A New York University professor emeritus at the Courant Institute of Mathematical Sciences, Peter Lax, has won the $980,000 Abel Prize, popularly known as the Nobel Prize of mathematics. That’s $1 million minus only $20,000, for those of who are not mathematically inclined.

The 78-year-old will travel to Oslo, Norway, May 24 to receive the prize, established by the Norwegian Academy of Science and Letters.

“Besides being the dominant figure in applied mathematics in his time, he’s also one of the world’s central figures in pure mathematics,” a New York University professor, Sylvain Cappell, said.

Of all fields of mathematics, that of differential equations, which allows an understanding of how quantities vary over time, is probably the most important for applications, a Princeton and NYU professor, Peter Sarnak, said. “Lax has made fundamental contributions to almost every aspect of this topic,” he said.

Mr. Lax immigrated to America from Budapest at 15. After traveling through Germany by train, he and his parents – both doctors – boarded the last boat from Portugal on December 5, 1941.

Before Mr. Lax was 16, the eminent John von Neumann paid him a visit him at his parents’ Upper West Side apartment after two of his former Budapest teachers recommended him as a promising mathematician. Mr. Lax, who attended Stuyvesant High School, had once won a competition of high school students involving geometry, and von Neumann probed him with questions about what problems he had worked on.

Over a tea in Princeton in spring 1942, the kindly mathematician Paul Erdos introduced Mr. Lax to Albert Einstein as a talented young Hungarian mathematician. Einstein turned to Erdos and asked: Why mention Hungarian?

Mr. Lax’s Ph.D. studies at New York University dealt with hyperbolic equations, which describe motions of sound, light, and electromagnetic waves, and compressible fluids.

During World War II, Mr. Lax was a GI whose basic training in Florida took place at an “infantry replacement training center,” which he said “sounded like cannon fodder.” Assigned to the Manhattan Project at Los Alamos, N.M., in 1945-46, he worked on neutron transport.

During trips in subsequent years to Los Alamos, von Neumann helped spark Mr. Lax’s interest in shock waves, an area to which Mr. Lax later made important research contributions.

Mr. Lax did foundational work on finding solution to equations that describe the way a single wave moves. It has been long noticed, for example, that a single water wave down a canal will preserve its shape for astonishing distances; his work furthered understanding of such phenomena. Mr. Lax’s varied contributions touch areas such as scattering theory (which addresses, for example, how a wave goes around an obstacle) and modern computational mathematics.

Mr. Lax’s ideas – often at the intersection of mathematics and physics – have importance for aerodynamics and weather prediction, as well as for CAT scans and oil rigs. He modestly said: “It is typical of mathematics that its ideas are very generally applicable.” He praised the Courant Institute’s supportive atmosphere and published a paper in 1956 with its founder, Richard Courant, his former thesis advisor, on how signals propagate.

Mr. Lax recalled the sense of humor of another teacher, Fritz John, who reputedly said, “What is the reward of mathematicians? The grudging admiration of a few friends.”

The Abel Prize, Mr. Lax said, shows that there are other rewards.

The call informing Mr. Lax that he had won the prize came at 5:30 a.m. He was asked if it had awoken him. It had. “It was a Norwegian accent, so I thought it was probably true,” he said.

Mr. Lax won the Wolf Prize in 1987 and the Chauvenet Prize in 1974, among other awards. President Reagan presented him the National Medal of Science in 1986. He has been president of the American Mathematical Society and directed the Courant Institute from 1972 to 1980. His late wife, an important leader in American college mathematics teaching, also taught at NYU. One son is a doctor; the other, who was working toward a Ph.D. at Columbia in history, was killed by a drunk driver.

Mr. Lax is currently working on a second edition of his book “Linear Algebra” (Wiley-InterScience) to make it more “user-friendly.”

“All of us who have admired his work are pleased that he has gotten this recognition,” said Ed Witten of the Institute for Advanced Study at Princeton, whose own research has utilized “Lax pairs” (named for Mr. Lax), by which integrable or soluble nonlinear equations are understood.

“Since his father was still playing tennis and had a girlfriend in his late 90s,” Mr. Cappell said, “we expect Lax to continue to earn awards.”