Stanislaw Marcin Ulam
Encyclopedia
Stanisław Marcin Ulam was a renowned mathematician
of Polish-Jewish origin. He participated in America's Manhattan Project
, originated the Teller–Ulam design of thermonuclear weapons, invented the Monte Carlo method of computation
, and proposed the idea of nuclear pulse propulsion
. In pure and applied mathematics, he produced many results, proved many theorems, and proposed several conjectures.
, on April 13, 1909. At this time, Galicia was in the Austro-Hungarian Empire
, but in 1918, it became part of the Second Polish Republic
, and the city took on its traditional Polish name, Lwów. In 1939, following the Molotov-Ribbentrop Pact
, the Soviets invaded Poland, and the city was renamed Lviv, which is the Ukrainian
form of its name, and by which it is known today.
The Ulams were a wealthy Polish Jewish banking and timber-processing family. Ulam's family was one of the richest in Lwów. His father, Józef Ulam, was born there and was a lawyer, his mother, Anna Auerbach, was born in Stryj
, and his uncle, Michael Ulam, was an architect. From 1916 until 1918, Józef's family lived temporarily in Vienna
. After they returned, Lwów became the epicenter of the Polish-Ukrainian War
, during which the city experienced a Ukrainian siege and a pogrom
.
In 1919, Ulam entered Lwów Gymnasium Nr. VII, from which he graduated in 1927. Soon, he began studies of mathematics at the Lwów Polytechnic Institute
. Here, under the supervision of Kazimierz Kuratowski
, he received his M. A. degree in 1932 and his D.Sc. in 1933. From 1931 until 1935, he traveled to and studied in Vilnius
, Vienna
, Zurich
, Paris
, and Cambridge, UK
.
Along with Stanislaw 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 University of Lwów
. Mathematicians of this "school" met for long hours at the Scottish Café
, where the problems they discussed were collected in the famous Scottish Book
, which is a thick notebook provided by Banach's wife. Ulam is a major presence in the Scottish 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.
, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study
in Princeton, NJ
, for a few months. In December of that year, Ulam sailed to America. In 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 met G. D. Birkhoff, who suggested that he apply for a position with the Harvard Society of Fellows
.
From 1936 to 1939, after following up on Birkhoff's suggestion, Ulam spent summers in Poland and academic years at Harvard University
in Cambridge, MA
. Here, he worked with John C. Oxtoby to establish important results regarding ergodic theory
, which appeared in Annals of Mathematics
in 1941.
On August 20, 1939, in Gdynia
, Józef Ulam, along with his brother Szymon, put his two sons, Stanislaw and 16 year old Adam
, on a ship headed for America. Within two weeks, 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 were victims of the Holocaust, Steinhaus was in hiding, Kuratowski was lecturing at the underground university
in Warsaw, Stożek and his two sons had been killed in the massacre of Lwów professors, Banach was surviving Nazi occupation by feeding lice at Rudolf Weigl's typhus research institute
, and the last problem had been recorded in the Scottish Book. 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 gives a chilling account of Lwów's chaotic scenes in late 1939.
In 1940, after being recommended by Birkhoff, Ulam became an assistant professor at the University of Wisconsin
in Madison, WI
. Here, in 1941, he became an American
citizen. That year, he married Françoise Aron. She had been a French exchange student at Mount Holyoke College
, whom he met in Cambridge, MA. They had one daughter, Claire. In Madison, Ulam met his friend and colleague C. J. Everett.
. The letter was signed by Hans Bethe
, who had been appointed director of the theoretical division of Los Alamos National Laboratory
by J. Robert Oppenheimer, its scientific director.
At this time, Ulam knew nothing of Los Alamos. To learn more, he checked out of the library a New Mexico guidebook. On the checkout slip, he found the names of his Wisconsin colleagues, Joan Hinton
, David Frisch
, and Joseph McKibben, who had mysteriously disappeared from Madison to secret war work. This was Ulam's introduction to the Manhattan Project
.
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 separation of uranium isotopes
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
, which suddenly releases 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.
multiplication within the chain reaction
, have implications with regard to implosion speed and symmetry. In November 1944, David Hawkins
and Ulam addressed this point in a report entitled "Theory of Multiplicative Processes I", whose last page gives some suggestions pertinent to bomb design. However, this report, which invokes 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 another pioneering exploration by Ulam and C. J. 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
. He stayed until December 1945, overlapping Ulam's stay by about a year, during which they formed a relationship that became very fruitful after the war.
The contributions of von Neumann and Ulam to the "Fat Man
" weapons of the Trinity test
and Nagasaki bombing were only part of a large scientific and engineering effort. Some other crucial contributions were Edward Teller
's realization that implosive compression would facilitate nuclear detonation by significantly increasing the density of the plutonium sphere, Luis Alvarez
's development of exploding-bridgewire detonator
s, which ensured that the explosive lenses would all fire at once, and Bruno Rossi
's RaLa experiment
s, which tested (without plutonium) various weapon designs to arrive at one that produced an accurately symmetrical implosion.
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
, 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. Much later, after Ulam's death, another friend, Gian-Carlo Rota
, asserted that the attack did change Ulam's personality; afterwards, he turned from rigorous pure mathematics to more speculative conjectures concerning the application of mathematics to physics
and biology
. However, this suggestion was not accepted by Françoise Ulam.
By late April 1946, Ulam had recovered enough to attend a secret conference at Los Alamos to discuss thermonuclear weapons
. Those in attendance were: Ulam, von Neumann, Metropolis, Teller, Stan Frankel
, and others. Throughout his participation in the Manhattan Project, Teller's efforts had been directed toward the development of a "super" bomb based on nuclear fusion
, 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, the Ulams returned to Los Alamos.
. 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, and in March 1947, proposed to Robert Richtmyer, leader of the theoretical division, a statistical approach to the problem of neutron diffusion in fissionable material. Because Ulam had often mentioned his uncle "who just had to go to Monte Carlo" to gamble, Metropolis dubbed the statistical approach "The Monte Carlo method
". In this context, the fact that Ulam's uncle Michael died in Monte Carlo
is interesting.
In 1948, ENIAC was moved from the University of Pennsylvania
's Moore School of Electrical Engineering
, where it had been conceived and designed by John Mauchly
and J. Presper Eckert
, to the Ballistic Research Laboratory
in Aberdeen, MD
. Here, with von Neumann's inspiration, Richard Clippinger suggested that it could be configured in a jury rigged version of the stored-program architecture
that has become standard on most computers. This architecture greatly facilitated programming, and on September 16, 1948, ENIAC was first run as a stored-program computer
. Soon, it was put to work on Monte Carlo calculations of neutron transport by Metropolis and von Neumann. In 1949, Metropolis and Ulam published the first unclassified paper on the Monte Carlo method.
Statistical techniques began in the 18th century, when Buffon's needle
was proposed as a way to approximate the number π
. Fermi used them in the 1930s, and when he heard of Ulam's breakthrough, created the FERMIAC
, which performs a mechanical simulation of random diffusion of neutrons. These ideas embody the context of Ulam's innovation, but not its essence, which is the probabilistic use of electronic computers to carry out rapidly the large numbers of tedious repetitions that are needed to achieve usable accuracy. As computers improved, these methods became more useful. In particular, Monte Carlo calculations carried out on modern massively parallel
supercomputers are embarrassingly parallel
applications, whose results can be very accurate.
tested its first fission bomb, the RDS-1. Created under the supervision of Lavrentiy Beria
, who sought to duplicate the American effort, this weapon was nearly identical to Fat Man, for its design was based on information provided by spies Klaus Fuchs
, Theodore Hall
, David Greenglass
, and others. In response, on January 31, 1950, President Truman
announced a crash program to develop a fusion bomb.
