Peter Lax, whose work at the intersection of mathematical theory and application redefined how scientists used new computing technology to solve the technical problems of the Cold War, from designing aircraft and weapons to predicting the weather, died on Friday at his home in Manhattan. He was 99.
His death was confirmed by his son Dr. James D. Lax, who said the cause was a cardiac amyloid.
As the computer age was dawning, Dr. Lax, a native of Hungary, led the way in figuring out how the new technology could be harnessed to mathematics for the purpose of analyzing complex phenomena in nature, technology and warfare. His theoretical breakthroughs and leadership in developing large-scale computing infrastructure produced new ways to characterize and predict phenomena as varied as storm fronts, shock waves and stock prices.
In 2005, he was the first applied mathematician to win the Abel Prize — in mathematics, the closest equivalent to the Nobel Prize. Presented in a ceremony in Oslo, Norway, the prized recognized his contributions to the field of partial differential equations, the mathematics of things that move and flow. He “has been described as the most versatile mathematician of his generation,” the prize citation said.
Dr. Lax’s engagement with the new field of electronic computing grew out of his wartime weapons research. Working with the Manhattan Project in Los Alamos, N.M., in 1945-46, he had performed intricate calculations for the development of the atomic bomb.
His work at the Courant Institute of Mathematical Sciences at New York University rapidly altered the trajectory of the computing field, supporting new uses of computers in the analysis of complex systems.
He played a key role in formulating government policy that bridged civilian and military computing resources, leading to the establishment of large national computing centers, which expanded the reach of supercomputers in science and engineering, paving the way for today’s era of big data. In a 1989 article, Dr. Lax compared the impact of computers on mathematics “to the role of telescopes in astronomy and microscopes in biology.”
Peter David Lax was born in Budapest on May 1, 1926, to Henry and Klara (Kornfeld) Lax, both of whom were physicians. Fascinated by mathematics, Peter was tutored in the subject as a youth by the renowned mathematician Rósza Péter, a founder of recursion theory, a branch of logic that investigates which mathematical problems can be resolved by computation. Dr. Péter connected him to her community of Hungarian-Jewish mathematicians, many of whom made significant contributions to midcentury mathematics.
Peter was a young teenager when he demonstrated his early promise. At Dr. Péter’s suggestion, he completed the problems that were being presented in Hungary’s national math competition for high school graduates. He produced solutions that would have won the contest had he been old enough to enter.
In December 1941, in the face of rising antisemitism in Hungary, an ally of Nazi Germany, Peter and his family fled the country, obtaining passage to the United States with the help of the American consul in Budapest, a patient and friend of Peter’s father. The family arrived as refugees in New York, where Peter, by then a 15-year-old prodigy, came under the wing of other Hungarian mathematicians, who connected him to the German émigré mathematician Richard Courant. At the time, Dr. Courant was blazing a new direction for applied mathematics and laying the foundation for the institute at N.Y.U. that would later bear his name.
Peter’s father became Dr. Courant’s physician, while Dr. Courant mentored Peter in mathematics.
At 18, having already published his first math paper, Peter was drafted into the U.S. Army. He was assigned to the Manhattan Project at Los Alamos in the summer of 1945, just in time to participate in the final stages of the race to build an atomic bomb. He worked as a calculator, executing the kind of elaborate multistep computations that would later be performed by electronic computers. His group analyzed the shock waves that would enable a neutron chain reaction, creating the atomic bomb’s enormously powerful explosion.
He became part of a community of Hungarian mathematicians at Los Alamos that included John von Neumann and John Kemeny, both of whom would later join him on the frontiers of postwar mathematics and computing.
After the war, he completed his undergraduate and doctoral degrees at New York University and was appointed assistant professor in 1949. He returned to Los Alamos in 1950 for a year and several subsequent summers to work on the next-generation hydrogen bombs. He became a full professor at N.Y.U. in 1958.
The connections Dr. Lax made at Los Alamos — to the people there, the problems they worked on and the equipment they used — would set the agenda for early postwar computing and guide the rest of his mathematical career.
