From the University of Wisconsin to Los Alamos

Mathematician Stanislaw Ulam taught in Madison before making a key contribution to nuclear science

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The story of Stanisław Ulam cannot be told without telling other stories: The story of Lviv, Ukraine, in the 1930s. The story of Madison in the early 1940s. The story of Los Alamos. And, depending on who you ask, the stories of several war criminals.

But let's start with Madison.

"The entire physical impression, the landscape, the lakes, the woods, the houses, and the size of the city were most agreeable," Ulam wrote in his 1976 autobiography, Adventures of a Mathematician, describing the community during World War II. "Living conditions were a pleasant surprise."

Ulam played a critical role in the creation of the implosion-type device used in the Trinity nuclear test, the first explosion of a nuclear device. The event happened 80 years ago today — July 16, 1945.

The test was the result of work Ulam and others did as part of the Manhattan Project at Los Alamos, New Mexico. The goal of the Manhattan Project, which was supervised by the American theoretical physicist J. Robert Oppenheimer, was the creation of nuclear weapons, which ultimately were used to end civilian lives in the Japanese cities of Hiroshima and Nagasaki.

Immediately before that, the Lviv-born mathematical wunderkind taught at UW-Madison from 1940 to 1943. He was promoted to the role of assistant professor before the start of his second year on campus.

Like many academics moving from the coasts to the Midwest at that time, he had a somewhat distorted view of the city before his migration from Boston, where he had for a period taught at Harvard University.

"I traveled to Madison by way of Chicago, where I changed to a smaller train that made several whistle stops, one at a town named Harvard," Ulam wrote. "The irony did not escape me, and I felt fate was playing a cruel joke on me."

Reality soon shifted his opinion. He mentioned that while living at UW-Madison's University Club, he enjoyed "meeting and taking meals with interesting colleagues."

"I found Madison not at all the intellectual desert I feared it would be," he wrote, encountering, instead, an academic community with "a tradition of excellence."

High standards

It's understandable that the scholar was picky about his surroundings. Ulam was first active mathematically at the Lviv mathematics school, a famous cafe society in what was then Poland. He was later affiliated with universities on the East Coast when Europe became too dangerous for Jews. He would also later teach in California and Colorado.

One of his most known impacts, however, came not in a university setting, but at Los Alamos National Laboratory, near Santa Fe, New Mexico, where his work on chain reactions was vital to the creation of the "gadget" used during the Trinity Test, and the devices used to bomb Nagasaki and run trial explosions at at various hydrogen bomb test sites.

According to William G. Mathews and Daniel O. Hirsch, who wrote the preface to the 1991 edition of Ulam's autobiography, during the waning days of World War II, Ulam focused his Los Alamos work on statistical studies of branching and multiplication of neutrons responsible for starting and maintaining a chain reaction. Mathews and Hirsch detail how for a period, Ulam's work on fission reactions was so secretive that even the word "implosion" was classified.

"But Ulam's most remarkable achievement at Los Alamos," Mathews and Hirsch wrote, "was his contribution to the postwar development of the thermonuclear or hydrogen bomb in which nuclear energy is released when two hydrogen or deuterium nuclei fuse together."

Ulam successfully suggested a means of compressing deuterium sufficiently to allow both ignition and self-sustaining propagation of a fusion reaction in a hydrogen bomb.

The idea involved using a fission explosion to create the necessary compression, allowing fusion to take place. It's a concept most middle schoolers now learn, but at the time, it was revolutionary.

Handpicked by Ulam for a Los Alamos role, Cornelius Everett, a former UW-Madison researcher, also contributed enormously to the development of fusion-based weapons.

An auspicious start

Ulam's story starts an ocean away from Madison and Los Alamos. He grew up in what was then known as Lvov, Poland — it's now known as Lviv and sits in the western part of Ukraine — and was raised surrounded by resources and curiosity.

"He grew up in quite a rich family, and his dad was a lawyer," says Solomiia Kharambura in an April 28 interview at the Lviv Polytechnic National University, where Ulam was a student. Kharambura is a specialist in the history of the university.

"Of course, his dad really envisioned [Stanislaw's] future as a lawyer as well, but from a young age — of around 10 — he already started being more interested in mathematics, and he wanted to read some scientific papers about math, including some of the Einstein works, so then even his father agreed that maybe it was better for him to be a scientist, rather than a lawyer."

Ulam attended the Lviv Polytechnic National University, where he showed great advancement, being able to step in for his professor on at least one occasion to teach his undergraduate classmates.

Outside of the classroom, he was similarly brilliant, joining the informal Lviv school of mathematics, a group that met in cafes, writing their oddball problems in a volume that became known as the Scottish Book. Community members who found solutions to the problems were rewarded with specific prizes that could be cheap or expensive and, in many cases, surreal, ranging from a cup of black coffee to hundreds of litres of beer. A live goose was even awarded once in 1972.