To advocate an aggressive development program, Ernest Lawrence
and Luis Alvarez
came to Los Alamos, where they conferred with Norris Bradbury
, the laboratory director, and with George Gamow
, Teller, 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 fusion reaction
had been ongoing since 1942, but the design was still essentially the one originally proposed by Edward Teller
. His concept was to put some 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 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 could not lead to a successful weapon, and many more had moral 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 cary out these studies, von Neumann decided to use electronic computers. This approach was made possible by his access to computers: ENIAC at Aberdeen, a new computer, MANIAC
, at Princeton, and its twin, which was under construction at Los Alamos. Ulam enlisted C. J. Everett to follow a completely different approach, which was guided by physical intuition. With the aid of a cadre of female "data analysts", including Françoise Ulam, who performed computations on mechanical calculator
s, and whose efforts were supplemented and confirmed by Everett's use of his slide rule
, they carried out laborious and extensive computations of many thermonuclear scenarios. 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. In late 1950, these conclusions were confirmed by von Neumann's results.
In January 1951, Ulam had another idea: Put the fission bomb and fusion fuel together inside a massive casing. When the bomb detonated, the casing would contain the explosion long enough for mechanical shock to heat and compress the fusion fuel, and for fission neutrons to ignite nuclear fusion
. On the recommendation of his wife, Ulam discussed this idea with Bradbury and J. Carson Mark
before he told Teller about it. Almost immediately, Teller saw its merit. However, he noted that soft X-radiation from the fission bomb would compress the thermonuclear fuel more strongly than mechanical shock and suggested ways to enhance this effect. On March 9, 1951, Teller and Ulam submitted a joint report describing these innovations. A few weeks later, Teller suggested the placement at the center of the fusion fuel of a fissile
rod or cylinder, the "spark plug", whose detonation 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 designated as the "Teller–Ulam design".
In May 1951, during Operation Greenhouse
, the explosions of devices "George" and "Item
" proved that a fission explosion could trigger non-sustaining fusion reactions in a mixture of deuterium and tritium. Although these tests did not produce a thermonuclear detonation, they showed that a small fusion component could enhance significantly a fission explosion. These results, validated Teller's concept of boosted fission
, which is incorporated in nearly all modern weapons.
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, Hans Bethe
returned to Cornell University
, but he was deeply involved as a consultant in the development of thermonuclear weapons. 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.
In September 1951, Teller went back to his prewar position at the University of Chicago
. At about the same time, Ulam went on leave as a visiting professor at Harvard. In 1952, Teller joined the newly established Livermore
branch of the University of California Radiation Laboratory
, where he was director from 1958 to 1960.
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 November 1. 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.
On August 12, 1953, the Soviets detonated their RDS-6s
device, which incorporated the Sloika design that had been developed by Andrei Sakharov
and Vitaly Ginzburg
. This code name, which refers to a Russian layered pastry, reflects the design, in which fusion fuel is layered within a fission bomb. This configuration is similar to that of Greenhouse Item
and of the "Alarm Clock", which Teller proposed as an implementation of his original ideas. Although the Soviet design did not lead to full thermonuclear detonation, it embodied Ginzburg's crucial idea of November 1948, which was to use lithium deuteride as a fusion fuel. When fission neutrons break apart the lithium nuclei, some of the fragments are tritium nuclei, which participate in a very effective fusion reaction with the deuterium that is already present. The great advantage is that, in effect, both tritium and deuterium are encapsulated in a dense chemical compound. There is no need to use the cryogenic equipment for liquid deuterium that made the Ivy Mike device impractical as a weapon. On March 1, 1954, this advantage was realized in the Castle Bravo
test, which was the largest American thermonuclear explosion, and which provided a prototype for nearly all subsequent thermonuclear weapons. On November 22, 1955, the Soviets set off RDS-37
, which was their first thermonuclear bomb. It embodied the Teller-Ulam design, which Sakharov and other Soviet scientists had worked out independently.
, 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 June 9, 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 pattern of spending academic years at the University of Chicago and summers at Los Alamos. During the summer of 1954, Pasta and Ulam 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 problem, which is often designated by the abbreviation FPU
With the aid of standard mathematics, the 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 amazing 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 FPU behavior can be understood in terms of solitons.
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, some of their ideas were pursued during Project Rover
, which explored the use of nuclear reactors to power rockets. It was administered by Los Alamos, but many of its activities were carried out elsewhere. In particular, fuel rods were developed at the Rocky Flats Plant
, and twenty rockets were tested at the Nuclear Reactor Development Station, which was located at Jackass Flats
within the Nevada Test Site
.
In 1955, Ulam and C. J. Everett 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 a famous article, "Death of a Project".
In 1957, Bradbury appointed Ulam and John H. Manley as research advisors to the laboratory director. 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, metalurgy, 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
, which is an extension of Fermi's theory of the acceleration of cosmic rays
. Another, with Paul Stein was titled "Quadratic Transformations" It was an early investigation of chaos theory
.
, 1963, and the University of Colorado
, 1961/62 and 1965/67. In 1967, the last of these positions became permanent, when Ulam was appointed as professor and Chairman of the Department of Mathematics at Colorado. However, he kept his residence in Santa Fe, which made it convenient to spend summers as a consultant in Los Alamos.
In Colorado, Ulam's research interests turned toward biology
. 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 some of his earlier ideas on branching processes to biological inheiritance. Another, report, with William Beyer, Temple F. Smith, and M. L. Stein, titled "Metrics in Biology", introduced some new ideas of quantification. 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.
When he retired from Colorado in 1975, Ulam had begun 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
, 1982/83, and at Rockefeller University
, 1980/84, this pattern of spending summers in Colorado and Los Alamos and winters in Florida continued until Ulam died in Santa Fe on May 13, 1984.
(including measurable cardinal
s and abstract measures
), topology
, ergodic theory
, and other fields.
Some results that bear his name are:
During his career, Ulam was awarded honorary degrees by the Universities of New Mexico
, Wisconsin, and Pittsburgh
.
The University of Florida maintains a journal named after Ulam, Ulam Quarterly Journal
In 1980, he appeared in the television documentary The Day After Trinity
.
Ulam's answer to a question by Senator John O. Pastore
at a congressional committee hearing, "Outer Space Propulsion by Nuclear Energy", on January 22, 1958:
Ulam was among the first to refer to the technological singularity
, and possibly the originator of the metaphor itself. In May 1958, while referring to a conversation with John von Neumann
:
, on seeing Ulam at a party in Santa Fe, NM:
Hans Bethe
1968:
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
of Polish-Jewish origin. He participated in America's Manhattan Project
Manhattan Project
The Manhattan Project was a research and development program, led by the United States with participation from the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army...
, originated the Teller–Ulam design of thermonuclear weapons, invented the Monte Carlo method of computation
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
, and proposed the idea of nuclear pulse propulsion
Nuclear pulse propulsion
Nuclear pulse propulsion is a proposed method of spacecraft propulsion that uses nuclear explosions for thrust. It was first developed as Project Orion by DARPA, after a suggestion by Stanislaw Ulam in 1947...
. In pure and applied mathematics, he produced many results, proved many theorems, and proposed several conjectures.
Poland
Ulam was born in Lemberg, GaliciaKingdom of Galicia and Lodomeria
The Kingdom of Galicia and Lodomeria was a crownland of the Habsburg Monarchy, the Austrian Empire, and Austria–Hungary from 1772 to 1918 .This historical region in eastern Central Europe is currently divided between Poland and Ukraine...
, on April 13, 1909. At this time, Galicia was in the Austro-Hungarian Empire
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...
, but in 1918, it became part of the Second Polish Republic
Second Polish Republic
The Second Polish Republic, Second Commonwealth of Poland or interwar Poland refers to Poland between the two world wars; a period in Polish history in which Poland was restored as an independent state. Officially known as the Republic of Poland or the Commonwealth of Poland , the Polish state was...
