Stanislaw Ulam
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Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
, originated the
Teller–Ulam design A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a low ...
of
thermonuclear weapon A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
s, discovered the concept of the
cellular automaton A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...
, invented the Monte Carlo method of computation, and suggested
nuclear pulse propulsion 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 Stanislaw ...
. In pure and
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
, he proved some theorems and proposed several conjectures. Born into a wealthy
Polish Jewish The history of the Jews in Poland dates back at least 1,000 years. For centuries, Poland was home to the largest and most significant Ashkenazi Jewish community in the world. Poland was a principal center of Jewish culture, because of the lon ...
family, Ulam studied mathematics at the Lwów Polytechnic Institute, where he earned his PhD in 1933 under the supervision of
Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, (t ...
and
Włodzimierz Stożek Włodzimierz Stożek (23 July 1883 – 3 or 4 July 1941) was a Polish mathematician of the Lwów School of Mathematics. Head of the Mathematics Faculty on the Lwów University of Technology. He was arrested and murdered together with his two son ...
. In 1935,
John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
, whom Ulam had met in Warsaw, invited him to come to the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in
Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
, for a few months. From 1936 to 1939, he spent summers in Poland and academic years at
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
in
Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...
, where he worked to establish important results regarding
ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
. On 20 August 1939, he sailed for the United States for the last time with his 17-year-old brother
Adam Ulam Adam Bruno Ulam (8 April 1922 – 28 March 2000) was a Polish-American historian of Jewish descent and political scientist at Harvard University. Ulam was one of the world's foremost authorities and top experts in Sovietology and Kremlinology ...
. He became an assistant professor at the
University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
in 1940, and a United States citizen in 1941. In October 1943, he received an invitation from
Hans Bethe Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel ...
to join the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
at the secret
Los Alamos Laboratory The Los Alamos Laboratory, also known as Project Y, was a secret laboratory established by the Manhattan Project and operated by the University of California during World War II. Its mission was to design and build the first atomic bombs. Ro ...
in New Mexico. There, he worked on the
hydrodynamic In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) a ...
calculations to predict the behavior of the
explosive lens An explosive lens—as used, for example, in nuclear weapons—is a highly specialized shaped charge. In general, it is a device composed of several explosive charges. These charges are arranged and formed with the intent to control the shape ...
es that were needed by an implosion-type weapon. He was assigned to
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care fo ...
's group, where he worked on Teller's "Super" bomb for Teller and
Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...
. After the war he left to become an associate professor at the
University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in C ...
, but returned to Los Alamos in 1946 to work on
thermonuclear weapons A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
. With the aid of a cadre of female "
computers A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs ...
", including his wife Françoise Aron Ulam, he found that Teller's "Super" design was unworkable. In January 1951, Ulam and Teller came up with the
Teller–Ulam design A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a low ...
, which became the basis for all thermonuclear weapons. Ulam considered the problem of
nuclear propulsion Nuclear propulsion includes a wide variety of propulsion methods that use some form of nuclear reaction as their primary power source. The idea of using nuclear material for propulsion dates back to the beginning of the 20th century. In 1903 it was ...
of rockets, which was pursued by
Project Rover Project Rover was a United States project to develop a nuclear-thermal rocket that ran from 1955 to 1973 at the Los Alamos Scientific Laboratory (LASL). It began as a United States Air Force project to develop a nuclear-powered upper stage for ...
, and proposed, as an alternative to Rover's
nuclear thermal rocket A nuclear thermal rocket (NTR) is a type of thermal rocket where the heat from a nuclear reaction, often nuclear fission, replaces the chemical energy of the propellants in a chemical rocket. In an NTR, a working fluid, usually liquid hydrog ...
, to harness small nuclear explosions for propulsion, which became Project Orion. With Fermi,
John Pasta John Robert Pasta (October 22, 1918 – June 5, 1981) was an American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physic ...
, and
Mary Tsingou Mary Tsingou (married name: Mary Tsingou-Menzel; born October 14, 1928) is an American physicist and mathematician of Greek descent. She was one of the first programmers on the MANIAC computer at Los Alamos National Laboratory and is best known ...
, Ulam studied the
Fermi–Pasta–Ulam–Tsingou problem In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi ...
, which became the inspiration for the field of non-linear science. He is probably best known for realising that electronic computers made it practical to apply statistical methods to functions without known solutions, and as computers have developed, the
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, 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 determi ...
has become a common and standard approach to many problems.


