logo
Peter Lax, preeminent Cold War mathematician, dies at 99

Peter Lax, preeminent Cold War mathematician, dies at 99

Boston Globe17-05-2025

Advertisement
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 prize 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.
Get Starting Point
A guide through the most important stories of the morning, delivered Monday through Friday.
Enter Email
Sign Up
Mr. 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, New Mexico, 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.
Advertisement
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, Mr. 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, Hungary, 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 renowned mathematician Rósza Péter, a founder of recursion theory, a branch of logic that investigates which mathematical problems can be resolved by computation. Péter connected him to her community of Hungarian Jewish mathematicians, many of whom made significant contributions to midcentury mathematics.
Mr. Lax was a young teenager when he demonstrated his early promise. At 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, Mr. Lax and his family fled the country, obtaining passage to the United States with the help of the U.S. consul in Budapest, a patient and friend of Henry Lax's. The family arrived as refugees in New York, where Peter Lax, by then a 15-year-old prodigy, came under the wing of other Hungarian mathematicians, who connected him to German emigre mathematician Richard Courant. At the time, Courant was blazing a new direction for applied mathematics and laying the foundation for the institute at NYU that would later bear his name.
Advertisement
Mr. Lax's father became Courant's physician, while Courant mentored Mr. Lax in mathematics.
At 18, having already published his first math paper, Mr. Lax 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 NYU 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 NYU in 1958.
The connections that Mr. 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 Mr. Lax and several of his NYU 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.
Advertisement
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, Mr. 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 Courant wrote in 1962, Mr. Lax embodied 'the unity of abstract mathematical analysis with the most concrete power in solving individual problems.'
Mr. 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, Mr. 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, Mr. 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.
Advertisement
Starting in 1963, Mr. 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 1977-80.
From 1980-86, Mr. 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 mathematician Anneli Cahn, a fellow doctoral student. After her death in 1999, he married Courant's daughter, Lori Berkowitz, the widow of another Courant Institute mathematician and principal violist for the American Symphony Orchestra. She died in 2015.
In addition to his son James, Mr. Lax is survived by his stepchildren, David and Susan Berkowitz; three grandchildren; and two great-grandchildren. Another son, John, was killed by a drunken driver in 1978.
Mr. Lax's 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.'
Advertisement
This article originally appeared in

Orange background

Try Our AI Features

Explore what Daily8 AI can do for you:

Comments

No comments yet...

Related Articles

Los Alamos Historical Society hopes to turn Oppenheimer House into museum, tourist site
Los Alamos Historical Society hopes to turn Oppenheimer House into museum, tourist site

Yahoo

time14 hours ago

  • Yahoo

Los Alamos Historical Society hopes to turn Oppenheimer House into museum, tourist site