, and the city took on its traditional Polish name, Lwów. In 1939, following the Molotov-Ribbentrop Pact
Molotov-Ribbentrop Pact
The Molotov–Ribbentrop Pact, named after the Soviet foreign minister Vyacheslav Molotov and the German foreign minister Joachim von Ribbentrop, was an agreement officially titled the Treaty of Non-Aggression between Germany and the Soviet Union and signed in Moscow in the late hours of 23 August 1939...
, the Soviets invaded Poland, and the city was renamed Lviv, which is the Ukrainian
Ukrainian language
Ukrainian is a language of the East Slavic subgroup of the Slavic languages. It is the official state language of Ukraine. Written Ukrainian uses a variant of the Cyrillic alphabet....
form of its name, and by which it is known today.
The Ulams were a wealthy Polish Jewish banking and timber-processing family. Ulam's family was one of the richest in Lwów. His father, Józef Ulam, was born there and was a lawyer, his mother, Anna Auerbach, was born in Stryj
Stryi
Stryi is a city located on the left bank of the river Stryi in the Lviv Oblast of western Ukraine . Serving as the administrative center of the Stryi Raion , the city itself is also designated as a separate raion within the oblast. Thus, the city has two administrations - the city and the raion...
, and his uncle, Michael Ulam, was an architect. From 1916 until 1918, Józef's family lived temporarily in Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
. After they returned, Lwów became the epicenter of the Polish-Ukrainian War
Polish-Ukrainian War
The Polish–Ukrainian War of 1918 and 1919 was a conflict between the forces of the Second Polish Republic and West Ukrainian People's Republic for the control over Eastern Galicia after the dissolution of Austria-Hungary.-Background:...
, during which the city experienced a Ukrainian siege and a pogrom
Lwów pogrom (1918)
The Lwów pogrom of the Jewish population of Lwów took place on November 21–23, 1918 during the Polish-Ukrainian War. In the course of the three days of unrest in the city, an estimated 52-150 Jewish residents were murdered and hundreds injured, with widespread looting carried out by Polish...
.
In 1919, Ulam entered Lwów Gymnasium Nr. VII, from which he graduated in 1927. Soon, he began studies of mathematics at the Lwów Polytechnic Institute
Lviv Polytechnic
Lviv Polytechnic National University is the largest scientific university in Lviv. Since its foundation in 1844, it was one of the most important centres of science and technological development in Central Europe. In the interbellum period, the Polytechnic was one of the most important technical...
. Here, under the supervision of Kazimierz Kuratowski
Kazimierz Kuratowski
Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.-Biography and studies:...
, he received his M. A. degree in 1932 and his D.Sc. in 1933. From 1931 until 1935, he traveled to and studied in Vilnius
Vilnius
Vilnius is the capital of Lithuania, and its largest city, with a population of 560,190 as of 2010. It is the seat of the Vilnius city municipality and of the Vilnius district municipality. It is also the capital of Vilnius County...
, Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
, Zurich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
, Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, and Cambridge, UK
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
.
Along with Stanislaw Mazur
Stanislaw Mazur
Stanisław Mazur was a Polish mathematician and a member of the Polish Academy of Sciences....
, Mark Kac
Mark Kac
Mark Kac was a Polish mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. Kac completed his Ph.D...
, Włodzimierz Stożek, Kuratowski, and others, Ulam was a member of the Lwów School of Mathematics
Lwów School of Mathematics
The Lwów School of Mathematics was a group of mathematicians who worked between the two World Wars in Lviv, then known as Lwów and located in Poland, but now located in western Ukraine. The mathematicians often met at the famous Scottish Café to discuss mathematical problems, and published in the...
. Its founders were Hugo Steinhaus
Hugo Steinhaus
Władysław Hugo Dionizy Steinhaus 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 University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics...
and Stefan Banach
Stefan Banach
Stefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
, who were professors at the University of Lwów
Lviv University
The Lviv University or officially the Ivan Franko National University of Lviv is the oldest continuously operating university in Ukraine...
. Mathematicians of this "school" met for long hours at the Scottish Café
Scottish Café
The Scottish Café was the café in Lwów where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology....
, where the problems they discussed were collected in the famous Scottish Book
Scottish Book
The Scottish Book was a thick notebook used by mathematicians of the Lwow School of Mathematics for jotting down problems meant to be solved. The notebook was named after the "Scottish Café" where it was kept....
, which is a thick notebook provided by Banach's wife. Ulam is a major presence in the Scottish 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.
Coming to America
In 1935, John von NeumannJohn von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, NJ
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, for a few months. In December of that year, Ulam sailed to America. In Princeton, he went to lectures and seminars, where he heard Oswald Veblen
Oswald Veblen
Oswald Veblen 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.-Life:...
, James Alexander
James Waddell Alexander II
James Waddell Alexander II was a mathematician and topologist of the pre-World War II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others...
, and Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
. During a tea party at von Neumann's house, he met G. D. Birkhoff, who suggested that he apply for a position with the Harvard Society of Fellows
Harvard Society of Fellows
The Harvard Society of Fellows is a group of scholars selected at the beginning of their careers by Harvard University for extraordinary scholarly potential, upon whom distinctive academic and intellectual opportunities are bestowed in order to foster their individual growth and intellectual...
.
From 1936 to 1939, after following up on Birkhoff's suggestion, Ulam spent summers in Poland and academic years at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in Cambridge, MA
Cambridge, Massachusetts
Cambridge is a city in Middlesex County, Massachusetts, United States, in the Greater Boston area. It was named in honor of the University of Cambridge in England, an important center of the Puritan theology embraced by the town's founders. Cambridge is home to two of the world's most prominent...
. Here, he worked with John C. Oxtoby to establish important results regarding ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, which appeared in Annals of Mathematics
Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...
in 1941.
On August 20, 1939, in Gdynia
Gdynia
Gdynia is a city in the Pomeranian Voivodeship of Poland and an important seaport of Gdańsk Bay on the south coast of the Baltic Sea.Located in Kashubia in Eastern Pomerania, Gdynia is part of a conurbation with the spa town of Sopot, the city of Gdańsk and suburban communities, which together...
, Józef Ulam, along with his brother Szymon, put his two sons, Stanislaw and 16 year old Adam
Adam Ulam
Adam Bruno Ulam was a Polish and American historian and political scientist at Harvard University. Ulam was one of the world's foremost authorities on Russia and the Soviet Union, and author of twenty books and many articles.-Biography:...
, on a ship headed for America. Within two weeks, 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 were victims of the Holocaust, Steinhaus was in hiding, Kuratowski was lecturing at the underground university
Education in Poland during World War II
This article covers the topic of underground education in Poland during World War II. Secret learning prepared new cadres for the post-war reconstruction of Poland and countered the German and Soviet threat to exterminate the Polish culture....
in Warsaw, Stożek and his two sons had been killed in the massacre of Lwów professors, Banach was surviving Nazi occupation by feeding lice at Rudolf Weigl's typhus research institute
Rudolf Weigl
Professor Rudolf Stefan Weigl was a famous Polish biologist and inventor of the first effective vaccine against epidemic typhus. Weigl founded the Weigl Institute in Lwów, Poland , where he did his vaccine-producing research.Of Austrian ethnic descent, Weigl was born in Přerov, Moravia...
, and the last problem had been recorded in the Scottish Book. In 1963, Adam Ulam
Adam Ulam
Adam Bruno Ulam was a Polish and American historian and political scientist at Harvard University. Ulam was one of the world's foremost authorities on Russia and the Soviet Union, and author of twenty books and many articles.-Biography:...
, who had become an eminent kremlinologist
Kremlinology
Kremlinology is the study and analysis of Soviet politics and policies based on efforts to understand the inner workings of an opaque central government. The term is named after the Kremlin, the seat of the Russian/Soviet government. Kremlinologist refers to academic, media, and commentary experts...
at Harvard, received a letter from George Volsky, who hid in Józef Ulam's house after deserting from the Polish army. This reminiscence gives a chilling account of Lwów's chaotic scenes in late 1939.