Poland

Ulam was born in
Lemberg Lviv ( uk, Львів) is the largest city in Western Ukraine, western Ukraine, and the List of cities in Ukraine, seventh-largest in Ukraine, with a population of . It serves as the administrative centre of Lviv Oblast and Lviv Raion, and is o ...
, Galicia, on 13 April 1909. At this time, Galicia was in the
Kingdom of Galicia and Lodomeria The Kingdom of Galicia and Lodomeria,, ; pl, Królestwo Galicji i Lodomerii, ; uk, Королівство Галичини та Володимирії, Korolivstvo Halychyny ta Volodymyrii; la, Rēgnum Galiciae et Lodomeriae also known as ...
of the
Austro-Hungarian Empire Austria-Hungary, often referred to as the Austro-Hungarian Empire,, the Dual Monarchy, or Austria, was a constitutional monarchy and great power in Central Europe between 1867 and 1918. It was formed with the Austro-Hungarian Compromise of ...
, which was known to Poles as the
Austrian partition The Austrian Partition ( pl, zabór austriacki) comprise the former territories of the Polish–Lithuanian Commonwealth acquired by the Habsburg monarchy during the Partitions of Poland in the late 18th century. The three partitions were conduct ...
. In 1918, it became part of the newly restored Poland, the
Second Polish Republic The Second Polish Republic, at the time officially known as the Republic of Poland, was a country in Central Europe, Central and Eastern Europe that existed between 1918 and 1939. The state was established on 6 November 1918, before the end of ...
, and the city took its Polish name again, Lwów. The Ulams were a wealthy
Polish Jewish The history of the Jews in Poland dates back at least 1,000 years. For centuries, Poland was home to the largest and most significant Ashkenazi Jewish community in the world. Poland was a principal center of Jewish culture, because of the lon ...
family of bankers, industrialists, and other professionals. Ulam's immediate family was "well-to-do but hardly rich". His father, Józef Ulam, was born in Lwów and was a lawyer, and his mother, Anna (née Auerbach), was born in Stryj. His uncle, Michał Ulam, was an architect, building contractor, and lumber industrialist. From 1916 until 1918, Józef's family lived temporarily in
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
. After they returned, Lwów became the epicenter of the
Polish–Ukrainian War The Polish–Ukrainian War, from November 1918 to July 1919, was a conflict between the Second Polish Republic and Ukrainian forces (both the West Ukrainian People's Republic and Ukrainian People's Republic). The conflict had its roots in ethn ...
, during which the city experienced a Ukrainian siege. In 1919, Ulam entered Lwów Gymnasium Nr. VII, from which he graduated in 1927. He then studied mathematics at the Lwów Polytechnic Institute. Under the supervision of
Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, (t ...
, he received his
Master of Arts A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...
degree in 1932, and became a
Doctor of Science Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...
in 1933. At the age of 20, in 1929, he published his first paper ''Concerning Function of Sets'' in the journal ''
Fundamenta Mathematicae ''Fundamenta Mathematicae'' is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical sys ...
''. From 1931 until 1935, he traveled to and studied in
Wilno Vilnius ( , ; see also #Etymology and other names, other names) is the capital and List of cities in Lithuania#Cities, largest city of Lithuania, with a population of 592,389 (according to the state register) or 625,107 (according to the munic ...
(Vilnius),
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, Zurich,
Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
, and
Cambridge, England Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became ...
, where he met
G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
and Subrahmanyan Chandrasekhar. Along with
Stanisław Mazur Stanisław Mieczysław Mazur (1 January 1905, Lwów – 5 November 1981, Warsaw) was a Polish mathematician and a member of the Polish Academy of Sciences. Mazur made important contributions to geometrical methods in linear and nonlinear functio ...
,
Mark Kac Mark Kac ( ; Polish: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, " Can one hear the shape of a drum?" set off research into spectral theory, the ...
,
Włodzimierz Stożek Włodzimierz Stożek (23 July 1883 – 3 or 4 July 1941) was a Polish mathematician of the Lwów School of Mathematics. Head of the Mathematics Faculty on the Lwów University of Technology. He was arrested and murdered together with his two son ...
, Kuratowski, and others, Ulam was a member of the
Lwów School of Mathematics The Lwów school of mathematics ( pl, 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 ...
. Its founders were
Hugo Steinhaus Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz Un ...
and
Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an origina ...
, who were professors at the
Jan Kazimierz University The University of Lviv ( uk, Львівський університет, Lvivskyi universytet; pl, Uniwersytet Lwowski; german: Universität Lemberg, briefly known as the ''Theresianum'' in the early 19th century), presently the Ivan Franko Na ...
