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Louis Nirenberg Obituary Louis Nirenberg (1925–2020) Mathematician who transformed the study of partial differential equations. fter the Second World War, PDE in Novosibirsk, which helped to redefine mathe matics in the United States the relationship between the Soviet Union flourished owing to a convergence of and the United States. There, he forged close interests. Mathematicians had shown friendships in an environment he compared to their worth to military and indus- a voyage at sea. A later geopolitically signifi- Atry patrons, who underwrote far-reaching cant trip took him to China toward the end of empires of theories and people, including the the Cultural Revolution. After being assigned consummate problem-solver Louis Nirenberg. a PhD thesis in Italian as the subject for a term One of the world’s most cited and paper during his graduate studies, he devel- productive mathematicians, Nirenberg was oped a lifelong affinity for Italy. also among the most collaborative. His work Nirenberg was known for using methods in continued to make waves until he was well their most fruitful generality. “I have made a into his eighties, and reshaped how mathe- living off the maximum principle,” he quipped, maticians understand and study dynamical referring to a fundamental technique for systems, from cells to markets. Winning the establishing inequalities in PDE. He demon- 2015 Abel Prize (shared with John Nash, made strated its versatile potential to researchers in NEW YORK UNIVERSITY ARCHIVES NEW YORK famous by the 2001 film A Beautiful Mind) was many fields. As a young man, he had worried just a bookend to a fêted career. He died on National Research Council, contributing to about his ability to formulate original prob- 26 January, aged 94. research on atomic weapons. On the advice lems. Yet Nirenberg gained a reputation for Nirenberg spent an illustrious seven of Sarah’s father-in-law, Richard Courant, a his exceptional insight and taste as a poser of decades at New York University (NYU), a leading mathematician at NYU, Nirenberg did problems that stretched the limits of research realization of the discipline’s post-war entan- a master’s in mathematics at the university. in mathematics and beyond. glements and their scholarly rewards. He He remained there for the rest of his career, His career awards included the first Crafoord joyfully nurtured people and ideas, skating heading the Courant Institute of Mathematical Prize in 1982 and the first Chern Medal of the above emerging distinctions between pure Sciences from 1970 to 1972. International Mathematical Union in 2010. and applied mathematics. Nirenberg trained with a who’s who of Although he knew Nash, their Abel Prize rec- Nirenberg transformed the field of partial twentieth-century mathematics, including ognized PDE work from separate parts of the differential equations (PDE), which explores his PhD supervisor James Stoker and his men- firmament. what can be known about mathematical func- tor Kurt Friedrichs as well as visiting scholars A famously congenial collaborator, tions from studying how their variations along from across Europe, the Soviet Union and the Nirenberg co-authored papers to an extent different dimensions relate to each other. Americas. With fellow students Peter Lax and unusual in mathematics. Some collaborations Emerging from eighteenth-century math- Cathleen Morawetz, he climbed the ranks to took place entirely by post, including the only ematical physics, PDE became a centrepiece of professor. work he published with his lifelong colleague a vast range of theoretical and applied subjects, Courant had courted federal contracts and Lax, conducted while Nirenberg was in Japan. from telecommunications and nuclear phys- support during the Second World War to lay Other collaborations — including with the ics to debates about the nature of numbers. the groundwork for his institute. Expansive 46 doctoral students he supervised — involved One famous and still-unresolved question in budgets from sources including the Office extended dialogues in front of a blackboard or which Nirenberg’s insights have been signifi- of Naval Research supported Nirenberg’s while walking to a restaurant, as he digested cant asks whether the equations governing the research on elliptic equations (with appli- new ideas in company. movement of water from a given initial state are cations from fluid dynamics to finance) and always compatible with a smooth flow. pseudo-differential operators (a foundation Brit Shields works on the cultural history A virtuoso of approximation, Nirenberg was for an enormous variety of approaches in of twentieth-century mathematics; she is renowned for manipulating inequalities that modern physics). One-quarter of his publica- senior lecturer in the School of Engineering govern the properties of unknown functions. tions, including his first four in 1953, were in and Applied Science at the University of Fellow mathematicians found his perspectives the institute’s own journal, Communications Pennsylvania in Philadelphia and a part-time and methods strikingly lucid. His works cata- on Pure and Applied Mathematics. programme administrator at the Courant lysed large bodies of research, from general Nirenberg considered the world’s Institute of Mathematical Sciences, where relativity to biology. mathematicians to be “one big family”, and she knew Nirenberg. Michael J. Barany Raised in a Yiddish-speaking family in found inspiration in visiting and hosting is lecturer in the history of science at the Montreal, Canada, Nirenberg acquired a taste colleagues from around the world. His first University of Edinburgh, UK, where he for mathematical puzzles from his Hebrew extended overseas research trip, in 1951–52, studies the global history and culture of tutor. After completing his undergraduate took him to Zurich, Switzerland, where he modern mathematics. Both had interviewed degree in mathematics and physics at McGill wrote up results from his thesis and attended Nirenberg for their research. University in Montreal in 1945, Nirenberg lectures from stars of Courant’s generation. In e-mails: [email protected]; joined his friend Sarah Courant at the nearby 1963, he took part in a landmark symposium on [email protected] Nature | Vol 578 | 20 February 2020 | 359 ©2020 Spri nger Nature Li mited. All ri ghts reserved. .
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