In 1940, after being recommended by Birkhoff, Ulam became an assistant professor at the University of Wisconsin
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
in Madison, WI
Madison, Wisconsin
Madison is the capital of the U.S. state of Wisconsin and the county seat of Dane County. It is also home to the University of Wisconsin–Madison....
. Here, in 1941, he became an American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
citizen. That year, he married Françoise Aron. She had been a French exchange student at Mount Holyoke College
Mount Holyoke College
Mount Holyoke College is a liberal arts college for women in South Hadley, Massachusetts. It was the first member of the Seven Sisters colleges, and served as a model for some of the others...
, whom he met in Cambridge, MA. They had one daughter, Claire. In Madison, Ulam met his friend and colleague C. J. Everett.
Manhattan Project
In late spring of 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, NMSanta Fe, New Mexico
Santa Fe is the capital of the U.S. state of New Mexico. It is the fourth-largest city in the state and is the seat of . Santa Fe had a population of 67,947 in the 2010 census...
. The letter was signed by Hans Bethe
Hans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...
, who had been appointed director of the theoretical division of Los Alamos National Laboratory
Los Alamos National Laboratory
Los Alamos National Laboratory is a United States Department of Energy national laboratory, managed and operated by Los Alamos National Security , located in Los Alamos, New Mexico...
by J. Robert Oppenheimer, its scientific director.
At this time, Ulam knew nothing of Los Alamos. To learn more, he checked out of the library a New Mexico guidebook. On the checkout slip, he found the names of his Wisconsin colleagues, Joan Hinton
Joan Hinton
Joan Hinton was a nuclear physicist and one of the few women who worked for the Manhattan Project in Los Alamos. She lived in the People's Republic of China after 1949, where she and her husband Erwin Engst participated in China’s efforts at developing a socialist economy, working extensively in...
, David Frisch
David H. Frisch
David H. Frisch was an American physicist who helped develop the atom bomb in World War II and later became active in the disarmament movement....
, and Joseph McKibben, who had mysteriously disappeared from Madison to secret war work. This was Ulam's introduction to the Manhattan Project
Manhattan Project
The Manhattan Project was a research and development program, led by the United States with participation from the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army...
.
Hydrodynamical calculations of implosion
A few weeks after Ulam reached Los AlamosLos Alamos, New Mexico
Los Alamos is a townsite and census-designated place in Los Alamos County, New Mexico, United States, built upon four mesas of the Pajarito Plateau and the adjoining White Rock Canyon. The population of the CDP was 12,019 at the 2010 Census. The townsite or "the hill" is one part of town while...
in February 1944, the project experienced a crisis. In April, Emilio Segrè
Emilio G. Segrè
Emilio Gino Segrè was an Italian-born, naturalized American, physicist and Nobel laureate in physics, who with Owen Chamberlain, discovered antiprotons, a sub-atomic antiparticle.-Biography:...
discovered that plutonium
Plutonium
Plutonium is a transuranic radioactive chemical element with the chemical symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, forming a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation...
made in reactors would not work in a gun-type
Gun-type fission weapon
Gun-type fission weapons are fission-based nuclear weapons whose design assembles their fissile material into a supercritical mass by the use of the "gun" method: shooting one piece of sub-critical material into another...
plutonium weapon like the "Thin Man
Thin Man nuclear bomb
The "Thin Man" nuclear bomb was a proposed plutonium gun-type nuclear bomb which the United States was developing during the Manhattan Project...
", which was being developed in parallel with a uranium weapon, the "Little Boy
Little Boy
"Little Boy" was the codename of the atomic bomb dropped on Hiroshima on August 6, 1945 by the Boeing B-29 Superfortress Enola Gay, piloted by Colonel Paul Tibbets of the 393rd Bombardment Squadron, Heavy, of the United States Army Air Forces. It was the first atomic bomb to be used as a weapon...
" that was dropped on Hiroshima. This problem threatened to waste an enormous investment in new reactors at the Hanford site
Hanford Site
The Hanford Site is a mostly decommissioned nuclear production complex on the Columbia River in the U.S. state of Washington, operated by the United States federal government. The site has been known by many names, including Hanford Works, Hanford Engineer Works or HEW, Hanford Nuclear Reservation...
and to make slow separation of uranium isotopes
Isotope separation
Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes, for example separating natural uranium into enriched uranium and depleted uranium. This is a crucial process in the manufacture of uranium fuel for nuclear power stations, and is...
the only way to prepare fissile
Fissile
In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission. By definition, fissile materials can sustain a chain reaction with neutrons of any energy. The predominant neutron energy may be typified by either slow neutrons or fast neutrons...
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 Kistiakowsky
George Bogdan Kistiakowsky was a Ukrainian-American chemistry professor at Harvard who participated in the Manhattan Project and later served as President Eisenhower's Science Advisor...
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
Critical mass
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 A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The...
, where neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
multiplication leads to a nuclear chain reaction
Nuclear chain reaction
A nuclear chain reaction occurs when one nuclear reaction causes an average of one or more nuclear reactions, thus leading to a self-propagating number of these reactions. The specific nuclear reaction may be the fission of heavy isotopes or the fusion of light isotopes...
, which suddenly releases a large amount of energy. Cylindrical implosive configurations had been studied by Seth Neddermeyer
Seth Neddermeyer
Seth Henry Neddermeyer was an American physicist who co-discovered the muon, and later championed the implosion design of the plutonium atomic bomb, at the Manhattan Project....
, 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
Explosive lens
An explosive lens—as used, for example, in nuclear weapons—is a highly specialized explosive charge, a special type of a shaped charge. In general, it is a device composed of several explosive charges that are shaped in such a way as to change the shape of the detonation wave passing through it,...
. 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
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
calculations were needed to predict and minimize asymmetries that would spoil a nuclear detonation. Of these calculations, Ulam said:
The hydrodynamical problem was simply stated, but very difficult to calculate – not only in detail, but even in order of magnitude. In this discussion, I stressed pure pragmatism and the necessity to get a heueristic survey of the problem by simpleminded brute force, rather than by massive numerical work.
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.
Statistics of branching and multiplicative processes
Even the inherent statistical fluctuations of neutronNeutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
multiplication within the chain reaction
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....
, have implications with regard to implosion speed and symmetry. In November 1944, David Hawkins
David Hawkins (philosopher)
David Hawkins, was a professor whoseinterests included the philosophy of science, mathematics, economics, childhood science education, and ethics.. He also served as the official historian of the Manhattan Project....
and Ulam addressed this point in a report entitled "Theory of Multiplicative Processes I", whose last page gives some suggestions pertinent to bomb design. However, this report, which invokes generating functions
Probability-generating function
In probability theory, the probability-generating function of a discrete random variable is a power series representation of the probability mass function of the random variable...
, is also an early entry in the extensive literature on statistics of branching
Branching process
In probability theory, a branching process is a Markov process that models a population in which each individual in generation n produces some random number of individuals in generation n + 1, according to a fixed probability distribution that does not vary from individual to...
and multiplicative processes. In 1948, its scope was extended by another pioneering exploration by Ulam and C. J. Everett.
Early in the Manhattan project, Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
'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
Nuclear poison
A neutron poison is a substance with a large neutron absorption cross-section in applications, such as nuclear reactors. In such applications, absorbing neutrons is normally an undesirable effect...
by a xenon isotope
Xenon-135
Xenon-135 is an unstable isotope of xenon with a half-life of about 9.2 hours. 135Xe is a fission product of uranium and Xe-135 is the most powerful known neutron-absorbing nuclear poison , with a significant effect on nuclear reactor operation...