. Mathematicians of this "school" met for long hours at the
Scottish Café The Scottish Café ( pl, 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 functio ...
, 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 John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
, whom Ulam had met in Warsaw, invited him to come to the
Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in
Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
, 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 Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...
, James Alexander, and
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
. 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 The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intell ...
. Following up on Birkhoff's suggestion, Ulam spent summers in Poland and academic years at
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
in
Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...
from 1936 to 1939, where he worked with John C. Oxtoby to establish results regarding
ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
. These appeared in
Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
in 1941. In 1938, Stanislaw's mother Anna hanna Ulam (maiden name Auerbach) died of cancer. On 20 August 1939, in
Gdynia Gdynia ( ; ; german: Gdingen (currently), (1939–1945); csb, Gdiniô, , , ) is a city in northern Poland and a seaport on the Baltic Sea coast. With a population of 243,918, it is the 12th-largest city in Poland and the second-largest in th ...
, Józef Ulam, along with his brother Szymon, put his two sons, Stanislaw and 17 year old
Adam Adam; el, Ἀδάμ, Adám; la, Adam is the name given in Genesis 1-5 to the first human. Beyond its use as the name of the first man, ''adam'' is also used in the Bible as a pronoun, individually as "a human" and in a collective sense as " ...
, on a ship headed for the US. Eleven days later, the Germans invaded Poland. Within two months, the Germans completed their
occupation Occupation commonly refers to: *Occupation (human activity), or job, one's role in society, often a regular activity performed for payment *Occupation (protest), political demonstration by holding public or symbolic spaces *Military occupation, th ...
of western Poland, and the Soviets
invaded An invasion is a military offensive in which large numbers of combatants of one geopolitical entity aggressively enter territory owned by another such entity, generally with the objective of either: conquering; liberating or re-establishing con ...
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 The Holocaust, also known as the Shoah, was the genocide of European Jews during World War II. Between 1941 and 1945, Nazi Germany and its collaborators systematically murdered some six million Jews across German-occupied Europe; a ...
,
Hugo Steinhaus Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz Un ...
was in hiding,
Kazimierz Kuratowski Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Biography and studies Kazimierz Kuratowski was born in Warsaw, (t ...
was lecturing at the underground university in Warsaw,
Włodzimierz Stożek Włodzimierz Stożek (23 July 1883 – 3 or 4 July 1941) was a Polish mathematician of the Lwów School of Mathematics. Head of the Mathematics Faculty on the Lwów University of Technology. He was arrested and murdered together with his two son ...
and his two sons had been killed in the
massacre of Lwów professors In July 1941, 25 Polish academics from the city of Lwów (now Lviv, Ukraine) along with the 25 of their family members were killed by Nazi German occupation forces. By targeting prominent citizens and intellectuals for elimination, the Nazis hop ...
, and the last problem had been recorded in the Scottish Book.
Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an origina ...
survived the Nazi occupation by feeding
lice Louse ( : lice) is the common name for any member of the clade Phthiraptera, which contains nearly 5,000 species of wingless parasitic insects. Phthiraptera has variously been recognized as an order, infraorder, or a parvorder, as a result o ...
at Rudolf Weigl's typhus research institute. In 1963,
Adam Ulam Adam Bruno Ulam (8 April 1922 – 28 March 2000) was a Polish-American historian of Jewish descent and political scientist at Harvard University. Ulam was one of the world's foremost authorities and top experts in Sovietology and Kremlinology ...
, 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 A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...
. Here, he became a
United States citizen Citizenship of the United States is a legal status that entails Americans with specific rights, duties, protections, and benefits in the United States. It serves as a foundation of fundamental rights derived from and protected by the Constituti ...
in 1941. That year, he married Françoise Aron. She had been a French exchange student at
Mount Holyoke College Mount Holyoke College is a private liberal arts women's college in South Hadley, Massachusetts. It is the oldest member of the historic Seven Sisters colleges, a group of elite historically women's colleges in the Northeastern United States. ...
, 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

