Stanisław Ulam

Stanisław Marcin Ulam was born in Lemberg, Galicia, on 13 April 1909. At this time, Galicia was in the Kingdom of Galicia and Lodomeria of the Austro-Hungarian Empire, which was known to Poles as the Austrian partition. In 1918, it became part of the newly restored Poland, the Second Polish Republic, and the city took its Polish name again, Lwów. From 1931 until 1935, he traveled to and studied in Wilno (Vilnius), Vienna, Zürich, Paris, and Cambridge, England, where he met G. H. Hardy and Subrahmanyan Chandrasekhar. Along with Stanisław Mazur, Mark Kac, Włodzimierz Stożek, Kuratowski, and others, Ulam was a member of the Lwów School of Mathematics. Its founders were Hugo Steinhaus and Stefan Banach, who were professors at the Jan Kazimierz University. Mathematicians of this "school" met for long hours at the Scottish Café, where the problems they discussed were collected in the Scottish Book, a thick notebook provided by Banach's wife. Ulam was a major contributor to the book. Of the 193 problems recorded between 1935 and 1941, he contributed 40 problems as a single author, another 11 with Banach and Mazur, and an additional 15 with others. In 1957, he received from Steinhaus a copy of the book, which had survived the war, and translated it into English. In 1981, Ulam's friend R. Daniel Mauldin published an expanded and annotated version. ==Move to the United States==

In 1935, John von Neumann, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study in Princeton, New Jersey, for a few months. In December of that year, Ulam sailed to the US. At Princeton, he went to lectures and seminars, where he heard Oswald Veblen, James Alexander, and Albert Einstein. During a tea party at von Neumann's house, he encountered G. D. Birkhoff, who suggested that he apply for a position with the Harvard Society of Fellows. Following up on Birkhoff's suggestion, Ulam spent summers in Poland and academic years at Harvard University in Cambridge, Massachusetts from 1936 to 1939, where he worked with John C. Oxtoby to establish results regarding ergodic theory. These appeared in Annals of Mathematics in 1941. On 20 August 1939, in Gdynia, Józef Ulam, along with his brother Szymon, put his two sons, Stanislaw and 17-year-old Adam, on a ship headed for the US. Eleven days later, the Germans invaded Poland. Within two months, the Germans completed their occupation of western Poland, and the Soviets invaded and occupied eastern Poland. Within two years, Józef Ulam and the rest of his family, including Stanislaw's sister Stefania Ulam, were victims of the Holocaust, Hugo Steinhaus was in hiding, Kazimierz Kuratowski was lecturing at the underground university in Warsaw, Włodzimierz Stożek and his two sons had been killed in the massacre of Lwów professors, and the last problem had been recorded in the Scottish Book. Stefan Banach survived the Nazi occupation by feeding lice at Rudolf Weigl's typhus research institute. In 1963, Adam Ulam, who had become an eminent kremlinologist at Harvard, received a letter from George Volsky, who hid in Józef Ulam's house after deserting from the Polish army. This reminiscence gave a chilling account of Lwów's chaotic scenes in late 1939. In later life Ulam described himself as "an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate". In 1940, after being recommended by Birkhoff, Ulam became an assistant professor at the University of Wisconsin–Madison. Here, he became a United States citizen in 1941. That year, he married Françoise Aron. She had been a French exchange student at Mount Holyoke College, whom he met in Cambridge. They had one daughter, Claire. In Madison, Ulam met his friend and colleague C. J. Everett, with whom he collaborated on a number of papers. ==Manhattan Project==