. He stayed until December 1945, overlapping Ulam's stay by about a year, during which they formed a relationship that became very fruitful after the war.
The contributions of von Neumann and Ulam to the "Fat Man
Fat Man
"Fat Man" is the codename for the atomic bomb that was detonated over Nagasaki, Japan, by the United States on August 9, 1945. It was the second of the only two nuclear weapons to be used in warfare to date , and its detonation caused the third man-made nuclear explosion. The name also refers more...
" weapons of the Trinity test
Trinity test
Trinity was the code name of the first test of a nuclear weapon. This test was conducted by the United States Army on July 16, 1945, in the Jornada del Muerto desert about 35 miles southeast of Socorro, New Mexico, at the new White Sands Proving Ground, which incorporated the Alamogordo Bombing...
and Nagasaki bombing were only part of a large scientific and engineering effort. Some other crucial contributions were Edward Teller
Edward Teller
Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...
's realization that implosive compression would facilitate nuclear detonation by significantly increasing the density of the plutonium sphere, Luis Alvarez
Luis Alvarez
Luis W. Alvarez was an American experimental physicist and inventor, who spent nearly all of his long professional career on the faculty of the University of California, Berkeley...
's development of exploding-bridgewire detonator
Exploding-bridgewire detonator
The exploding-bridgewire detonator is a type of detonator used to initiate the detonation reaction in explosive materials, similar to a blasting cap in that it is fired using an electric current...
s, which ensured that the explosive lenses would all fire at once, and Bruno Rossi
Bruno Rossi
Bruno Benedetto Rossi was a leading Italian-American experimental physicist. He made major contributions to cosmic ray and particle physics from 1930 through the 1950s, and pioneered X-ray astronomy and space plasma physics in the 1960s.-Biography:Rossi was born in Venice, Italy...
's RaLa experiment
RaLa Experiment
The RaLa Experiment, or RaLa, was a series of tests during and after the Manhattan Project designed to study the behavior of converging shock waves to achieve the spherical implosion necessary for compression of the plutonium pit of the nuclear weapon...
s, which tested (without plutonium) various weapon designs to arrive at one that produced an accurately symmetrical implosion.
Post war Los Alamos
In September 1945, Ulam left Los Alamos to become an associate professor at the University of Southern CaliforniaUniversity of Southern California
The University of Southern California is a private, not-for-profit, nonsectarian, research university located in Los Angeles, California, United States. USC was founded in 1880, making it California's oldest private research university...
in Los Angeles
Los Angeles, California
Los Angeles , with a population at the 2010 United States Census of 3,792,621, is the most populous city in California, USA and the second most populous in the United States, after New York City. It has an area of , and is located in Southern California...
. 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
Nicholas Metropolis
Nicholas Constantine Metropolis was a Greek American physicist.-Work:Metropolis received his B.Sc. and Ph.D. degrees in physics at the University of Chicago...
from Los Alamos and the famous mathematician Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, 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. Much later, after Ulam's death, another friend, Gian-Carlo Rota
Gian-Carlo Rota
Gian-Carlo Rota was an Italian-born American mathematician and philosopher.-Life:Rota was born in Vigevano, Italy...
, asserted that the attack did change Ulam's personality; afterwards, he turned from rigorous pure mathematics to more speculative conjectures concerning the application of mathematics to physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
. However, this suggestion was not accepted by Françoise Ulam.
By late April 1946, Ulam had recovered enough to attend a secret conference at Los Alamos to discuss thermonuclear weapons
Nuclear weapon design
Nuclear weapon designs are physical, chemical, and engineering arrangements that cause the physics package of a nuclear weapon to detonate. There are three basic design types...
. Those in attendance were: Ulam, von Neumann, Metropolis, Teller, Stan Frankel
Stan Frankel
Stanley Phillips "Stan" Frankel was an American computer scientist. He was born in Los Angeles, attended graduate school at the University of Rochester, received his PhD in physics from the University of California, Berkeley, and began his career as a post-doc student under J. Robert Oppenheimer...
, and others. Throughout his participation in the Manhattan Project, Teller's efforts had been directed toward the development of a "super" bomb based on nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
, 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, 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 ENIACENIAC
ENIAC was the first general-purpose electronic computer. It was a Turing-complete digital computer capable of being reprogrammed to solve a full range of computing problems....
. Shortly after returning to Los Alamos, Ulam participated in a review of results from these calculations. Earlier, while playing solitaire
Patience (game)
Patience is a genre of tabletop games, consisting of card games that can be played by a single player. Patience games can also be played in a multiplayer fashion....
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
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
immediately saw the significance of this insight, and in March 1947, proposed to Robert Richtmyer, leader of the theoretical division, a statistical approach to the problem of neutron diffusion in fissionable material. Because Ulam had often mentioned his uncle "who just had to go to Monte Carlo" to gamble, Metropolis dubbed the statistical approach "The Monte Carlo method
Monte Carlo method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
". In this context, the fact that Ulam's uncle Michael died in Monte Carlo
Monte Carlo
Monte Carlo is an administrative area of the Principality of Monaco....
is interesting.
In 1948, ENIAC was moved from the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
's Moore School of Electrical Engineering
Moore School of Electrical Engineering
The Moore School of Electrical Engineering at the University of Pennsylvania came into existence as a result of an endowment from Alfred Fitler Moore on June 4, 1923. It was granted to Penn's School of Electrical Engineering, located in the Towne Building...
, where it had been conceived and designed by John Mauchly
John Mauchly
John William Mauchly was an American physicist who, along with J. Presper Eckert, designed ENIAC, the first general purpose electronic digital computer, as well as EDVAC, BINAC and UNIVAC I, the first commercial computer made in the United States.Together they started the first computer company,...
and J. Presper Eckert
J. Presper Eckert
John Adam Presper "Pres" Eckert Jr. was an American electrical engineer and computer pioneer. With John Mauchly he invented the first general-purpose electronic digital computer , presented the first course in computing topics , founded the first commercial computer company , and...
, to the Ballistic Research Laboratory
Ballistic Research Laboratory
The Ballistic Research Laboratory at Aberdeen Proving Ground, Maryland was the center for the United States Army's research efforts in ballistics and vulnerability/lethality analysis....
in Aberdeen, MD
Aberdeen, Maryland
As of the census of 2000, there were 13,842 people, 5,475 households, and 3,712 families residing in the city. The population density was 2,166.2 people per square mile . There were 5,894 housing units at an average density of 922.4 per square mile...
. Here, with von Neumann's inspiration, Richard Clippinger suggested that it could be configured in a jury rigged version of the stored-program architecture
Von Neumann architecture
The term Von Neumann architecture, aka the Von Neumann model, derives from a computer architecture proposal by the mathematician and early computer scientist John von Neumann and others, dated June 30, 1945, entitled First Draft of a Report on the EDVAC...
that has become standard on most computers. This architecture greatly facilitated programming, and on September 16, 1948, ENIAC was first run as a stored-program computer
Stored-program computer
A stored-program computer is one which stores program instructions in electronic memory. Often the definition is extended with the requirement that the treatment of programs and data in memory be interchangeable or uniform....
. Soon, it was put to work on Monte Carlo calculations of neutron transport by Metropolis and von Neumann. In 1949, Metropolis and Ulam published the first unclassified paper on the Monte Carlo method.
Statistical techniques began in the 18th century, when Buffon's needle
Buffon's needle
In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry...
was proposed as a way to approximate the number π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
. Fermi used them in the 1930s, and when he heard of Ulam's breakthrough, created the FERMIAC
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 :...