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 Santa Fe ( ; , Spanish for 'Holy Faith'; tew, Oghá P'o'oge, Tewa for 'white shell water place'; tiw, Hulp'ó'ona, label=Tiwa language, Northern Tiwa; nv, Yootó, Navajo for 'bead + water place') is the capital of the U.S. state of New Mexico. ...
. The letter was signed by
Hans Bethe Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel ...
, who had been appointed as leader of the theoretical division of
Los Alamos National Laboratory Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, ...
by
Robert Oppenheimer J. Robert Oppenheimer (; April 22, 1904 – February 18, 1967) was an American theoretical physicist. A professor of physics at the University of California, Berkeley, Oppenheimer was the wartime head of the Los Alamos Laboratory and is often ...
, 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 Joan Hinton (Chinese name: 寒春, Pinyin: ''Hán Chūn''; 20 October 1921 – 8 June 2010) was a nuclear physicist and one of the few women scientists who worked for the Manhattan Project in Los Alamos. She lived in the People's Republic of C ...
, David Frisch, and Joseph McKibben, all of whom had mysteriously disappeared. This was Ulam's introduction to the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
, 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 Emilio Gino Segrè (1 February 1905 – 22 April 1989) was an Italian-American physicist and Nobel laureate, who discovered the elements technetium and astatine, and the antiproton, a subatomic antiparticle, for which he was awarded the Nobe ...
discovered that
plutonium Plutonium is a radioactive chemical element with the symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibi ...
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 "Little Boy" was the type of atomic bomb dropped on the Japanese city of Hiroshima on 6 August 1945 during World War II, making it the first nuclear weapon used in warfare. The bomb was dropped by the Boeing B-29 Superfortress ''Enola Gay'' p ...
" that was dropped on
Hiroshima is the capital of Hiroshima Prefecture in Japan. , the city had an estimated population of 1,199,391. The gross domestic product (GDP) in Greater Hiroshima, Hiroshima Urban Employment Area, was US$61.3 billion as of 2010. Kazumi Matsui h ...
. This problem threatened to waste an enormous investment in new reactors at the
Hanford site The Hanford Site is a decommissioned nuclear production complex operated by the United States federal government on the Columbia River in Benton County in the U.S. state of Washington. The site has been known by many names, including SiteW a ...
and to make slow uranium
isotope separation Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes. The use of the nuclides produced is varied. The largest variety is used in research (e.g. in chemistry where atoms of "marker" n ...
the only way to prepare
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be typ ...
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 George may refer to: People * George (given name) * George (surname) * George (singer), American-Canadian singer George Nozuka, known by the mononym George * George Washington, First President of the United States * George W. Bush, 43rd Preside ...
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 In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fi ...
, where
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
multiplication leads to a
nuclear chain reaction In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nu ...
, releasing a large amount of energy. Cylindrical implosive configurations had been studied by
Seth Neddermeyer Seth Henry Neddermeyer (September 16, 1907 – January 29, 1988) was an American physicist who co-discovered the muon, and later championed the Implosion-type nuclear weapon while working on the Manhattan Project at the Los Alamos Laborato ...
, but von Neumann, who had experience with
shaped charge A shaped charge is an explosive charge shaped to form an explosively formed penetrator (EFP) to focus the effect of the explosive's energy. Different types of shaped charges are used for various purposes such as cutting and forming metal, ini ...
s used in
armor-piercing ammunition Armour-piercing ammunition (AP) is a type of projectile designed to penetrate either body armour or vehicle armour. From the 1860s to 1950s, a major application of armour-piercing projectiles was to defeat the thick armour carried on many warsh ...
, was a vocal advocate of spherical implosion driven by
explosive lens An explosive lens—as used, for example, in nuclear weapons—is a highly specialized shaped charge. In general, it is a device composed of several explosive charges. These charges are arranged and formed with the intent to control the shape ...
es. 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 The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
multiplication within a
chain reaction A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events. Chain reactions are one way that sys ...
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 function In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are oft ...
s, 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 Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...
'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 The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in C ...
in
Los Angeles Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the world' ...
. In January 1946, he suffered an acute attack of
encephalitis Encephalitis is inflammation of the brain. The severity can be variable with symptoms including reduction or alteration in consciousness, headache, fever, confusion, a stiff neck, and vomiting. Complications may include seizures, hallucinations, ...
, which put his life in danger, but which was alleviated by emergency brain surgery. During his recuperation, many friends visited, including
Nicholas Metropolis Nicholas Constantine Metropolis (Greek: ; June 11, 1915 – October 17, 1999) was a Greek-American physicist. Metropolis received his BSc (1937) and PhD in physics (1941, with Robert Mulliken) at the University of Chicago. Shortly afterwards, ...
from Los Alamos and the famous mathematician
Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...
, who remarked: "Stan, you are just like before." This was encouraging, because Ulam was concerned about the state of his mental faculties, for he had lost the ability to speak during the crisis. Another friend,
Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, pro ...
, asserted in a 1987 article that the attack changed Ulam's personality: afterwards, he turned from rigorous pure mathematics to more speculative conjectures concerning the application of mathematics to physics and
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
; Rota also cites Ulam's former collaborator Paul Stein as noting that Ulam was sloppier in his clothing afterwards, and John Oxtoby as noting that Ulam before the encephalitis could work for hours on end doing calculations, while when Rota worked with him, was reluctant to solve even a quadratic equation. This assertion was not accepted by Françoise Aron Ulam. By late April 1946, Ulam had recovered enough to attend a secret conference at Los Alamos to discuss
thermonuclear weapons A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
. Those in attendance included Ulam, von Neumann, Metropolis, Teller,
Stan Frankel Stanley Phillips Frankel (1919 – May, 1978) was an American computer scientist. He worked in the Manhattan Project and developed various computers as a consultant. Early life He was born in Los Angeles, attended graduate school at the Univers ...
, and others. Throughout his participation in the Manhattan Project, Teller's efforts had been directed toward the development of a "super" weapon based on
nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is manifest ...
, rather than toward development of a practical fission bomb. After extensive discussion, the participants reached a consensus that his ideas were worthy of further exploration. A few weeks later, Ulam received an offer of a position at Los Alamos from Metropolis and
Robert D. Richtmyer Robert Davis Richtmyer (October 10, 1910 – September 24, 2003) was an American physicist, mathematician, educator, author, and musician. Biography Richtmyer was born on October 10, 1910 in Ithaca, New York. His father was physicist Floyd K. R ...
, the new head of its theoretical division, at a higher salary, and the Ulams returned to Los Alamos.