The Los Alamos home where Manhattan Project scientific director J. Robert Oppenheimer lived with his family during World War II has never been open to the public. That will change soon if a fundraising campaign being mounted by the Los Alamos Historical Society is successful. The nonprofit is seeking to raise $5 million to renovate and restore the Oppenheimer House, create some exhibits and programming related to the time the famed scientist spent in Los Alamos, and integrate the home into the Los Alamos History Museum campus. A little less than $2 million has been raised already, said Todd Nickols, the executive director of the historical society. That leaves approximately $3 million to be generated through the campaign that will begin this fall. Nickols said getting the house — which he described as a jewel of Los Alamos history — restored to the point that it could be opened to public tours is the focus of the fundraising drive. But that will be easier said than done. The historical society did not take possession of the home until 2020, three-quarters of a century after the Oppenheimer family moved out, and the organization will face many challenges in restoring it, Nickols said. 'It was in pretty bad shape,' he said. The owners who turned the home over to the historical society, Helene and Bergen 'Jerry' Suydam, had done what they could to care for the property, he said. But the Suydams were challenged by their own health issues, he said, and that diverted their attention from maintaining the house. Job one: Build a foundation The job of restoring the home already has begun with work on the roof. But the bigger task will be shoring up the underside of the house. Nickols said the Oppenheimer House was not built on a foundation; its main joists sit directly on the ground. As a result, it has slid approximately 2 feet south-southeast since it was built in 1929 as part of the Los Alamos Ranch School. Plans call for building a foundation under the house, something that will have to be accomplished by removing the wood flooring to accommodate the pouring of concrete for helical piers, Nickols said. 'We have to go from inside [the house],' he said. 'There's no crawl space.' A good deal of surveying and soil testing will be done first, he said, but those time-consuming steps are a necessary part of the process. 'We have a one-time shot to do this correct,' he said. 'So it's better to take the extra time to do it well.' The foundation work also will be very costly, he said, eating up a significant amount of the project's $5 million price tag. 'It's crazy expensive,' he said. 'That's just how it goes.' Other work on the house will include asbestos abatement, repainting of exterior and interior walls, tree removal, plumbing improvements, a new electrical system, a fire suppression system and making it accessible to people with disabilities. Movie spurs Oppenheimer interest Nickols said it would have been nice to have the project done before director Christopher Nolan and his crew showed up in Los Alamos in 2022 to film his Oppenheimer biopic, the 2024 Academy Award winner for Best Picture. Many scenes from the movie were shot at the Oppenheimer House, and Nickols said Nolan and his crew could not have been better to work with. The famed director himself remarked on how Oppenheimer's essence seemed to linger in the house, Nickols said. He credited the film with igniting interest in the house. 'What it really did for us was it brought visitors and put us back on the map,' Nickols said. The Los Alamos History Museum doubled its annual visitation in the wake of the release of Oppenheimer. The filming of Oppenheimer in the place where so many of its historic events unfolded contributed its own chapter to the city's legacy, he said. 'That filming is part of our history,' Nickols said. It also caused interest in Oppenheimer himself to surge among people younger than 30, he said — something that has led historical society officials to cater to that crowd specifically in their planning for the exhibits at the house. 'This is where it's going to get fun,' Nickols said, adding the exhibits will include reliance on the latest technology, including artificial intelligence. 'I have a personal goal of having a hologram or a robot that looks like Oppenheimer welcoming people to the house.' When the project is done, the house will not feature many artifacts from Oppenheimer or his family, Nickols said, for one simple reason: The ultra-high secrecy surrounding the Manhattan Project meant the people who worked on it essentially were allowed to bring only their clothes with them to Los Alamos. 'You were brought into the Lamy train station, and all your possessions were dumped out of your luggage, and they threw away your bags,' Nickols said, explaining government officials feared some of the luggage might have been outfitted with clandestine surveillance devices. 'You were not allowed to take much of anything with you.' That same veil of secrecy means there are not many photos of Oppenheimer in Los Alamos. But there are several photos of the house dating back to its time before Oppenheimer occupied it and after the Atomic Energy Commission vacated it in the mid-1960s, he said. 'So we have evidence to know what changes had been made to it, and our goal is to put it back together to [what it looked like] when Oppenheimer was there.' Preservation fund Nickols said the society also hopes to raise $1 million for a preservation fund devoted to the home's future maintenance needs. Partnering with the historical society on the project is Enterprise Bank & Trust, which has pledged to match donations up to $500,000 by contributing up to $125,000 annually for four years. The first matching gift will be presented in January 2026, a news release touting the fundraising campaign said. Nickols noted the decadeslong relationship between the bank and the historical society and said Enterprise's contributions will help his organization transform the home into 'a powerful and immersive educational experience for visitors from around the world.'

How game theory explains vaccination rates and parents' choices
How game theory explains vaccination rates and parents' choices