|alt=A mug shot style ID photo, with the serial H 0 In early 1943, Ulam asked von Neumann to find him a war job. In October, he received an invitation to join an unidentified project near Santa Fe, New Mexico. The letter was signed by Hans Bethe, who had been appointed as leader of the theoretical division of Los Alamos National Laboratory by Robert Oppenheimer, its scientific director. Knowing nothing of the area, he borrowed a New Mexico guide book. On the checkout card, he found the names of his Wisconsin colleagues, Joan Hinton, David Frisch, and Joseph McKibben, all of whom had mysteriously disappeared. This was Ulam's introduction to the Manhattan Project, which was the US's wartime effort to create the atomic bomb. Hydrodynamical calculations of implosion A few weeks after Ulam reached Los Alamos in February 1944, the project experienced a crisis. In April, Emilio Segrè discovered that plutonium made in reactors would not work in a gun-type plutonium weapon like the "Thin Man", which was being developed in parallel with a uranium weapon, the "Little Boy" that was dropped on Hiroshima. This problem threatened to waste an enormous investment in new reactors at the Hanford site and to make slow uranium isotope separation the only way to prepare fissile material suitable for use in bombs. To respond, Oppenheimer implemented, in August, a sweeping reorganization of the laboratory to focus on development of an implosion-type weapon and appointed George Kistiakowsky head of the implosion department. He was a professor at Harvard and an expert on precise use of explosives. The basic concept of implosion is to use chemical explosives to crush a chunk of fissile material into a critical mass, where neutron multiplication leads to a nuclear chain reaction, releasing a large amount of energy. Cylindrical implosive configurations had been studied by Seth Neddermeyer, but von Neumann, who had experience with shaped charges used in armor-piercing ammunition, was a vocal advocate of spherical implosion driven by explosive lenses. He realized that the symmetry and speed with which implosion compressed the plutonium were critical issues, and enlisted Ulam to help design lens configurations that would provide nearly spherical implosion. Within an implosion, because of enormous pressures and high temperatures, solid materials behave much like fluids. This meant that hydrodynamical calculations were needed to predict and minimize asymmetries that would spoil a nuclear detonation. Of these calculations, Ulam said: Nevertheless, with the primitive facilities available at the time, Ulam and von Neumann did carry out numerical computations that led to a satisfactory design. This motivated their advocacy of a powerful computational capability at Los Alamos, which began during the war years, continued through the cold war, and still exists. Otto Frisch remembered Ulam as "a brilliant Polish topologist with a charming French wife. At once he told me that he was a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points!" Statistics of branching and multiplicative processes Even the inherent statistical fluctuations of neutron multiplication within a chain reaction have implications with regard to implosion speed and symmetry. In November 1944, David Hawkins and Ulam addressed this problem in a report entitled "Theory of Multiplicative Processes". This report, which invokes probability-generating functions, is also an early entry in the extensive literature on statistics of branching and multiplicative processes. In 1948, its scope was extended by Ulam and Everett. Early in the Manhattan project, Enrico Fermi's attention was focused on the use of reactors to produce plutonium. In September 1944, he arrived at Los Alamos, shortly after breathing life into the first Hanford reactor, which had been poisoned by a xenon isotope. Soon after Fermi's arrival, Teller's "Super" bomb group, of which Ulam was a part, was transferred to a new division headed by Fermi. Fermi and Ulam formed a relationship that became very fruitful after the war. ==Post-war Los Alamos==