Monte Carlo method

Late in the war, under the sponsorship of von Neumann, Frankel and Metropolis began to carry out calculations on the first general-purpose electronic computer, the
ENIAC ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one packa ...
at the Aberdeen Proving Ground in Maryland. Shortly after returning to Los Alamos, Ulam participated in a review of results from these calculations. Earlier, while playing solitaire during his recovery from surgery, Ulam had thought about playing hundreds of games to estimate statistically the probability of a successful outcome. With ENIAC in mind, he realized that the availability of computers made such statistical methods very practical. John von Neumann immediately saw the significance of this insight. In March 1947 he proposed a statistical approach to the problem of neutron diffusion in fissionable material. Because Ulam had often mentioned his uncle, Michał Ulam, "who just had to go to Monte Carlo" to gamble, Metropolis dubbed the statistical approach "The
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, 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 determi ...
". Metropolis and Ulam published the first unclassified paper on the Monte Carlo method in 1949. Fermi, learning of Ulam's breakthrough, devised an
analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In c ...
known as the Monte Carlo trolley, later dubbed the
FERMIAC The Monte Carlo trolley, or FERMIAC, was an analog computer invented by physicist Enrico Fermi to aid in his studies of neutron transport. Operation The FERMIAC employed the Monte Carlo method to model neutron transport in various types of n ...
. The device performed a mechanical simulation of random diffusion of neutrons. As computers improved in speed and programmability, these methods became more useful. In particular, many Monte Carlo calculations carried out on modern
massively parallel Massively parallel is the term for using a large number of computer processors (or separate computers) to simultaneously perform a set of coordinated computations in parallel. GPUs are massively parallel architecture with tens of thousands of t ...
supercomputer A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second ( FLOPS) instead of million instructions ...
s are
embarrassingly parallel In parallel computing, an embarrassingly parallel workload or problem (also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel) is one where little or no effort is needed to separate the problem ...
applications, whose results can be very accurate.