Fast Company

timea day ago

  • Fast Company

How game theory explains vaccination rates and parents' choices

When outbreaks of vaccine-preventable diseases such as measles occur despite highly effective vaccines being available, it's easy to conclude that parents who don't vaccinate their children are misguided, selfish, or have fallen prey to misinformation. As professors with expertise in vaccine policy and health economics, we argue that the decision not to vaccinate isn't simply about misinformation or hesitancy. In our view, it involves game theory, a mathematical framework that helps explain how reasonable people can make choices that collectively lead to outcomes that endanger them. Game theory reveals that vaccine hesitancy is not a moral failure, but simply the predictable outcome of a system in which individual and collective incentives aren't properly aligned. Game theory meets vaccines Game theory examines how people make decisions when their outcomes depend on what others choose. In his research on the topic, Nobel Prize-winning mathematician John Nash, portrayed in the movie A Beautiful Mind, showed that in many situations, individually rational choices don't automatically create the best outcome for everyone. Vaccination decisions perfectly illustrate this principle. When a parent decides whether to vaccinate their child against measles, for instance, they weigh the small risk of vaccine side effects against the risks posed by the disease. But here's the crucial insight: The risk of disease depends on what other parents decide. If nearly everyone vaccinates, herd immunity —essentially, vaccinating enough people—will stop the disease's spread. But once herd immunity is achieved, individual parents may decide that not vaccinating is the less risky option for their kid. In other words, because of a fundamental tension between individual choice and collective welfare, relying solely on individual choice may not achieve public health goals. This makes vaccine decisions fundamentally different from most other health decisions. When you decide whether to take medication for high blood pressure, your outcome depends only on your choice. But with vaccines, everyone is connected. This interconnectedness has played out dramatically in Texas, where the largest U.S. measles outbreak in a decade originated. As vaccination rates dropped in certain communities, the disease—once declared eliminated in the U.S.—returned. One county's vaccination rate fell from 96% to 81% over just five years. Considering that about 95% of people in a community must be vaccinated to achieve herd immunity, the decline created perfect conditions for the current outbreak. This isn't coincidence; it's game theory playing out in real time. When vaccination rates are high, not vaccinating seems rational for each individual family, but when enough families make this choice, collective protection collapses. The free-rider problem This dynamic creates what economists call a free-rider problem. When vaccination rates are high, an individual might benefit from herd immunity without accepting even the minimal vaccine risks. Game theory predicts something surprising: Even with a hypothetically perfect vaccine—faultless efficacy, zero side effects—voluntary vaccination programs will never achieve 100% coverage. Once coverage is high enough, some rational individuals will always choose to be free riders, benefiting from the herd immunity provided by others. And when rates drop, as they have, dramatically, over the past five years, disease models predict exactly what we're seeing: the return of outbreaks. Game theory reveals another pattern: For highly contagious diseases, vaccination rates tend to decline rapidly following safety concerns, while recovery occurs much more slowly. This, too, is a mathematical property of the system because decline and recovery have different incentive structures. When safety concerns arise, many parents get worried at the same time and stop vaccinating, causing vaccination rates to drop quickly. But recovery is slower because it requires both rebuilding trust and overcoming the free-rider problem—each parent waits for others to vaccinate first. Small changes in perception can cause large shifts in behavior. Media coverage, social networks, and health messaging all influence these perceptions, potentially moving communities toward or away from these critical thresholds. Mathematics also predicts how people's decisions about vaccination can cluster. As parents observe others' choices, local norms develop, so the more parents skip the vaccine in a community, the more others are likely to follow suit. Game theorists refer to the resulting pockets of low vaccine uptake as susceptibility clusters. These clusters allow diseases to persist even when overall vaccination rates appear adequate. A 95% statewide or national average could mean uniform vaccine coverage, which would prevent outbreaks. Alternatively, it could mean some areas with near-100% coverage and others with dangerously low rates that enable local outbreaks. Not a moral failure All this means that the dramatic fall in vaccination rates was predicted by game theory, and therefore more a reflection of system vulnerability than of a moral failure of individuals. What's more, blaming parents for making selfish choices can also backfire by making them more defensive and less likely to reconsider their views. Much more helpful would be approaches that acknowledge the tensions between individual and collective interests and that work with, rather than against, the mental calculations informing how people make decisions in interconnected systems. Research shows that communities experiencing outbreaks respond differently to messaging that frames vaccination as a community problem versus messaging that implies moral failure. In a 2021 study of a community with falling vaccination rates, approaches that acknowledged parents' genuine concerns while emphasizing the need for community protection made parents 24% more likely to consider vaccinating, while approaches that emphasized personal responsibility or implied selfishness actually decreased their willingness to consider it. This confirms what game theory predicts: When people feel their decision-making is under moral attack, they often become more entrenched in their positions rather than more open to change. Better communication strategies Understanding how people weigh vaccine risks and benefits points to better approaches to communication. For example, clearly conveying risks can help: The 1-in-500 death rate from measles far outweighs the extraordinarily rare serious vaccine side effects. That may sound obvious, but it's often missing from public discussion. Also, different communities need different approaches: High-vaccination areas need help staying on track, while low-vaccination areas need trust rebuilt. Consistency matters tremendously. Research shows that when health experts give conflicting information or change their message, people become more suspicious and decide to hold off on vaccines. And dramatic scare tactics about disease can backfire by pushing people toward extreme positions. Making vaccination decisions visible within communities—through community discussions and school-level reporting, where possible—can help establish positive social norms. When parents understand that vaccination protects vulnerable community members, like infants too young for vaccines or people with medical conditions, it helps bridge the gap between individual and collective interests.

DOWNLOAD THE APP

Get Started Now: Download the App

Ready to dive into the world of global news and events? Download our app today from your preferred app store and start exploring.
app-storeplay-store