Jeck and Nancy Morawetz; a son, John; a sister, Isabel Seddon; six grandchildren; three great-grandchildren; and four step-grandchildren.

In an interview with the journal Science in 1979, Morawetz recalled that when her children were young --a time when few women pursued professional careers -- people often asked whether she worried about them while she was at work.

Her reply: "No, I'm much more likely to worry about a theorem when I'm with my children."

KENNETH CHANG

Published: August 15, 2017 © New York Times