Teller–Ulam design

On 29 August 1949, the
Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
tested its first fission bomb, the
RDS-1 The RDS-1 (russian: РДС-1), also known as Izdeliye 501 (device 501) and First Lightning (), was the nuclear bomb used in the Soviet Union's first nuclear weapon test. The United States assigned it the code-name Joe-1, in reference to Joseph ...
. Created under the supervision of
Lavrentiy Beria Lavrentiy Pavlovich Beria (; rus, Лавре́нтий Па́влович Бе́рия, Lavréntiy Pávlovich Bériya, p=ˈbʲerʲiə; ka, ლავრენტი ბერია, tr, ;  – 23 December 1953) was a Georgian Bolsheviks ...
, who sought to duplicate the US effort, this weapon was nearly identical to
Fat Man "Fat Man" (also known as Mark III) is the codename for the type of nuclear bomb the United States detonated over the Japanese city of Nagasaki on 9 August 1945. It was the second of the only two nuclear weapons ever used in warfare, the fir ...
, for its design was based on information provided by spies Klaus Fuchs, Theodore Hall, and David Greenglass. In response, on 31 January 1950, President of the United States, President Harry S. Truman announced a crash program to develop a fusion bomb. To advocate an aggressive development program, Ernest Lawrence and Luis Walter Alvarez, Luis Alvarez came to Los Alamos, where they conferred with Norris Bradbury, the laboratory director, and with George Gamow,
Edward Teller Edward Teller ( hu, Teller Ede; January 15, 1908 – September 9, 2003) was a Hungarian-American theoretical physicist who is known colloquially as "the father of the hydrogen bomb" (see the Teller–Ulam design), although he did not care fo ...
, and Ulam. Soon, these three became members of a short-lived committee appointed by Bradbury to study the problem, with Teller as chairman. At this time, research on the use of a fission weapon to create a Nuclear fusion, fusion reaction had been ongoing since 1942, but the design was still essentially the one originally proposed by Teller. His concept was to put tritium and/or deuterium in close proximity to a fission bomb, with the hope that the heat and intense flux of neutrons released when the bomb exploded, would ignite a self-sustaining Nuclear fusion, fusion reaction. Reactions of these isotopes of hydrogen are of interest because the energy per unit mass of fuel released by their fusion is much larger than that from fission of heavy nuclei. Because the results of calculations based on Teller's concept were discouraging, many scientists believed it History of the Teller–Ulam design#Teller's "Super", could not lead to a successful weapon, while others had moral and economic grounds for not proceeding. Consequently, several senior people of the Manhattan Project opposed development, including Bethe and Oppenheimer. To clarify the situation, Ulam and von Neumann resolved to do new calculations to determine whether Teller's approach was feasible. To carry out these studies, von Neumann decided to use electronic computers: ENIAC at Aberdeen, a new computer, MANIAC I, MANIAC, at Princeton, and its twin, which was under construction at Los Alamos. Ulam enlisted Everett to follow a completely different approach, one guided by physical intuition. Françoise Aron Ulam, Françoise Ulam was one of a cadre of women "
computers A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs ...
" who carried out laborious and extensive computations of thermonuclear scenarios on mechanical calculators, supplemented and confirmed by Everett's slide rule. Ulam and Fermi collaborated on further analysis of these scenarios. The results showed that, in workable configurations, a thermonuclear reaction would not ignite, and if ignited, it would not be self-sustaining. Ulam had used his expertise in combinatorics to analyze the chain reaction in deuterium, which was much more complicated than the ones in uranium and plutonium, and he concluded that no self-sustaining chain reaction would take place at the (low) densities that Teller was considering. In late 1950, these conclusions were confirmed by von Neumann's results. In January 1951, Ulam had another idea: to channel the mechanical shock of a nuclear explosion so as to compress the fusion fuel. On the recommendation of his wife, Ulam discussed this idea with Bradbury and Mark before he told Teller about it. Almost immediately, Teller saw its merit, but noted that soft X-rays from the fission bomb would compress the thermonuclear fuel more strongly than mechanical shock and suggested ways to enhance this effect. On 9 March 1951, Teller and Ulam submitted a joint report describing these innovations. A few weeks later, Teller suggested placing a
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be typ ...
rod or cylinder at the center of the fusion fuel. The detonation of this "spark plug" would help to initiate and enhance the fusion reaction. The design based on these ideas, called staged radiation implosion, has become the standard way to build thermonuclear weapons. It is often described as the "
Teller–Ulam design A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a low ...
". In September 1951, after a series of differences with Bradbury and other scientists, Teller resigned from Los Alamos, and returned to the University of Chicago. At about the same time, Ulam went on leave as a visiting professor at Harvard for a semester. Although Teller and Ulam submitted a joint report on their design and jointly applied for a patent on it, they soon became involved in a dispute over who deserved credit. After the war, Bethe returned to Cornell University, but he was deeply involved in the development of thermonuclear weapons as a consultant. In 1954, he wrote an article on the history of the H-bomb, which presents his opinion that both men contributed very significantly to the breakthrough. This balanced view is shared by others who were involved, including Mark and Fermi, but Teller persistently attempted to downplay Ulam's role. "After the H-bomb was made," Bethe recalled, "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." With the basic fusion reactions confirmed, and with a feasible design in hand, there was nothing to prevent Los Alamos from testing a thermonuclear device. On 1 November 1952, the first thermonuclear explosion occurred when Ivy Mike was detonated on Enewetak Atoll, within the US Pacific Proving Grounds. This device, which used liquid deuterium as its fusion fuel, was immense and utterly unusable as a weapon. Nevertheless, its success validated the Teller–Ulam design, and stimulated intensive development of practical weapons.