, which performs a mechanical simulation of random diffusion of neutrons. These ideas embody the context of Ulam's innovation, but not its essence, which is the probabilistic use of electronic computers to carry out rapidly the large numbers of tedious repetitions that are needed to achieve usable accuracy. As computers improved, these methods became more useful. In particular, Monte Carlo calculations carried out on modern massively parallel
Massively parallel
Massively parallel is a description which appears in computer science, life sciences, medical diagnostics, and other fields.A massively parallel computer is a distributed memory computer system which consists of many individual nodes, each of which is essentially an independent computer in itself,...
supercomputers are embarrassingly parallel
Embarrassingly parallel
In parallel computing, an embarrassingly parallel workload is one for which little or no effort is required to separate the problem into a number of parallel tasks...
applications, whose results can be very accurate.
Teller–Ulam design
On August 29, 1949, the Soviet UnionSoviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
tested its first fission bomb, the RDS-1. Created under the supervision of Lavrentiy Beria
Lavrentiy Beria
Lavrentiy Pavlovich Beria was a Georgian Soviet politician and state security administrator, chief of the Soviet security and secret police apparatus under Joseph Stalin during World War II, and Deputy Premier in the postwar years ....
, who sought to duplicate the American effort, this weapon was nearly identical to Fat Man, for its design was based on information provided by spies Klaus Fuchs
Klaus Fuchs
Klaus Emil Julius Fuchs was a German theoretical physicist and atomic spy who in 1950 was convicted of supplying information from the American, British and Canadian atomic bomb research to the USSR during and shortly after World War II...
, Theodore Hall
Theodore Hall
Theodore Alvin Hall was an American physicist and an atomic spy for the Soviet Union, who, during his work on US efforts to develop the first atomic bomb during World War II , gave a detailed description of the "Fat Man" plutonium bomb, and of processes for purifying plutonium, to Soviet...
, David Greenglass
David Greenglass
David Greenglass was an atomic spy for the Soviet Union who worked in the Manhattan project. He was the brother of Ethel Rosenberg.-Biography:...
, and others. In response, on January 31, 1950, President Truman
Harry S. Truman
Harry S. Truman was the 33rd President of the United States . As President Franklin D. Roosevelt's third vice president and the 34th Vice President of the United States , he succeeded to the presidency on April 12, 1945, when President Roosevelt died less than three months after beginning his...
announced a crash program to develop a fusion bomb.
To advocate an aggressive development program, Ernest Lawrence
Ernest Lawrence
Ernest Orlando Lawrence was an American physicist and Nobel Laureate, known for his invention, utilization, and improvement of the cyclotron atom-smasher beginning in 1929, based on his studies of the works of Rolf Widerøe, and his later work in uranium-isotope separation for the Manhattan Project...
and Luis Alvarez
Luis Alvarez
Luis W. Alvarez was an American experimental physicist and inventor, who spent nearly all of his long professional career on the faculty of the University of California, Berkeley...
came to Los Alamos, where they conferred with Norris Bradbury
Norris Bradbury
Norris Edwin Bradbury , was an American physicist who was born in Santa Barbara, California. He served as director of the Los Alamos National Laboratory for 25 years , succeeding J. Robert Oppenheimer, who personally chose Bradbury for the position of director after working closely with him on the...
, the laboratory director, and with George Gamow
George Gamow
George Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...
, Teller, 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 fusion reaction
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
had been ongoing since 1942, but the design was still essentially the one originally proposed by Edward Teller
Edward Teller
Edward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...
. His concept was to put some tritium
Tritium
Tritium is a radioactive isotope of hydrogen. The nucleus of tritium contains one proton and two neutrons, whereas the nucleus of protium contains one proton and no neutrons...
and/or deuterium
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
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 fusion reaction
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
. Reactions of these isotopes of hydrogen
Isotopes of hydrogen
Hydrogen has three naturally occurring isotopes, sometimes denoted 1H, 2H, and 3H. Other, highly unstable nuclei have been synthesized in the laboratory but not observed in nature. The most stable radioisotope is tritium, with a half-life of 12.32 years...
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 could not lead to a successful weapon, and many more had moral 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 cary out these studies, von Neumann decided to use electronic computers. This approach was made possible by his access to computers: ENIAC at Aberdeen, a new computer, MANIAC
MANIAC I
The MANIAC was an early computer built under the direction of Nicholas Metropolis at the Los Alamos Scientific Laboratory...
, at Princeton, and its twin, which was under construction at Los Alamos. Ulam enlisted C. J. Everett to follow a completely different approach, which was guided by physical intuition. With the aid of a cadre of female "data analysts", including Françoise Ulam, who performed computations on mechanical calculator
Mechanical calculator
A mechanical calculator is a device used to perform the basic operations of arithmetic. Mechanical calculators are comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator....
s, and whose efforts were supplemented and confirmed by Everett's use of his slide rule
Slide rule
The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction.Slide rules come in a...
, they carried out laborious and extensive computations of many thermonuclear scenarios. 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. In late 1950, these conclusions were confirmed by von Neumann's results.
In January 1951, Ulam had another idea: Put the fission bomb and fusion fuel together inside a massive casing. When the bomb detonated, the casing would contain the explosion long enough for mechanical shock to heat and compress the fusion fuel, and for fission neutrons to ignite nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
. On the recommendation of his wife, Ulam discussed this idea with Bradbury and J. Carson Mark
J. Carson Mark
J. Carson Mark was a Canadian-born American mathematician known especially for his work on developing nuclear weapons for the United States at Los Alamos National Laboratory.-Biography:...
before he told Teller about it. Almost immediately, Teller saw its merit. However, he noted that soft X-radiation from the fission bomb would compress the thermonuclear fuel more strongly than mechanical shock and suggested ways to enhance this effect. On March 9, 1951, Teller and Ulam submitted a joint report describing these innovations. A few weeks later, Teller suggested the placement at the center of the fusion fuel of a fissile
Fissile
In nuclear engineering, a fissile material is one that is capable of sustaining a chain reaction of nuclear fission. By definition, fissile materials can sustain a chain reaction with neutrons of any energy. The predominant neutron energy may be typified by either slow neutrons or fast neutrons...
rod or cylinder, the "spark plug", whose detonation 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 designated as the "Teller–Ulam design".
In May 1951, during Operation Greenhouse
Operation Greenhouse
Operation Greenhouse was the fifth American nuclear test series, the second conducted in 1951 and the first to test principles that would lead to developing thermonuclear weapons . Conducted at the new Pacific Proving Ground, all of the devices were mounted in large steel towers, to simulate air...
, the explosions of devices "George" and "Item
Greenhouse Item
Greenhouse Item was an American nuclear test conducted on May 25, 1951, as part of Operation Greenhouse at the Pacific Proving Ground, specifically on the island of Engebi in the Eniwetok Atoll in the Central Pacific Ocean. This test explosion was the first test of a boosted fission weapon...
" proved that a fission explosion could trigger non-sustaining fusion reactions in a mixture of deuterium and tritium. Although these tests did not produce a thermonuclear detonation, they showed that a small fusion component could enhance significantly a fission explosion. These results, validated Teller's concept of boosted fission
Boosted fission weapon
A boosted fission weapon usually refers to a type of nuclear bomb that uses a small amount of fusion fuel to increase the rate, and thus yield, of a fission reaction. The neutrons released by the fusion reactions add to the neutrons released in the fission, as well as inducing the fission reactions...
, which is incorporated in nearly all modern weapons.
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, Hans Bethe
Hans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...
returned to Cornell University
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
, but he was deeply involved as a consultant in the development of thermonuclear weapons. 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.
In September 1951, Teller went back to his prewar position at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
. At about the same time, Ulam went on leave as a visiting professor at Harvard. In 1952, Teller joined the newly established Livermore
Lawrence Livermore National Laboratory
The Lawrence Livermore National Laboratory , just outside Livermore, California, is a Federally Funded Research and Development Center founded by the University of California in 1952...
branch of the University of California Radiation Laboratory
Lawrence Berkeley National Laboratory
The Lawrence Berkeley National Laboratory , is a U.S. Department of Energy national laboratory conducting unclassified scientific research. It is located on the grounds of the University of California, Berkeley, in the Berkeley Hills above the central campus...