In 1954, the Atomic Energy Commission put Dr. Lax and several of his N.Y.U. colleagues in charge of operating an early supercomputer to calculate the risk of flooding to a major nuclear reactor if a nearby dam were sabotaged; they showed that the reactor would be safe.
His work on computing dovetailed with his contributions to the theory of hyperbolic partial differential equations, an area of research essential to understanding shock waves from bombs, as well as a wide variety of physical phenomena, from weather prediction to aerodynamic design. Among mathematicians, he was most renowned for theoretical breakthroughs that others used to analyze specific phenomena.
Again and again, Dr. Lax demonstrated the theoretical richness of applied mathematics, providing, in the words of his early doctoral student Reuben Hersh, “a singular exception to the usual mutual disrespect between these two inseparable and incompatible twins, the pure and the applied.”
As Dr. Courant wrote in 1962, Dr. Lax embodied “the unity of abstract mathematical analysis with the most concrete power in solving individual problems.”
Dr. Lax’s impact is suggested by the number of concepts that bear his name. They include the Lax equivalence principle, which explains when numerical computer approximations will be reliable; the Lax-Milgram lemma, which relates the interior of a system to its boundary; and Lax pairs, a milestone in understanding the motion of solitons, a kind of traveling wave related to tsunamis.
With Ralph Phillips, Dr. Lax developed the Lax-Phillips semigroup in scattering theory, which explains how waves move around obstacles and shows how to use the pattern of frequencies in a wave to understand its motion. That theory yielded many uses, including the interpretation of radar signals.
In 1960, Dr. Lax made his first of eight scientific visits to the Soviet Union. His exchanges with Soviet mathematicians — in which “vodka flowed like water,” he said — led to lasting friendships and represented a warmer side of his Cold War science.
Starting in 1963, Dr. Lax directed the Courant Institute’s cutting-edge computing facilities, funded by the Atomic Energy Commission. He led the institute as director from 1972-80. He also increasingly represented the mathematics profession on the national stage, culminating in his presidency of the American Mathematical Society from 1977 to 1980.
From 1980-86, Dr. Lax served on the National Science Board, which sets American research funding policies. In 1982, his “Report of the Panel on Large Scale Computing in Science and Engineering,” commonly known as the Lax Report, set a lasting agenda for academic- and military-networked research with government supercomputers.
His personal life was as integrated with the Courant Institute as his professional life. His first marriage, in 1948, was to the mathematician Anneli Cahn, a fellow doctoral student. After her death in 1999, he married Dr. Courant’s daughter, Lori Berkowitz, the widow of another Courant Institute mathematician and principal violist for the American Symphony Orchestra. She died in 2015.
Besides his son James, Dr. Lax is survived by his stepchildren, David and Susan Berkowitz; three grandchildren; and two great-grandchildren. Another son, John Lax, was killed by a drunk driver in 1978.
Dr. Lax also wrote poetry, in English and Hungarian. In a 1999 report to the American Philosophical Society, he summarized one of his findings about differential equations with a haiku:
Speed depends on size
Balanced by dispersion
Oh, solitary splendor.
Dr. Lax represented the pragmatic side of mathematicians’ engagement with the Cold War. He kept his politics close to his chest, but often privately supported mathematicians involved in antiwar activism. At the same time, he retained the good relations with their ideological opposites that were necessary to keep money flowing to the mathematical research he valued. Though he believed that the atomic weapons he helped develop shortened World War II and deterred later conflicts, he emphasized the intellectual rewards of his military research.
His work bridged worlds — military and civilian, pure and applied mathematics, abstract theory and computation — reflecting a belief that the underlying math was universal. In a 2005 interview with The New York Times, he cited the fact that geometry and algebra, “which were so very different 100 years ago, are intricately connected today.”
“Mathematics is a very broad subject,” he said. “It is true that nobody can know it all, or even nearly all. But it is also true that as mathematics develops, things are simplified and unusual connections appear.”
Ash Wu contributed reporting.
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