Fermi–Pasta–Ulam–Tsingou problem

When Ulam returned to Los Alamos, his attention turned away from weapon design and toward the use of computers to investigate problems in physics and mathematics. With
John Pasta John Robert Pasta (October 22, 1918 – June 5, 1981) was an American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physic ...
, who helped Metropolis to bring MANIAC on line in March 1952, he explored these ideas in a report "Heuristic Studies in Problems of Mathematical Physics on High Speed Computing Machines", which was submitted on 9 June 1953. It treated several problems that cannot be addressed within the framework of traditional analytic methods: billowing of fluids, rotational motion in gravitating systems, magnetic lines of force, and hydrodynamic instabilities. Soon, Pasta and Ulam became experienced with electronic computation on MANIAC, and by this time, Enrico Fermi had settled into a routine of spending academic years at the University of Chicago and summers at Los Alamos. During these summer visits, Pasta, Ulam, and
Mary Tsingou Mary Tsingou (married name: Mary Tsingou-Menzel; born October 14, 1928) is an American physicist and mathematician of Greek descent. She was one of the first programmers on the MANIAC computer at Los Alamos National Laboratory and is best known ...
, a programmer in the MANIAC group, joined him to study a variation of the classic problem of a string of masses held together by springs that exert forces linearly proportional to their displacement from equilibrium. 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 In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi ...
, 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 theorem, equipartition of energy. It remained mysterious until 1965, when Martin David Kruskal, Kruskal and Norman Zabusky, 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 Nuclear propulsion includes a wide variety of propulsion methods that use some form of nuclear reaction as their primary power source. The idea of using nuclear material for propulsion dates back to the beginning of the 20th century. In 1903 it was ...
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 Project Rover was a United States project to develop a nuclear-thermal rocket that ran from 1955 to 1973 at the Los Alamos Scientific Laboratory (LASL). It began as a United States Air Force project to develop a nuclear-powered upper stage for ...
, 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 Nuclear thermal rocket, 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 Fermi acceleration, the acceleration of cosmic rays. Another, with Paul Stein and
Mary Tsingou Mary Tsingou (married name: Mary Tsingou-Menzel; born October 14, 1928) is an American physicist and mathematician of Greek descent. She was one of the first programmers on the MANIAC computer at Los Alamos National Laboratory and is best known ...
, 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

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. He was an elected member of the American Academy of Arts and Sciences, the United States National Academy of Sciences, and the American Philosophical Society. In Colorado, where he rejoined his friends Gamow, Richtmyer, and Hawkins, Ulam's research interests turned toward
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
. In 1968, recognizing this emphasis, the University of Colorado Denver, 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. Another, report, with William Beyer, Temple F. Smith, and M. L. Stein, titled "Metrics in Biology", introduced new ideas about numerical taxonomy and evolutionary distances. When he retired from Colorado in 1975, Ulam began to spend winter semesters at the University of Florida, where he was a graduate research professor. 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 Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...
noted that "he died suddenly of heart failure, without fear or pain, while he could still prove and conjecture." In 1987, Françoise Aron Ulam, 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.


Challenge to economics

Alfred Marshall and his disciples dominated economic theory until the end of WWII. With the Cold War, the theory changed, emphasizing that a market economy was superior and the only sensible way. In Paul Samuelson's "Economics: An Introductory Analysis", 1948, Adam Smith's "invisible hand" was only a footnote. In later editions, it became the central theme. As Samuelson remembers, all this was challenged by Stanislaw Ulam: "[Y]ears ago... I was in the Society of Fellows at Harvard along with the mathematician Stanislaw Ulam. Ulam, who was to become an originator of the Monte Carlo method and co-discoverer of the hydrogen-bomb,... used to tease me by saying, 'Name me one proposition in all of the social sciences which is both true and non-trivial.' This was the test that I always failed. But now, some thirty years later ... an appropriate answer occurs to me: The David Ricardo, Ricardian theory of comparative advantage ... That it is logically true need not be argued before a mathematician; that it is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them."