, where he was director from 1958 to 1960.
Ivy Mike
Ivy Mike was the codename given to the first United States test of a thermonuclear weapon, in which a major part of the explosive yield came from nuclear fusion. It was detonated on November 1, 1952 by the United States at on Enewetak, an atoll in the Pacific Ocean, as part of Operation Ivy...
was detonated on Enewetak Atoll, within the US Pacific Proving Grounds
Pacific Proving Grounds
The Pacific Proving Grounds was the name used to describe a number of sites in the Marshall Islands and a few other sites in the Pacific Ocean, used by the United States to conduct nuclear testing at various times between 1946 and 1962...
. 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.
On August 12, 1953, the Soviets detonated their RDS-6s
Joe 4
Joe 4 was an American nickname for the first Soviet test of a thermonuclear weapon on August 12, 1953. It utilized a scheme in which fission and fusion fuel were "layered", a design known as the Sloika model in the Soviet Union...
device, which incorporated the Sloika design that had been developed by Andrei Sakharov
Andrei Sakharov
Andrei Dmitrievich Sakharov was a Soviet nuclear physicist, dissident and human rights activist. He earned renown as the designer of the Soviet Union's Third Idea, a codename for Soviet development of thermonuclear weapons. Sakharov was an advocate of civil liberties and civil reforms in the...
and Vitaly Ginzburg
Vitaly Ginzburg
Vitaly Lazarevich Ginzburg ForMemRS was a Soviet theoretical physicist, astrophysicist, Nobel laureate, a member of the Russian Academy of Sciences and one of the fathers of Soviet hydrogen bomb...
. This code name, which refers to a Russian layered pastry, reflects the design, in which fusion fuel is layered within a fission bomb. This configuration is similar to that of Greenhouse Item
Greenhouse Item
Greenhouse Item was an American nuclear test conducted on May 25, 1951, as part of Operation Greenhouse at the Pacific Proving Ground, specifically on the island of Engebi in the Eniwetok Atoll in the Central Pacific Ocean. This test explosion was the first test of a boosted fission weapon...
and of the "Alarm Clock", which Teller proposed as an implementation of his original ideas. Although the Soviet design did not lead to full thermonuclear detonation, it embodied Ginzburg's crucial idea of November 1948, which was to use lithium deuteride as a fusion fuel. When fission neutrons break apart the lithium nuclei, some of the fragments are tritium nuclei, which participate in a very effective fusion reaction with the deuterium that is already present. The great advantage is that, in effect, both tritium and deuterium are encapsulated in a dense chemical compound. There is no need to use the cryogenic equipment for liquid deuterium that made the Ivy Mike device impractical as a weapon. On March 1, 1954, this advantage was realized in the Castle Bravo
Castle Bravo
Castle Bravo was the code name given to the first U.S. test of a dry fuel thermonuclear hydrogen bomb device, detonated on March 1, 1954 at Bikini Atoll, Marshall Islands, as the first test of Operation Castle. Castle Bravo was the most powerful nuclear device ever detonated by the United States ,...
test, which was the largest American thermonuclear explosion, and which provided a prototype for nearly all subsequent thermonuclear weapons. On November 22, 1955, the Soviets set off RDS-37
RDS-37
RDS-37 was the Soviet Union's first "true" hydrogen bomb, first tested on November 22, 1955. The weapon had a nominal yield of approximately 3 megatons. It was scaled down to 1.6 megatons for the live test....
, which was their first thermonuclear bomb. It embodied the Teller-Ulam design, which Sakharov and other Soviet scientists had worked out independently.
Fermi-Pasta-Ulam 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 PastaJohn Pasta
John R. Pasta was a computer scientist who is remembered today for the Fermi–Pasta–Ulam experiment, a result much discussed among physicists and researchers in dynamical systems and chaos theory, and as the head of the department of Computer Science at the University of Illinois at...
, 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 June 9, 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 pattern of spending academic years at the University of Chicago and summers at Los Alamos. During the summer of 1954, Pasta and Ulam 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 problem, which is often designated by the abbreviation FPU
With the aid of standard mathematics, the 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 amazing behavior is very different from the expected equipartition of energy
Equipartition theorem
In classical statistical mechanics, the equipartition theorem is a general formula that relates the temperature of a system with its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition...
. It remained mysterious until 1965, when Kruskal and Zabusky
Norman Zabusky
Norman J. Zabusky is an American physicist, who is noted for the discovery of the soliton in the Korteweg–de Vries equation, in work completed with Martin Kruskal. This result early in his career was followed by an extensive body of work in computational fluid dynamics, which led him more...
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
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
solutions. This means that FPU behavior can be understood in terms of solitons.
Nuclear propulsion
During the war, Ulam and Frederick ReinesFrederick Reines
Frederick Reines was an American physicist. He was awarded the 1995 Nobel Prize in Physics for his co-detection of the neutrino with Clyde Cowan in the neutrino experiment, and may be the only scientist in history "so intimately associated with the discovery of an elementary particle and the...
considered nuclear propulsion
Nuclear propulsion
Nuclear propulsion includes a wide variety of propulsion methods that fulfil the promise of the Atomic Age by using some form of nuclear reaction as their primary power source.- Surface ships and submarines :...
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, some of their ideas were pursued during Project Rover
Project Rover
Project Rover was an American project to develop a nuclear thermal rocket. The program ran at the Los Alamos Scientific Laboratory from 1955 through 1972 and involved the Atomic Energy Commission, and NASA. The project was managed by the Space Nuclear Propulsion Office.Nuclear reactors for the...
, which explored the use of nuclear reactors to power rockets. It was administered by Los Alamos, but many of its activities were carried out elsewhere. In particular, fuel rods were developed at the Rocky Flats Plant
Rocky Flats Plant
The Rocky Flats Plant was a United States nuclear weapons production facility near Denver, Colorado that operated from 1952 to 1992. It was under the control of the United States Atomic Energy Commission until 1977, when it was replaced by the Department of Energy .-1950s:Following World War II,...
, and twenty rockets were tested at the Nuclear Reactor Development Station, which was located at Jackass Flats
Area 25
Area 25 is the largest named area in the Nevada Test Site at , and has its own direct access from Route 95. The majority of Area 25 is composed of a shallow alluvial basin called Jackass Flats....
within the Nevada Test Site
Nevada Test Site
The Nevada National Security Site , previously the Nevada Test Site , is a United States Department of Energy reservation located in southeastern Nye County, Nevada, about northwest of the city of Las Vegas...
.
In 1955, Ulam and C. J. Everett proposed, in contrast to Rover's continuous heating of rocket exhaust
Nuclear thermal rocket
In a nuclear thermal rocket a working fluid, usually liquid hydrogen, is heated to a high temperature in a nuclear reactor, and then expands through a rocket nozzle to create thrust. In this kind of thermal rocket, the nuclear reactor's energy replaces the chemical energy of the propellant's...
, to harness small nuclear explosions for propulsion. Project Orion
Project Orion (nuclear propulsion)
Project Orion was a study of a spacecraft intended to be directly propelled by a series of explosions of atomic bombs behind the craft...
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
Freeman Dyson
Freeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...
, who commented on the decision to end Orion in a famous article, "Death of a Project".
In 1957, Bradbury appointed Ulam and John H. Manley as research advisors to the laboratory director. 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, metalurgy, 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
Fermi–Ulam model
The Fermi–Ulam model is a dynamical system that was introduced by Polish mathematician Stanislaw Ulam in 1961.FUM is a variant of Enrico Fermi's primary work on acceleration of cosmic rays, namely Fermi acceleration. The system consists of a particle that collides elastically between a fixed...
