Stanisław Marcin Ulam

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File:Stanislaw Ulam.jpg
Stanisław Ulam in the 1950s.

Stanisław Marcin Ulam (April 13, 1909May 13, 1984) was a Polish mathematician who helped develop the Teller-Ulam design which powers the hydrogen bomb, as well as a number of other important mathematical tools.


Stanisław Ulam was born in Lviv (German: Lemberg; Polish: Lwów), Galicja, in Austria-Hungary, now in Ukraine. He was part of the city's Polish majority population. His mentor in mathematics was Stefan Banach, a great Polish mathematician and one of the moving spirits of the Lwów School of Mathematics and more broadly of the remarkable Interbellum Polish School of Mathematics.

Ulam went to the US in 1938 as a Harvard Junior Fellow. When his fellowship was not renewed, he served on the faculty at the University of Wisconsin, and supported his brother, Adam, who had fled from Poland on the eve of the Second World War. While there, in the midst of the war, his friend John von Neumann invited him to a secret project in New Mexico. Ulam researched the invitation by checking out a book on New Mexico from the university library. There he found a list, on the library check-out card, of all those who had successively disappeared from the campus at the UW. Ulam then joined the Manhattan Project at Los Alamos.

File:Stanislaw Ulam ID badge.png
Ulam's ID badge photo from Los Alamos.

While there, he suggested the Monte Carlo method for evaluating complicated mathematical integrals that arise in the theory of nuclear chain reactions (not knowing that Fermi and others had used a similar method earlier). This suggestion led to the more systematic development of Monte Carlo by Von Neumann, Metropolis, and others.

Ulam — in collaboration with C.J. Everett, who did the detailed calculations — showed Edward Teller's early model of the hydrogen bomb to be inadequate. Ulam then went on to suggest a better method. He was the first to realize that one could place all the H-bomb's components inside one casing, put a fission bomb at one end and thermonuclear material at the other, and use X-ray radiation from the fission bomb to compress and detonate fusion fuel.

Teller at first resisted this idea at, then saw its merit and suggested the use of a plutonium "spark plug," located at the center of the fusion fuel, to initiate and enhance the fusion reaction. This design, generally referred to as staged radiation implosion, has been the standard method of creating H-bombs ever since. Although this approach was worked out independently by Soviet physicist Andrei Sakharov, it is often refered to as the "Teller-Ulam design". Ulam and Teller jointly applied for a patent on the hydrogen bomb.

Ulam also invented nuclear pulse propulsion and, at the end of his life, declared it the invention of which he was proudest.

He was an early proponent of using computers to perform "mathematical experiments." His most notable contribution here may have been his part in the Fermi-Pasta-Ulam experiments, an early numerical study of a dynamic system.

In pure mathematics, he worked in set theory (including measurable cardinals and abstract measures), topology, ergodic theory, and other fields. After World War II he largely turned from rigorous pure mathematics to speculative and imaginative work, posing problems and making conjectures (which had always been specialties of his) that often concerned the application of mathematics to physics and biology. His friend Gian-Carlo Rota ascribed this change to an attack of encephalitis in 1946 that Rota claimed changed Ulam's personality (though detail had never been Ulam's strong point). This suggestion is believed by many but rejected by Ulam's widow, Françoise, among others.

In May 1958, while referring to a conversation with von Neumann, Ulam said what would later became a foundation of the technological singularity theory: "One conversation centered on the ever accelerating progress of technology and changes in the mode of 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."

Ulam took a position at the University of Colorado in 1965. As he remained a consultant at Los Alamos, he divided his time between Boulder, Colorado, USA and Santa Fe, New Mexico, from which he commuted to Los Alamos. Later he and his wife spent winters in Gainesville, Florida, where he had a position with the University of Florida. He died in Santa Fe on May 13, 1984.

Ulam's Theorem

Note to other people who will edit this: Please clean up the following and place it were appropriate. Ulam's Theorem states that any positive whole number can be decreased to one through a series of calculations. If the number is even, divide it by two. If the number is odd, multiply it by three and then add one. Eventually, this series of calculations will yield 1.
57. 1. 57*3+1 = 172 2. 172/2 = 86 3. 86/2 = 43 4. 43*3+1 = 130 5. 130/2 = 65 6. 65*3+1 = 196 7. 196/2 = 98 8. 98/2 = 49 9. 49*3+1 = 148 10. 148/2 = 74 11. 74/2 = 37 12. 37*3+1 = 112 13. 112/2 = 56 14. 56/2 = 28 15. 28/2 = 14 16. 14/2 = 7 17. 7*3+1 = 22 18. 22/2 = 11 19. 11*3+1 = 34 20. 34/2 = 17 21. 17*3+1 = 52 22. 52/2 = 26 23. 26/2 =13 24. 13*3+1 = 40 25. 40/2 = 20 26. 20/2 = 10 27. 10/2 = 5 28. 5*3+1 = 16(This is the important number right here: it is 2^4. You'll see why this is important shortly.) 29. 16/2 = 8 30. 8/2 = 4 31. 4/2 = 2 32. 2/2 = 1 Do you see what happened? Eventually, one winds up with a number that is a power of 2. If you divide a number that is a power of 2 by 2 many times, you wind up with 2, and then with 1. This is always true.


  • Stanisław Ulam, The Scottish Book: a Collection of Problems, Los Alamos, 1957.
  • Stanisław Ulam, A Collection of Mathematical Problems, New York, Interscience Publishers, 1960.
  • Mark Kac and Stanisław Ulam, Mathematics and Logic: Retrospect and Prospects, New York, Praeger, 1968.
  • Stanisław Ulam, Sets, Numbers and Universes, Cambridge, Massachusetts, 1974.
  • Stanisław Ulam, Adventures of a Mathematician, New York, Charles Scribner's Sons, 1983 (autobiography).

See also

Bethe on Ulam

  • "After the H-bomb was made, reporters started to call Teller the father of the H-bomb. For the sake of history, I think it is more precise to say that Ulam is the father, because he provided the seed, and Teller is the mother, because he remained with the child. As for me, I guess I am the midwife." (Hans Bethe, 1968, as quoted by Schweber, p.166.)

External links

O'Connor, John J., and Edmund F. Robertson. "Stanisław Marcin Ulam". MacTutor History of Mathematics archive.

Further reading

Necia Grant Cooper, Roger Eckhardt, Nancy Shera, editors, From Cardinals to Chaos, Cambridge University Press (1989). Reminiscences by people close to Ulam, memorial articles on aspects of his work, and previously unpublished informal work by him.

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