Impact and legacy

Participated in the creation of a hydrogen bomb as part of the
Los Alamos Laboratory The Los Alamos Laboratory, also known as Project Y, was a secret laboratory established by the Manhattan Project and operated by the University of California during World War II. Its mission was to design and build the first atomic bombs. Ro ...
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. Topics represented by a significant number of papers are: set theory (including measurable cardinals and abstract measure (mathematics), measures), topology, Transformation (function), transformation theory,
ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
, group theory, Variety (universal algebra), projective algebra, number theory, combinatorics, and graph theory. In March 2009, the Mathematical Reviews database contained 697 papers with the name "Ulam". Notable results of this work are: *Borsuk–Ulam theorem *Mazur–Ulam theorem *Kuratowski–Ulam theorem *Hyers–Ulam–Rassias stability *Lucky number *Ulam spiral *Collatz conjecture, Ulam conjecture (in Number Theory) *Reconstruction conjecture, Ulam conjecture (in Graph theory) *Ulam's packing conjecture *Ulam's game *Ulam matrix *Ulam numbers With his pivotal role in the development of thermonuclear weapons, Stanislaw Ulam changed the world. According to Françoise Ulam: "Stan would reassure me that, barring accidents, the H-bomb rendered nuclear war impossible." In 1980, Ulam and his wife appeared in the television documentary ''The Day After Trinity''. The
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, 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 determi ...
has become a ubiquitous and standard approach to computation, and the method has been applied to a vast number of scientific problems. In addition to problems in physics and mathematics, the method has been applied to Monte Carlo methods in finance, finance, social science, environmental impact assessment, environmental risk assessment, linguistics, radiation therapy, and sports. The
Fermi–Pasta–Ulam–Tsingou problem In physics, the Fermi–Pasta–Ulam–Tsingou problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi ...
is credited not only as "the birth of experimental mathematics", but also as inspiration for the vast field of Nonlinear Science. In his Lilienfeld Prize lecture, David K. Campbell noted this relationship and described how FPUT gave rise to ideas in Chaos theory, chaos, solitons, and Dynamical systems theory, dynamical systems. In 1980, Donald Kerr, laboratory director at Los Alamos, with the strong support of Ulam and
Mark Kac Mark Kac ( ; Polish: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, " Can one hear the shape of a drum?" set off research into spectral theory, the ...
, founded the Center for Nonlinear Studies (CNLS). In 1985, CNLS initiated the ''Stanislaw M. Ulam Distinguished Scholar'' program, which provides an annual award that enables a noted scientist to spend a year carrying out research at Los Alamos. The fiftieth anniversary of the original FPUT paper was the subject of the March 2005 issue of the journal Chaos, and the topic of the 25th Annual International Conference of CNLS. The University of Southern Mississippi and the University of Florida supported the ''Ulam Quarterly'', which was active from 1992 to 1996, and which was one of the first online mathematical journals. Florida's Department of Mathematics has sponsored, since 1998, the annual ''Ulam Colloquium Lecture'', and in March 2009, the ''Ulam Centennial Conference''. Ulam's work on non-Euclidean distance, Euclidean distance metrics in the context of molecular biology made a significant contribution to sequence analysis and his contributions in theoretical biology are considered watersheds in the development of Cellular automata#History, cellular automata theory, population biology, pattern recognition, and biometrics generally (David Sankoff, however, challenged conclusions of Walter by writing that Ulam had only modest influence on early development of sequence alignment methods.). Colleagues noted that some of his greatest contributions were in clearly identifying problems to be solved and general techniques for solving them. In 1987, Los Alamos issued a special issue of its ''Science'' publication, which summarized his accomplishments, and which appeared, in 1989, as the book ''From Cardinals to Chaos''. Similarly, in 1990, the University of California Press issued a compilation of mathematical reports by Ulam and his Los Alamos collaborators: ''Analogies Between Analogies''. During his career, Ulam was awarded honorary degrees by the Universities of University of New Mexico, New Mexico, University of Wisconsin, Wisconsin, and University of Pittsburgh, Pittsburgh. In 2021, German film director Thorsten Klein made the :de:Adventures of a Mathematician, film adaptation of the book ''Adventures of a Mathematician'' about Ulam's life


Bibliography

* * * * (autobiography). * *


See also

* List of things named after Stanislaw Ulam * Biopic about Stanislaw Ulam, based on his autobiography, starring Jakub Gierszał, Jakub Gierszal


References


External links


1979 Audio Interview with Stanislaus Ulam by Martin Sherwin
Voices of the Manhattan Project
1965 Audio Interview with Stanislaus Ulam by Richard Rhodes
Voices of the Manhattan Project * * – 1976 lecture on ''The First International Research Conference on the History of Computing''. {{DEFAULTSORT:Ulam, Stanislaw 1909 births 1984 deaths Politicians from Lviv Jews from Galicia (Eastern Europe) People from the Kingdom of Galicia and Lodomeria Polish agnostics Jewish emigrants from Nazi Germany to the United States Polish set theorists Harvard University faculty University of Wisconsin–Madison faculty University of Colorado Boulder faculty University of Colorado Denver faculty University of Florida faculty Members of the United States National Academy of Sciences Manhattan Project people People from Los Alamos, New Mexico Jewish American scientists Lwów School of Mathematics Mathematics popularizers Monte Carlo methodologists Cellular automatists Jewish agnostics Lviv Polytechnic alumni Jewish physicists Burials at Montparnasse Cemetery Members of the American Philosophical Society