In September 1945, Ulam left Los Alamos to become an associate professor at the University of Southern California in Los Angeles. In January 1946, he suffered an acute attack of encephalitis, which put his life in danger, but which was alleviated by emergency brain surgery. During his recuperation, many friends visited, including Nicholas Metropolis from Los Alamos and the famous mathematician Paul Erdős, Fermi proposed to add to this force a nonlinear component, which could be chosen to be proportional to either the square or cube of the displacement, or to a more complicated "broken linear" function. This addition is the key element of the Fermi–Pasta–Ulam–Tsingou problem, which is often designated by the abbreviation FPUT. A classical spring system can be described in terms of vibrational modes, which are analogous to the harmonics that occur on a stretched violin string. If the system starts in a particular mode, vibrations in other modes do not develop. With the nonlinear component, Fermi expected energy in one mode to transfer gradually to other modes, and eventually, to be distributed equally among all modes. This is roughly what began to happen shortly after the system was initialized with all its energy in the lowest mode, but much later, essentially all the energy periodically reappeared in the lowest mode. This behavior is very different from the expected equipartition of energy. It remained mysterious until 1965, when Kruskal and Zabusky showed that, after appropriate mathematical transformations, the system can be described by the Korteweg–de Vries equation, which is the prototype of nonlinear partial differential equations that have soliton solutions. This means that FPUT behavior can be understood in terms of solitons. Nuclear propulsion Starting in 1955, Ulam and Frederick Reines considered nuclear propulsion of aircraft and rockets. This is an attractive possibility, because the nuclear energy per unit mass of fuel is a million times greater than that available from chemicals. From 1955 to 1972, their ideas were pursued during Project Rover, which explored the use of nuclear reactors to power rockets. In response to a question by Senator John O. Pastore at a congressional committee hearing on "Outer Space Propulsion by Nuclear Energy", on January 22, 1958, Ulam replied that "the future as a whole of mankind is to some extent involved inexorably now with going outside the globe." Ulam and C. J. Everett also proposed, in contrast to Rover's continuous heating of rocket exhaust, to harness small nuclear explosions for propulsion. Project Orion was a study of this idea. It began in 1958 and ended in 1965, after the Partial Nuclear Test Ban Treaty of 1963 banned nuclear weapons tests in the atmosphere and in space. Work on this project was spearheaded by physicist Freeman Dyson, who commented on the decision to end Orion in his article, "Death of a Project". Bradbury appointed Ulam and John H. Manley as research advisors to the laboratory director in 1957. These newly created positions were on the same administrative level as division leaders, and Ulam held his until he retired from Los Alamos. In this capacity, he was able to influence and guide programs in many divisions: theoretical, physics, chemistry, metallurgy, weapons, health, Rover, and others. In addition to these activities, Ulam continued to publish technical reports and research papers. One of these introduced the Fermi–Ulam model, an extension of Fermi's theory of the acceleration of cosmic rays. Another, with Paul Stein and Mary Tsingou, titled "Quadratic Transformations", was an early investigation of chaos theory and is considered the first published use of the phrase "chaotic behavior". ==Return to academia==

, prime numbers, represented by dots, tend to collect along diagonal lines.|alt=A lot of dots, but forming diagonal lines During his years at Los Alamos, Ulam was a visiting professor at Harvard from 1951 to 1952, MIT from 1956 to 1957, the University of California, San Diego, in 1963, and the University of Colorado at Boulder from 1961 to 1962 and 1965 to 1967. In 1967, the last of these positions became permanent, when Ulam was appointed Professor and Chairman of the Department of Mathematics at the University of Colorado. He kept a residence in Santa Fe, which made it convenient to spend summers at Los Alamos as a consultant. In Colorado, where he rejoined his friends Gamow, Richtmyer, and Hawkins, Ulam's research interests turned toward biology. In 1968, recognizing this emphasis, the University of Colorado School of Medicine appointed Ulam as Professor of Biomathematics, and he held this position until his death. With his Los Alamos colleague Robert Schrandt he published a report, "Some Elementary Attempts at Numerical Modeling of Problems Concerning Rates of Evolutionary Processes", which applied his earlier ideas on branching processes to evolution. Except for sabbaticals at the University of California, Davis from 1982 to 1983, and at Rockefeller University from 1980 to 1984, this pattern of spending summers in Colorado and Los Alamos and winters in Florida continued until Ulam died of an apparent heart attack in Santa Fe on 13 May 1984. Paul Erdős noted that "he died suddenly of heart failure, without fear or pain, while he could still prove and conjecture." In 1987, Françoise Ulam deposited his papers with the American Philosophical Society Library in Philadelphia. She continued to live in Santa Fe until she died in 2011, at the age of 93. Both Françoise and her husband were buried with her family in Montparnasse Cemetery in Paris. ==Coining of the term "singularity"==

Ulam reported in 1958 an earlier discussion with John von Neumann "centered on the accelerating progress of technology and changes in human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue". ==Impact and legacy==

Ulam participated in the creation of a hydrogen bomb as part of the Los Alamos Laboratory nuclear project. From the publication of his first paper as a student in 1929 until his death, Ulam was constantly writing on mathematics. The list of Ulam's publications includes more than 150 papers. The Monte Carlo method has become a ubiquitous and standard approach to computation, and the method has been applied to a vast number of scientific problems. In 2021, German film director Thorsten Klein made a film adaptation of Ulam's autobiography, Adventures of a Mathematician. In 2019, Polish entomologist Marcin Kamiński introduced the generic name Ulamus to honor Ulam's work. Ulamus belongs to the molluscan family Pteriidae. ==Bibliography==