The section of Ulam's autobiography covering the Lviv years is full of a sense of potential, but also an aching regret over what could have been, with multiple friends being described in loving detail, only for the phrase "murdered by the Nazis" to come up in one form or another.

It was no surprise, then, that Ulam soon fled to the United States on the urging of his friend and collaborator, John von Neumann.

"Von Neumann expressed great pessimism about the possibility of a war in Europe," Ulam wrote about his first visit with the computational pioneer in Princeton after arriving in New Jersey. "This was about three years before the actual outbreak."

On the East Coast, Ulam filled undercompensated roles at Princeton and Harvard where, despite interacting with some of the smartest people in the world, he found the environment somewhat stuffy, uncreative, stressful and limiting.

Then, looking for work, he accepted an offer to come to Madison. He would find no such limitations in Wisconsin.

A snapshot of American life

Ulam's portrait of Madison in the early 1940s is, to an extent, a freeze-dried cross section of United States culture at the time.

Three times in his autobiography, he mentions the importance of billiards, for example, writing that one new Madison friend, a professor of English literature, guided him through the game at the University Club.

"Henley was a good billiard player," Ulam stated. "He insisted on teaching me how to play, though he was rather appalled at my ineptitude. This, I found, is a very nice and very American trait — the desire to coach and instruct."

Likewise, Ulam enjoyed international contacts on the relatively cosmopolitan UW campus, including "Vassilief, a Russian émigré, a great expert on Byzantine history, and almost a character out of Vladimir Nabokov's book Pnin. At dinner he always ordered a second bowl of soup and would say to me, 'Americans are funny; even when the soup is excellent, they never think of ordering a second bowl.'" He is said to have carried and regularly imbibed from a pocket flask, which was not unusual for some foreign faculty members in that period.

According to Madison Public Library records, Ulam lived for part of his Madison period in Apartment 3 at 425 Hawthorne Court. It was during his time in Madison that he married his wife, Françoise Ulam, née Aron.

Ulam's story about another colorful UW faculty member, William Ellery Leonard, highlights how different the transportation landscape was at the time: Leonard, who wrote the book, The Locomotive God, was reputed among the faculty to have an intense, neurotic fear of trains, and in the 1940s, that was enough to warrant the rumor that his low salary "never was increased, because he would never leave anyway." Interstate 90 would not officially be christened until 1957, around 15 years later.

Another throwaway line in the autobiography gives a hint at darker things that were happening in American society, touching on the forced relocation of Japanese American people. "I went to [an Air Force] recruiting center not far from Madison for a physical examination," Ulam writes. "It was given by West Coast Japanese medics who had been relocated in this Middle Western camp."

Ulam's Air Force application was rejected because of his poor eyesight.

The intellectual atmosphere in Madison was "lively," Ulam wrote. "On the whole the professors did not put on airs as a few have at Harvard. On the contrary, perhaps in order to bear comparison with the famous older universities, they worked more energetically, but the 'oh, excuse me, I've got to get to work' syndrome was not as evident as at Harvard."

Similarly, Ulam noticed, the university was able to use its surroundings' physical beauty to its advantage, attracting higher-quality faculty members than some other nearby state universities while offering less pay. The mathematician joked that "every time we looked at the beautiful lake, it was costing us about two dollars."

Among the people Ulam met in Madison were the astronomer Joel Stebbins, who pioneered photoelectric photometry in astronomy, and the mathematician Everett, who would later collaborate with him on some of the most important discoveries in 1940s nuclear physics.

Everett, Ulam wrote, was "totally devoted to mathematics — they were his only interest. I found in him much that resembled my friend Mazur in Poland, the same kind of epigrammatic comments and jokes. Physically, they had a certain similarity, both being thin, bony, and less than medium height."

Ulam wrote that Everett complemented his tendency to have general, "sometimes only vague" ideas, supplying "the rigor, the ingenuities in the details of the proof, and the final constructions."

With this stimulating environment lodged in his memory, it was natural that Ulam chose to bring Everett to Los Alamos when he departed Madison in 1944. But the work in New Mexico — both before and after the end of the war — was not without controversy.

The bomb maker from Lviv

The cartoon on a page in the middle of Ulam's autobiography is as whimsical as it is terrifying. Drawings of Ulam, the Hungarian-American fusion expert Edward Teller and the Soviet-American theoretical physicist George Gamow sit in conversation along the bottom of the illustration, with the angelic figures of Joseph Stalin and J. Robert Oppenheimer looking down from above. Stalin, who is portrayed in bird-like form, holds a bomb in his talons.

The sketch shows just how tightly linked Ulam's work was with the larger goals Oppenheimer had laid out. And those larger goals are, increasingly, coming under intense scrutiny.

"Does Oppenheimer's responsibility extend to all the scientists (including Ulam) who worked on the Manhattan Project?," Seiji Yamada says in an email to Isthmus. "Personally, I think so."

