Peter Lax, an innovator in applied mathematics who left Hungary during World War II and worked on U.S. atomic bomb calculations as a college student while developing equations that would later influence fields such as medicine and weather forecasting, died May 16 at his home in Manhattan. He was 99.

The death was announced by the Norwegian Academy of Science and Letters, which in 2005 awarded Dr. Lax the Abel Prize, often called one of the mathematics equivalents of the Nobel Prize. No cause was given.

A mathematics prodigy, Dr. Lax began as a teenager to seek ways to express in numeric terms the movements of the natural world such as how a shock wave dissipates or how a ripple travels down a narrow canal. His equations to convey physical properties — including fluid and wave dynamics — helped provided a foundation for the age of computer modeling in engineering and science.

“I like to start with some phenomenon, the more striking the better, and then use mathematics to try to understand it,” he told the Simons Foundation, a private research group, in 2014.

His breakthroughs in translating aspects of physics into mathematical structure led to some of the most productive early interplays of human imagination and computing power. Dr. Lax used early mainframe systems to run his math through complex variations simulating the real world.

Dr. Lax — who spent nearly his entire career at the Courant Institute of Mathematical Sciences at New York University — once described the influence of computers in mathematics as profound as “the role of telescopes in astronomy and microscopes in biology.”

Over the decades, Dr. Lax’s legacy was reflected in numerous scientific advances such as magnetic resonance imaging, or MRI, building on his equations on electromagnetic wave behavior. Some of the first iterations of computer-aided weather forecasting used algorithms inspired by Dr. Lax’s formulations on atmospheric systems. In aviation, Dr. Lax’s work allowed for more precise computer models of aerodynamics to test wing design. For oil drillers, his mathematical equations on fluid movement enhanced techniques to pump from deep reservoirs.

“Mathematics is a very broad subject,” he told the New York Times in 2005. “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.”

As a member of the National Science Board in the 1980s, Dr. Lax also helped reshape American research by appealing for wider access to supercomputers, which at the time were mostly available to the military and major tech companies. A 1982 study, widely known as the Lax Report, helped open greater academic use of U.S.-based supercomputers and spur significance growth in computational research.

Dr. Lax often said he was most interested in seeing a practical outcome for mathematics, citing as his early influence his New York University mentor, mathematician Richard Courant. “He would be more interested in creating a new mathematical theory of traffic control than in finding a more elegant solution to some old problem,’‘ Dr. Lax said in 1983.

During World War II, Dr. Lax was a 19-year-old draftee just out of basic training — and only four years removed from his arrival in New York with his parents after fleeing Nazi-allied Hungary — when he was reassigned. He was sent into the New Mexico desert in the summer of 1945 for the final stages of the Manhattan Project, the secret effort to design and test a possible atomic bomb.

As an undergraduate at New York University, he was seen as a rising star in mathematics — publishing his first paper at 18 and working on equations tracking the motions of sound, light, fluids and electromagnetic waves.

At the Los Alamos compound of the Manhattan Project, he was part of a group tasked with calculating the shock waves needed to trigger the bomb’s nuclear chain reaction and devastating explosive power. At one point, Cpl. Lax worked alongside Nobel laureate physicist Enrico Fermi. (He also recalled that he beat Fermi in tennis.)

“The first time I spent in Los Alamos, and especially the later exposure, shaped my mathematical thinking,” Dr. Lax later said. “First of all, it was the experience of being part of a scientific team — not just of mathematicians, but people with different outlooks — with the aim being, not a theorem, but a product.”

For the rest of his life, however, he would try to justify the consequences of that “product” — bombs that obliterated Hiroshima and Nagasaki and claimed more than 150,000 lives. He contended that the horror of the attacks showed that they can never happen again.

“The world was inoculated against using nuclear weaponry by its use,” he was quoted as saying in the 2014 biography “Peter Lax, Mathematician” by scholar Reuben Hersh. “I’m not saying that justified it and it certainly was not the justification of its use. But I think that is a historical fact.”

Peter David Lax was born May 1, 1926, in Budapest. His parents, both doctors, arranged for Peter to have special tutoring by Rózsa Péter, a prominent mathematician who introduced him to a wider circle of academics and intellectuals in the city’s Jewish community.

In 1941, when Peter was 15, his parents decided to flee Hungary as antisemitism raged among Germany’s supporters in Budapest and fears of roundups gripped Hungarian Jews. “And so,” he recalled, “we went by train across Europe, through Germany in train compartments filled with Wehrmacht troops.”

The Lax family boarded a ship in Lisbon bound for New York in early December 1941. Two days later, while the vessel was at sea, Japanese warplanes bombed Pearl Harbor, bringing the United States into the war.

When they arrived in New York, Peter’s parents contacted a relative, Gabor Szegö, who was chairman of the math department at Stanford University. He suggested that Peter continue his studies under Courant, founder of the mathematics center at NYU.

After the war, Dr. Lax returned to NYU to complete his undergraduate degree and, in 1949, received his doctorate in applied mathematics. He was appointed assistant professor that year. Dr. Lax was called back to Los Alamos to help with the development of hydrogen bombs as the Cold War arms race began.

He became a full professor at NYU in 1958. His many awards include the National Medal of Science in 1986, presented by President Ronald Reagan at a White House ceremony.

In 1948, he married fellow mathematician Anneli Cahn, who died in 1999. Their son John Lax was killed by a drunk driver in 1978. Dr. Lax then married Lori Berkowitz, a principal violist at the American Symphony Orchestra. She died in 2015.

Survivors include a son; two stepchildren from his second marriage; three grandchildren; and two great-grandchildren.

In 1970, a group of NYU students protesting the Vietnam War occupied the Courant Institute’s computer room housing the CDC 6600 mainframe, which was worth about $2 million at the time. “Today, $1,000 would buy more computing power,” Dr. Lax said.

The protesters left after a 48-hour standoff, and Dr. Lax and colleagues peered through a window to check the damage. They saw a crude, but potentially disastrous, contraption left behind: lit fuses made of rolled up toilet paper connected to canisters with potentially flammable liquid.

Dr. Lax and the others raced in to grab the canisters.

“When I finally got home and told my wife, she said: ‘Are you crazy? There were bombs in the computer, and you rushed in?’” Dr. Lax recalled. “I said, ‘I was so angry. I wanted to save the computer.’”