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Celebratio Mathematica

Cathleen Morawetz

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Introduction

by Irene Gamba and Christina Sormani

Morawetz, an avid sailor, invited us all to “sail with her, near the speed of sound.”
Photo courtesy of the Morawetz family.
In this me­mori­al we cel­eb­rate the math­em­at­ics of Cath­leen Synge Mor­awetz (1923–2017). She was awar­ded the Na­tion­al Medal of Sci­ence in 1998 “for pi­on­eer­ing ad­vances in par­tial dif­fer­en­tial equa­tions and wave propaga­tion res­ult­ing in ap­plic­a­tions to aero­dy­nam­ics, acous­tics and op­tics.” In 2004 she won the Steele Prize for life­time achieve­ment and in 2006 she won the Birk­hoff Prize “for her deep and in­flu­en­tial work in par­tial dif­fer­en­tial equa­tions, most not­ably in the study of shock waves, tran­son­ic flow, scat­ter­ing the­ory, and con­form­ally in­vari­ant es­tim­ates for the wave equa­tion.”

As it is im­possible to re­view all her pro­found con­tri­bu­tions to pure and ap­plied math­em­at­ics, we have chosen in­stead to present some of her most in­flu­en­tial work in depth. Ter­ence Tao presents the Mor­awetz En­er­gies and Mor­awetz In­equal­it­ies, which are ubi­quit­ous in the ana­lys­is of non­lin­ear wave equa­tions. Leslie Greengard and Tona­tiuh Sánchez-Vizuet have writ­ten about her work on scat­ter­ing the­ory. Kev­in R. Payne de­scribes the im­port­ance of her early work on tran­son­ic flows which both provided a new un­der­stand­ing of mixed-type par­tial dif­fer­en­tial equa­tions and led to new meth­ods of ef­fi­cient air­craft design. In this in­tro­duc­tion, we provide a little his­tory about her ca­reer, and we close the art­icle with a quote of hers thank­ing one of the math­em­aticians who sup­por­ted her the most when she was young.

Morawetz was awarded the National Medal of Science in 1998 “for pioneering advances in partial differential equations and wave propagation.”
Photo courtesy of New York University.

Mor­awetz was en­cour­aged to study math­em­at­ics by her moth­er and a fam­ily friend, Cecil­ia Kreger, who was a math­em­at­ics pro­fess­or at the Uni­versity of Toronto. Her fath­er, who was also a math­em­atician at Toronto, did not en­cour­age her pur­suit of math­em­at­ics, but did en­cour­age her to be “am­bi­tious.” Mor­awetz gradu­ated with a bach­el­ors in math­em­at­ics at Toronto in 1945 and com­pleted her mas­ters at MIT the fol­low­ing year.

In 1946 Mor­awetz was hired at New York Uni­versity to edit the manuscript “Su­per­son­ic Flow and Shock Waves” by Richard Cour­ant and Kurt Otto Friedrichs. She de­scribed this later in life as “an in­valu­able and im­mers­ive learn­ing ex­per­i­ence.” Upon com­plet­ing her doc­tor­ate in 1951 with Friedrichs, Mor­awetz first ac­cep­ted a re­search as­so­ci­ate po­s­i­tion at MIT. However she quickly re­turned to New York Uni­versity, where she stayed for the re­mainder of her ca­reer. Ori­gin­ally hired as re­search as­so­ci­ate, she be­came as­sist­ant pro­fess­or in 1957. At that time Cour­ant also hired oth­er NYU gradu­ates to join the fac­ulty, in­clud­ing Har­old Grad, An­neli Cahn Lax, then Peter Lax and Louis Niren­berg. They re­mained close friends throughout her life. Mor­awetz was ten­ured in 1960 and earned a full pro­fess­or­ship in 1965, the year be­fore be­ing awar­ded her first of two Gug­gen­heim Fel­low­ships. She was a Gibbs Lec­turer in 1981, gave an in­vited ad­dress for SIAM in 1982, and was No­eth­er Lec­turer in 1983 and 1988. She served as the dir­ect­or of the Cour­ant In­sti­tute at NYU from 1984 to 1988.

Cathleen Morawetz and fellow New York University PhD, Harold Grad, back at NYU on the faculty (1964).
Photo courtesy of New York University.

Mor­awetz was an astound­ing ment­or and a ded­ic­ated coau­thor. Irene Gamba worked with her in 1992–1994 as an NSF postdoc­tor­al fel­low. She writes:

Our dis­cus­sions las­ted for end­less hours and were most il­lu­min­at­ing and pro­lif­ic. They cul­min­ated with two joint pub­lic­a­tions re­lated to the ap­prox­im­a­tion to tran­son­ic flow prob­lems, and the life chan­ging op­por­tun­ity of join­ing the fac­ulty as an as­sist­ant pro­fess­or in the fall of 1994. She was an ex­traordin­ary role mod­el for me.

Mor­awetz col­lab­or­ated of­ten with young­er math­em­aticians, in­clud­ing Gregory Kriegs­man, Wal­ter Strauss, Alv­in Bayliss, Kev­in Payne, Susan Fried­lander, Jane Gil­man, and James Ral­ston. Among her doc­tor­al stu­dents were Chris­ti­an Klin­gen­berg and Les­ley Sib­n­er.

Morawetz with Irene Gamba on the day Morawetz gave her Noether Lecture at the International Congress of Mathematicians in 1998. Their work was an extraordinary leap into an area that today remains quite unexplored.
Photo courtesy of Sylvia Wiegand and the Association for Women in Mathematics.

Mor­awetz was elec­ted pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety in 1993. At that time fund­ing in core math­em­at­ics was un­der threat, the US gov­ern­ment was shut down twice, the job mar­ket for new doc­tor­ates in math­em­at­ics was ter­rible, and uni­versit­ies were re­con­sid­er­ing the im­port­ance of hav­ing re­search math­em­aticians teach­ing their math­em­at­ics courses. We are fa­cing these same dif­fi­culties today and can learn from her ex­ample.

As AMS pres­id­ent, Mor­awetz joined forces with the SIAM pres­id­ent, Mar­garet Wright, to de­fend the fund­ing of both pure and ap­plied math­em­at­ics. “To­geth­er, they for­mu­lated care­fully worded state­ments for Con­gress and agency lead­ers, al­ways stress­ing (equally) the re­mark­able track re­cord of use­ful math­em­at­ics as well as the un­ex­pec­ted be­ne­fits that con­sist­ently emerge from un­dir­ec­ted ba­sic re­search.”1 Their work led even­tu­ally to­wards the cre­ation of the NSF DMS Grants for Ver­tic­al In­teg­ra­tion of Re­search and Edu­ca­tion (VI­GRE) “to in­crease the num­ber of well-pre­pared US cit­izens, na­tion­als, and per­man­ent res­id­ents who pur­sue ca­reers in the math­em­at­ic­al sci­ences.” This pro­gram provided fund­ing for postdocs, gradu­ate stu­dents, and un­der­gradu­ates en­gaged in re­search with one an­oth­er and has dir­ectly in­flu­enced the ca­reers of many young math­em­aticians.

Morawetz with Bella Manel (left) and Christina Sormani (right) at NYU in 1996. Manel received her doctorate at NYU in 1939.
Photo courtesy of Roy Goodman.

Mor­awetz was a power­ful lead­er, a won­der­ful ment­or, and an amaz­ing math­em­atician. All of us that were for­tu­nate enough to be in­flu­enced by her aura through her ninety-four years of life can ad­mire her re­lent­less pur­suit of ex­cel­lence. Per­haps we too can strive to make a dif­fer­ence.

See also