Stanisław Ulam in the context of "University of Wisconsin–Madison"

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers.

Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x − x + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has ever been proved to generate infinitely many primes, much less to have a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be.

The Lwów school of mathematics (Polish: Lwowska szkoła matematyczna) was a group of Polish mathematicians who worked in the interwar period in Lwów, Poland (since 1945 Lviv, Ukraine). The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the journal Studia Mathematica, founded in 1929. The school was renowned for its productivity and its extensive contributions to subjects such as point-set topology, set theory and functional analysis.

The Teller–Ulam design is the technical concept behind thermonuclear weapons, also known as hydrogen bombs. The design relies on the radiation implosion principle, using thermal X-rays released from a fission nuclear primary to compress and ignite nuclear fusion in a secondary. This is in contrast to the simpler design and usage of nuclear fusion in boosted fission weapons.

The design is named for scientists Edward Teller and Stanisław Ulam, who originally devised the concept in January 1951 for the United States nuclear weapons program, though their individual roles have been subsequently debated. The US Greenhouse George test in May 1951, the world's first artificial thermonuclear fusion, validated the radiation implosion principle. The US first tested the "true" Teller-Ulam design with the very high-yield Ivy Mike test in 1952. The design was independently devised and then tested by teams of nuclear weapons scientists working for at least four more governments: the Soviet Union in 1955 (RDS-37), the United Kingdom in 1957 (Operation Grapple), China in 1966 (Project 639), and France in 1968 (Canopus). There is not enough public information to determine whether India, Israel, or North Korea possess multi-stage weapons. Pakistan is not considered to have developed them. The Teller-Ulam design is the basis for all nuclear weapons tests above one megaton yield.

The Scottish Café (Polish: Kawiarnia Szkocka) was a café in Lwów, Poland (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in functional analysis and topology.

Stanisław Ulam recounts that the tables of the café had marble tops, so they could write in pencil, directly on the table, during their discussions. To keep the results from being lost, and after becoming annoyed with their writing directly on the table tops, Stefan Banach's wife provided the mathematicians with a large notebook, which was used for writing the problems and answers and eventually became known as the Scottish Book. The book—a collection of solved, unsolved, and even probably unsolvable problems—could be borrowed by any of the guests of the café. Solving any of the problems was rewarded with prizes, with the most difficult and challenging problems having expensive prizes (during the Great Depression and on the eve of World War II), such as a bottle of fine brandy.

Monte Carlo methods, (sometimes called Monte Carlo experiments or Monte Carlo simulations) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits.

Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically.

Nuclear pulse propulsion or external pulsed plasma propulsion is a hypothetical method of spacecraft propulsion that uses nuclear explosions for thrust. It originated as Project Orion with support from DARPA, after a suggestion by Stanisław Ulam in 1947. Newer designs using inertial confinement fusion have been the baseline for most later designs, including Project Daedalus and Project Longshot.

Edward Teller (Hungarian: Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist and chemical engineer who is known colloquially as "the father of the hydrogen bomb" and one of the creators of the Teller–Ulam design inspired by Stanisław Ulam. He had a volatile personality, and was "driven by his megaton ambitions, had a messianic complex, and displayed autocratic behavior." He devised a thermonuclear Alarm Clock bomb with a yield of 1000 MT (1 GT of TNT) and proposed delivering it by boat or submarine to incinerate a continent.

Born in Austria-Hungary in 1908, Teller emigrated to the US in the 1930s, one of the many so-called "Martians", a group of Hungarian scientist émigrés. He made numerous contributions to nuclear and molecular physics, spectroscopy, and surface physics. His extension of Enrico Fermi's theory of beta decay, in the form of Gamow–Teller transitions, provided an important stepping stone in its application, while the Jahn–Teller effect and Brunauer–Emmett–Teller (BET) theory have retained their original formulation and are mainstays in physics and chemistry. Teller analyzed his problems using basic principles of physics and often discussed with his cohorts to make headway through difficult problems. This was seen when he worked with Stanislaw Ulam to get a workable thermonuclear fusion bomb design, but later temperamentally dismissed Ulam's aid. Herbert York stated that Teller utilized Ulam's general idea of compressive heating to start thermonuclear fusion to generate his own sketch of a workable "Super" bomb. Before Ulam's idea, Teller's classical Super was essentially a system for heating uncompressed liquid deuterium to the point, Teller hoped, that it would sustain thermonuclear burning. It was, in essence, a simple idea from physical principles, which Teller pursued with a ferocious tenacity, even if he was wrong and shown that it would not work. To get support from Washington for his Super weapon project, Teller proposed a thermonuclear radiation implosion experiment as the "George" shot of Operation Greenhouse.