, which is an extension of Fermi's theory of the acceleration of cosmic rays
Fermi acceleration
Fermi acceleration , sometimes referred to as diffusive shock acceleration , is the acceleration that charged particles undergo when being repeatedly reflected, usually by a magnetic mirror. This is thought to be the primary mechanism by which particles gain non thermal energies in astrophysical...
. Another, with Paul Stein was titled "Quadratic Transformations" It was an early investigation of chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
.
Return to academia
During his years at Los Alamos, Ulam was a visiting professor at: Harvard, 1951/52, MIT, 1956/57, the University of California, San DiegoUniversity of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
, 1963, and the University of Colorado
University of Colorado at Boulder
The University of Colorado Boulder is a public research university located in Boulder, Colorado...
, 1961/62 and 1965/67. In 1967, the last of these positions became permanent, when Ulam was appointed as professor and Chairman of the Department of Mathematics at Colorado. However, he kept his residence in Santa Fe, which made it convenient to spend summers as a consultant in Los Alamos.
In Colorado, Ulam's research interests turned toward biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
. 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 some of his earlier ideas on branching processes to biological inheiritance. Another, report, with William Beyer, Temple F. Smith, and M. L. Stein, titled "Metrics in Biology", introduced some new ideas of quantification. In 1968, recognizing this emphasis, the University of Colorado School of Medicine
University of Colorado Denver
The University of Colorado Denver, shortened as CU Denver, UC Denver, or UCD, is a public university in the United States state of Colorado. It is one of three schools of the University of Colorado system. The university has two campuses — one in downtown Denver at the Auraria Campus, and the other...
appointed Ulam as Professor of Biomathematics, and he held this position until his death.
When he retired from Colorado in 1975, Ulam had begun to spend winter semesters at the University of Florida
University of Florida
The University of Florida is an American public land-grant, sea-grant, and space-grant research university located on a campus in Gainesville, Florida. The university traces its historical origins to 1853, and has operated continuously on its present Gainesville campus since September 1906...
, where he was a graduate research professor.
Except for sabbaticals at the University of California, Davis
University of California, Davis
The University of California, Davis is a public teaching and research university established in 1905 and located in Davis, California, USA. Spanning over , the campus is the largest within the University of California system and third largest by enrollment...
, 1982/83, and at Rockefeller University
Rockefeller University
The Rockefeller University is a private university offering postgraduate and postdoctoral education. It has a strong concentration in the biological sciences. It is also known for producing numerous Nobel laureates...
, 1980/84, this pattern of spending summers in Colorado and Los Alamos and winters in Florida continued until Ulam died in Santa Fe on May 13, 1984.
Mathematics
In pure mathematics, he worked in set theorySet theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
(including measurable cardinal
Measurable cardinal
- Measurable :Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ...
s and abstract measures
Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...
), topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, and other fields.
Some results that bear his name are:
- Borsuk-Ulam theorem
- Mazur–Ulam theorem
- Hyers–Ulam–Rassias stabilityHyers–Ulam–Rassias stabilityThe stability problem of functional equations originated from a question of Stanislaw Ulam, posed in 1940, concerning the stability of group homomorphisms. In the next year, Donald H. Hyers gave a partial affirmative answer to the question of Ulam in the context of Banach spaces, that was the first...
- Lucky numberLucky numberIn number theory, a lucky number is a natural number in a set which is generated by a "sieve" similar to the Sieve of Eratosthenes that generates the primes.Begin with a list of integers starting with 1:...
(1955) - Ulam spiralUlam spiralThe Ulam spiral, or prime spiral is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes...
(1963)
- Ulam conjecture (in Number Theory)
- Ulam's Conjecture (in Graph theory)
also called the Reconstruction conjectureReconstruction conjectureInformally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam.-Formal statements:... - Ulam's gameUlam's gameIn mathematics, Ulam's game, or the Rényi–Ulam game, is the problem of trying to guess an object with yes-no questions, where some of the answers may be wrong. introduced the game, though his paper was overlooked for many years, and...
- Ulam numbersUlam numbersAn Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence starts with U1 = 1 and U2 = 2...
Impact and legacy
With his pivotal role in the development of thermonuclear weapons, Stanislaw Ulam changed the world. He felt very little guilt. According to Françoise Ulam: "Stan would reassure me that, barring accidents, the H-bomb rendered nuclear war impossible." Since the end of World War II, this prediction has held.During his career, Ulam was awarded honorary degrees by the Universities of New Mexico
University of New Mexico
The University of New Mexico at Albuquerque is a public research university located in Albuquerque, New Mexico, in the United States. It is the state's flagship research institution...
, Wisconsin, and Pittsburgh
University of Pittsburgh
The University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...
.
The University of Florida maintains a journal named after Ulam, Ulam Quarterly Journal
In 1980, he appeared in the television documentary The Day After Trinity
The Day After Trinity
The Day After Trinity is a 1980 documentary film directed and produced by Jon H. Else in association with KTEH public television in San Jose, California. The film tells the story of J...
.
Quotations of Ulam
It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.
It seems to me that the impact and role of the electronic computer will significantly affect pure mathematics.
Ulam's answer to a question by Senator John O. Pastore
John O. Pastore
John Orlando Pastore was a Rhode Island Democratic Party politician who was a United States Senator from Rhode Island and the 61st Governor of Rhode Island , and was the first Italian American to hold either position.-Early life and career:Born in Providence on March 17, 1907, he attended...
at a congressional committee hearing, "Outer Space Propulsion by Nuclear Energy", on January 22, 1958:
Anyway, the future as a whole of mankind is to some extent involved inexorably now with going outside the globe.
Ulam was among the first to refer to the technological singularity
Technological singularity
Technological singularity refers to the hypothetical future emergence of greater-than-human intelligence through technological means. Since the capabilities of such an intelligence would be difficult for an unaided human mind to comprehend, the occurrence of a technological singularity is seen as...
, and possibly the originator of the metaphor itself. In May 1958, while referring to a conversation with John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
:
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.
Quotations about Ulam
Georgia O'KeeffeGeorgia O'Keeffe
Georgia Totto O'Keeffe was an American artist.Born near Sun Prairie, Wisconsin, O'Keeffe first came to the attention of the New York art community in 1916, several decades before women had gained access to art training in America’s colleges and universities, and before any of its women artists...
, on seeing Ulam at a party in Santa Fe, NM:
Who is that man?
Hans Bethe
Hans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...
1968:
After the H-bomb was made, reporters started to call TellerEdward TellerEdward Teller was a Hungarian-American theoretical physicist, known colloquially as "the father of the hydrogen bomb," even though he did not care for the title. Teller made numerous contributions to nuclear and molecular physics, spectroscopy , and surface physics...
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.
Books
- Stanisław Ulam, A Collection of Mathematical Problems, New York, Interscience Publishers, 1960.
- Mark KacMark KacMark Kac was a Polish mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. Kac completed his Ph.D...
and Stanisław Ulam, Mathematics and Logic: Retrospect and Prospects, New York, Praeger, 1968. Dover paperback reprint edition ca. 1990. - Stanisław Ulam, Sets, Numbers and Universes, Cambridge, Massachusetts, 1974.
- Stanisław Ulam, Adventures of a Mathematician, New York, Charles Scribner's Sons, 1983 (autobiography).
- Necia Grant Cooper, Roger Eckhardt, Nancy Shera, editors, From Cardinals to Chaos, Cambridge University Press (1989).
- Stanisław Ulam, Analogies Between Analogies: The Mathematical Reports of S.M. Ulam and his Los Alamos Collaborators. Berkeley: University of California Press, 1990.
External links
- Stanisław Ulam’s Contributions to Theoretical Theory in Letters in Mathematical Physics, 1985. Ulam's contributions to theoretical biology are reviewed in terms of his work in cellular automata theory, population biology, Fermi-Pasta-Ulam results, pattern recognition, and biometric spaces.