The question that led to von Neumann’s involvement with Edvac in 1944-1945 was whether Teller’s design (the “Super”) for a hydrogen bomb was feasible. The question that von Neumann wanted to settle was whether in Teller’s design a fission explosion causes a self-sustained propagation of fusion in fusible material.
When Eniac was ready for the first trials in December 1945, von Neumann had convinced its owner, the Ballistics Research Laboratory, to give the ultra-secret computation from Los Alamos priority. Only the researchers from Los Alamos, Metropolis and Frankel, had the requisite security clearance to know the subject of the computation. The necessary personnel to help operating the Eniac did not. The problem was finessed by ruling that the equations and the data only were demoted from their lofty top-secret classification. Eniac performed splendidly, all 18,000 tubes working in unison for a sufficient proportion of time to get the computation completed in six weeks.
In April 1946 a conference was convened to discuss the prospects of the Super. The inner circle of researchers from the Manhattan project participated, including such people as Fermi and Bethe. Klaus Fuchs, who had been imported from Britain during the war to participate in the Manhattan project, attended as well.
Teller claimed that the computational results were encouraging. Bethe observed that certain effects were not taken into account; effects important enough to render the results meaningless. It had been out of the question to include these effects in the computation; in its limited scope the computation had already taxed the available resources. The consensus of the conference was that the computation had been inconclusive and that much further work was needed to settle the feasibility of the Super. On his own initiative Teller attached a note to the report that gave a much more positive impression.
Politically the consensus was that the development of A-bombs should continue, but that there was no need for a device with an explosive power a thousand times of the bombs dropped on Japan. This pointed to a much reduced laboratory at Los Alamos, without work on the Super. Yet Norris Bradbury, the successor of Oppenheimer as director of the laboratory, envisaged the work of the theoretical division to be shared equally on fission work and the Super. For him the laboratory was for research as much as for development.
Ulam had been among the majority who left Los Alamos in 1945. He did not return to his old job, but got an appointment at the University of Southern California. He was disappointed with the quality of the students and faculty. Soon after his appointment Ulam became seriously ill with encephalitis. On his recovery he was for a considerable time very weak, but recovered. By April 1946 he was well enough to attend the conference on the prospects of the Super. Soon after the conference Ulam received an offer for a position at Los Alamos, which he accepted.
Ulam’s normal mode of life was to be engaged in deep and difficult thoughts. However there was no question of this during his convalescence. Instead he whiled away the time with games of solitaire. He wondered what the probability of success was with a given variant of the game. He found the combinatorics of the situation forbidding . This suggested to Ulam that random sampling would be able to give a good approximation at the expense of playing, say, a hundred games.
On Ulam’s return to the Theoretical Division at Los Alamos the feasibility of the Teller Super was on the agenda. It occurred to him that rather than modeling the initiation process by means of partial differential equations, as had been done in the Eniac run of December 1945 – January 1946, it might be more effective to treat the history of each individual particle as a game of solitaire, with the physics of the interactions taking the place of the rules of the card game.
As before, von Neumann was Ulam’s partner in pursuing new ideas. This one in particular appealed to von Neumann, who caught on to the idea and called it the “Monte Carlo method”, after the eponymous casino in Monaco, at the time one of the few in world.
By 1947 the method was sufficiently developed to consider coding it for a computer. That is, if one were available. Edvac’s development was stalled: Eckert and Mauchly had left; von Neumann had decided to start a project to build a machine of his own design at the Institute of Advanced Study (IAS) in Princeton. Eniac took a while to recover from the move from the Moore School of Engineering in the University of Pennsylvania to its owners, the Ballistics Research Laboratory in Aberdeen, Maryland.
Von Neumann was ever on the look-out for opportunities for progress with the project. He arranged for a calculation to be performed on the SSEC, an impressive-looking electromechanical machine that was the showpiece at IBM’s headquarters at Fifth Avenue and 57th in Manhattan, displayed for the crowds passing by on the sidewalk [4, page 197].
Another feat of von Neumann was his scheme for converting Eniac to operate as a stored-program computer. The details were worked out by R.H. Clippenger and N. Metropolis in 1949. As a result the machine could be readied for a new calculation in an hour or so instead of a full day of unplugging and plugging cables.