Yamada has spent a lot of time thinking about Los Alamos. His father, a nuclear physicist who worked at Fermilab, near Chicago, was a Hiroshima survivor. In a 2023 essay, Yamada argues poignantly that Oppenheimer was a war criminal.

"Having grown up among physicists (and having at one time aspired to become one), I can understand how one can become so caught up in the scientific and technical aspects of one's work that one becomes unable to appreciate the larger contours of the project or its moral and ethical consequences," Yamada continues. "Such tunnel vision is not limited to scientists, of course. Robert McNamara's focus on the body count while he was secretary of defense during the U.S. invasion and occupation of Vietnam comes to mind."

Yamada's essay makes mention of a petition started in Chicago by Leó Szilárd before the first use of nuclear weapons. The petition was an attempt to allow nuclear scientists to voice their desire that any nuclear weapons be used solely against military targets, sparing civilians.

"My understanding is that his petition reached [U.S. military officer] Leslie Groves, who locked it in a safe and thereby kept it from circulating any further and from being released to any higher authorities," Yamada says. The decision by Groves likely contributed to the loss of at least 100,000 lives in Japan.

And that is where things start to get a little complicated. When pressed about whether the attack on Nagasaki — which used Ulam's technology, unlike the Hiroshima attack, which relied on a “gun-barrel”-type device — was a war crime, Tine Molendijk, an associate professor at the Netherlands Defence Academy, said in an email to Isthmus that some people have argued "that it brought a swifter end to the war and thereby reduced overall casualties."

The core divisive issue, Molendijk said, is "whether the use of the atomic bomb was necessary to secure victory in the Pacific, and more generally whether it was proportionate. Japan was already weakened by August 1945, and Nagasaki occurred only days after Hiroshima, with little time for Japan to respond."

The Trinity test, he says, as an experimental detonation, did not constitute an act of war in itself, but was rather "a step in the development of a weapon. The bombing of Nagasaki, however, directly involved civilian casualties. From the standpoint of just war theory, this raises profound moral concerns, even if it is not immediately or obviously classifiable as immoral."

There is no doubt that Ulam continued enthusiastically working on hydrogen bomb designs, long after it became clear that such bombs were likely to be used against civilian population centers.

That said, Molendijk says that "creating a weapon is not morally equivalent to using it."

Modeling the world

Ulam's work after 1945 was not restricted to military devices. A strong proponent of the idea of nuclear powered space travel, he may be best known today for his popularization of Monte Carlo simulations, a profoundly useful way of modeling the outcomes of natural processes.

In a Monte Carlo simulation, the behavior of a natural system is learned about by feeding random or pseudorandom values into the system, then seeing what comes out the other end.

Such modeling represents "a powerful application of the Monte Carlo method, particularly in physics-related problems," says David Sarrut of the Center for Research in Image Acquisition and Processing for Health in Lyon, France, who published research on the technique.

"The core idea is to simulate the behavior of a vast number of individual particles (such as photons or electrons)” by sampling their trajectories and interactions to model complex physical effects that are difficult to predict through purely analytical means, adds Sarrut. That can yield applications in everything from climate change prediction to chemistry.

For his part, Yamada says that while he considers Manhattan Project physicists Arthur H. Compton, Enrico Fermi, Ernest O. Lawrence and J. Robert Oppenheimer to be war criminals, he does not want to paint with a broad brush.

"I consider members of the Manhattan Project who opposed the use of the weapons on civilians, such as Robert Rathbun Wilson and the signatories of Leó Szilárd's petition, not to be war criminals. I am ambivalent as to whether other members of the Manhattan Project should be considered war criminals," he wrote to Isthmus.

A University of Wisconsin spokesperson declined to comment on whether Ulam should now be considered a war criminal.

Ulam, as is clear from his autobiography, was a cheery but traumatized figure who wanted to help win a war for the side of the United States, a country that saved his life and fought against a regime that murdered many of his friends. And his life after moving to the U.S. is a mixed bag of horrors and wonders, partially directed toward that goal.

So what's the ratio of good to bad? Can anyone ever really know how many lives their own lives have touched? And is anyone fit to judge? Sarrut said that in the area of radiology alone, there's a strong argument to be made for Monte Carlo simulations having saved many people from death.

"To illustrate the societal impact, millions of patients are treated with radiation therapy systems (approximately 6 million annually)," he wrote. "And tens of millions of nuclear imaging exams are performed each year, with these critical technologies having been developed or significantly advanced through the use of Monte Carlo simulations."

Hurt people hurt people. And they sometimes help.

Patrick Maynard's portrait for Isthmus of former UW mathematician Stanisław Ulam was written from Ukraine and Germany. Some interview material for the piece was translated by Anna Gurynovych of the Lviv Polytechnic National University.