Stanislaw Ulam, the mathematician who 'fixed' the H-bomb

Stanislaw Ulam was instrumental in designing the hydrogen bomb.Bettmann (Bettmann Archive/Getty Images)

In 1942, the United States, in collaboration with Canada and the United Kingdom, created the Manhattan Project, with the objective of making the atomic bomb before the Axis powers.

In the theoretical design of the bomb, which was carried out in the secret laboratory of Los Alamos (New Mexico), many European scientists who had emigrated to the United States fleeing from the Nazis participated.

Among them was Stanislaw Ulam (born April 13, 1909 and died in 1984), a brilliant Polish mathematician who would contribute decisively to the design of the hydrogen bomb.

Ulam grew up in a wealthy family in the city of Lviv (now in Ukraine), where he became part of a vibrant mathematical community.

However, the offer of places in Polish universities was scarce, which, together with his Jewish status, led him to emigrate to America in 1935. Four years later, Germany invaded Poland.

All of his family would die in the Holocaust, except for his brother, who had accompanied him to the United States.

Ulam tried to enlist in the American aviation, but was fortunately rejected due to his vision problems and continued working at the university until 1943, when he was invited by the German physicist Hans Bethe to go to Los Alamos to work on the design of the atomic bomb.

Atomic energy can be obtained in two ways: with the fission process, which consists of splitting large atoms, such as uranium or plutonium, or with the fusion process, that is, joining small atoms, such as hydrogen.

In both cases the process begins with an "ignition" that causes the division (or union) of a few atoms, followed by a "chain reaction", in which the process spreads to the rest of the atoms.

The fusion process is more complicated and releases much more energy than the fission process.

But the fission process can be ignited with a traditional explosive, while the fusion process requires an enormous amount of energy, which can only be achieved using a fission bomb.

Therefore, to build a fusion bomb it is necessary to have obtained the fission bomb first.

When these processes are carried out at once, an enormous amount of energy is released and a bomb is obtained.

The bomb that uses the fusion process is usually called a “hydrogen bomb”, reserving the term “atomic bomb” for the bomb that uses the fission process.

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At Los Alamos, Ulam joined Edward Teller's team, which was investigating the design of the hydrogen bomb.

In July 1945 the Manhattan Project successfully tested the first atomic bomb and in August Hiroshima and Nagasaki were devastated by the first nuclear weapons in history.

The war was over, and most of the scientists at Los Alamos returned to their universities.

However, four years later, Russia obtained its first atomic bomb and US President Harry Truman then gave priority to the construction of the hydrogen bomb.

Teller got his team together again and resumed the project, which he directed in a very personal way.

The treatment between Ulam and Teller was tense from the beginning, which was not helped by the fact that the Pole, along with his collaborator Cornelius Everett, spent the first six months of their stay making detailed calculations on the viability of Teller's project. .

Casinos and simulations

To do this, he used a method, devised by himself, which he called the Monte Carlo method in honor of an uncle of his, who frequented the casino.

It consists of solving a problem from a large number of simulations.

For example, to find the area of ​​a complicated geometric figure (for which we cannot apply the formulas we learned at school) the traditional solution is to approximate the area with larger and larger simple figures contained in the geometric figure.

The Monte Carlo method, on the other hand, proposes to first take a square that contains the figure, and then calculate the probability that a random point of the square is on the figure by running a large number of simulations.

If, for example, the square measures six square meters and we estimate that 33% of the points of the square are in the figure,

The Monte Carlo method is usually much faster at solving problems than the traditional method.

Although he was not the first to conceive of such a method—it was already used in Buffon's needle experiment in the 18th century—Ulam was the first to realize its enormous potential, thanks to early computers being developed by his friend, the mathematician Hungarian John von Neumann.

Today the method is still used: it is basic in science and engineering and is used in fields as diverse as 3D animation or evolutionary biology.

These results, together with others he obtained with the Italian physicist Enrico Fermi, were withering: Teller's method did not allow the chain reaction to start or be maintained.

Soon after, the calculations would be repeated and confirmed with von Neumann's MANIAC computer.

However, in 1951 Ulam himself discovered that if hydrogen was sufficiently compressed using an atomic bomb, then the chain reaction would work.

After incorporating this change into Teller's design, known as the Teller-Ulam process, the hydrogen bomb project continued until the first explosion was achieved on Enewetak Atoll in 1952. The power of this bomb was 400 times greater. than the atomic bombs that fell on Japan in 1945.

Ulam's life is collected in the interesting autobiography

, which was made into a movie in 2020. There he explained his position regarding the investigation of atomic weapons: "Unlike those who violently opposed the bomb [...] , I never had doubts about purely theoretical works.

It did not seem immoral to me to try to calculate physical phenomena […].

What he thought is that one should not start projects that lead to catastrophe.

But once we know that such possibilities exist, isn't it better to examine whether they are real or not?

An even greater delusion is to believe that if you don't do it, it won't be able to be done […]”.

Federico Cantero Morán

Coffee and Theorems

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