The calculations on the Super continued according to the Monte Carlo method. Progress on the IAS machine was slow: at the institute there were no engineering facilities; space needed to be found for workshops, which had to be built from scratch and that against the opposition to any engineering or even experimental work among von Neumann’s colleagues. As a result the IAS machine was not the first von Neumann machine to be completed. It was preceded by projects started by students in the courses given at the Moore school. The first to become operational, in 1949, was Wilkes’s Edsac in Cambridge, England. Another early one was Seac at the National Bureau of Standards. When it started operating around Easter 1950, people from Los Alamos showed up asking if they could use the machine after midnight [4, page 210].
In the meantime the political climate had deteriorated compared to the sense of security that prevailed in 1946. In June of 1948 the Soviet Union reneged on its agreements by blockading the Western zone of Berlin. It had always been assumed that the Soviets would develop a nuclear bomb sooner or later. The assessment of their scientific and industrial capability was that it would be take at least a few years. In September 1949 the US detected an A-bomb test by the Soviets. In January 1950 Fuchs confessed having passed extensive and detailed information on the atomic bomb to the Soviets while he was working at Los Alamos during the war. It was then clear that the Soviet atomic scientists obtained detailed and extensive information throughout the Manhattan project with a delay of a few months. Fuchs was co-inventor with von Neumann of a secret patent filed in 1946 in connection with the H-bomb . “Until October 6, 1949, the President of the United States had never heard of the hydrogen bomb” [2, page 381]. We can safely assume that this was about three years after the Soviets had obtained detailed information about the US work on this subject.
On January 31 1950 president Truman announced that he had directed “the AEC to continue its work on all forms of atomic weapons, including the so-called hydrogen or super-bomb”. [2, page 407.4]. The fact that work on “all forms” were now authorized all the way from the President down energized Teller even more. At Los Alamos he kept hinting to Ulam that not enough work was being done on his original scheme for ignition of the Super. Ulam became irritated by this insistence. With Cornelius Everett he started on what Ulam called a “schematic pilot scheme” to get a ballpark estimate of the promise of Teller’s scheme. They started to work four to six hours each day with slide rules organizing their work writing with pencil on accountant’s spreadsheets [3 , p. 213-214, 2, p. 449].
After a few months it became clear that the Teller scheme was not going to work. Ulam was the first to blow the whistle [4, p. 210]. Thus the question that motivated von Neumann’s involvement in electronic computing and led to his invention of the modern computer, was answered in the end of 1950 by real brains supported by slide rules, pencil, and paper. Von Neumann’s own project, the IAS machine was ready for testing in January 1952, preceded by at least five von Neumann machines: Edsac and Manchester Mark I in England, Univac, SEAC, SWAC, and Whirlwind in the US.
To top it all off, Ulam went on to invent a design for an H-bomb that did work. Oppenheimer, who had always been luke-warm about work on the H-bomb, was so struck by the elegance of Ulam’s scheme that he judged that Los Alamos should go forward with a design that was technically “so sweet”.
Postscript: Erasing Ulam
Teller never forgave Ulam for being the one who provided the breakthrough. He pushed Ulam aside and from then on never meaningfully interacted with him. [2, p. 471]. Teller’s colleagues were appalled at Teller’s treatment of Ulam. Especially in response to Fermi’s urging, Teller published an account of the work leading down to the H-bomb as “The Work of Many People”, which appeared in Science in 1955. Note how Ulam is watered down to one of “many people”. Later in his memoirs Teller disowned even this, claiming the article to be a “white lie” to soothe wounded feelings .
 As of 2004 the experts in the field could do no better than confirm Ulam’s casual observation. “It is one of the embarrassments of applied mathematics that we cannot determine the odds of winning the common game of solitaire.” quoted from: “Solitaire: man versus machine” by X. Yan, P. Diaconis, P. Rusmevichientong, and B. Van Roy. Department of Statistics, Stanford University, 2004.
 Wikipedia article “Edward Teller”, April 1, 2013
 Wikipedia article “Radiation Implosion”, April 2, 2013