# Ann Varela: Stanislaw M. Ulam and the Adventures of a Mathematician

An Interview with Ann Varela: Stanislaw M. Ulam and the Adventures of a Mathematician

Michael F. Shaughnessy –

- Ann first of all, where was Stanislaw Marcin Ulam born, and what do we know about his early childhood years?

Lemberg, Poland was the place of Stanislaw Ulam’s birth in 1909. Today, that location is known as Lviv, Ukraine. Ulam’s relatives were successful as financiers and entrepreneurs, while his father made a comfortable living as a lawyer.

Turbulent times existed during Ulam’s youth, as the Polish-Ukrainian War was surging between 1918 and 1919. That battle was based on ethnic, social, and political diversities between the Polish and Ukrainian citizens living in the province. During most of this time, the Ulam family was living in Vienna, Austria. Once Ulam’s family returned to Lemberg, a six-month long conflict ensued between West Ukrainian People’s Republic and the Polish Army, ending in victory for Poland. Currently, the city is called Lviv by the Ukrainians, Lwów by the Poles, and Lemberg by the Austrians.

Ulam attended Lwów Gymnasium (equivalent to high school in the United States) until he graduated in 1927. After that, he was accepted to Lwów Polytechnic Institute, where he earned his Master of Arts degree in 1932, and a doctor of Science the following year. Studying, traveling to various European countries, and collaborating with professors was also a part of his college career. As a member of the Lwów School of Mathematics, Ulam and his fellow members met regularly at the Scottish Café. It was there that the *Scottish Book, *affectionately named after the café, was written. Originally, the members were known to write down mathematical problems to be solved directly on the café tabletops. Fortunately, someone in the group (rumored to be someone’s wife) had the clever idea to write the ideas and problems down in a book, so as not to lose or forget them. See Figure 1. Ulam contributed about 34% of the problems in the book either on his own or in collaboration with other members. I believe the café owner appreciated that as well.

Figure 1

It deeply saddens me to mention that the Nazi German occupation forces publicly executed most of the members of the Lwów School of Mathematics during the German invasion of Poland in 1939. Ulam’s father also perished in the invasion.

- Apparently, he was involved in the Manhattan Project at Los Alamos. What was he working on there and what were his contributions?

Ulam’s first encounter with John von Neumann in 1935 occurred when he began teaching at Princeton University in New Jersey. The next year, Ulam transferred to Harvard University in Boston Massachusetts. Four years later, Ulam was employed at the University of Wisconsin. In 1943, his friend John von Neumann invited Ulam to Los Alamos. Ulam was not sure about why he was invited to join von Neumann in Los Alamos, New Mexico; however, his detective work was brilliant to determine the nature of the new assignment. Apparently, Ulam checked out a book about Los Alamos at the library and noticed the names of other scientists who checked out the same book. Upon researching the expertise of those scientists, Ulam was able to determine the essence of the secret project awaiting him in the Land of Enchantment.

Ulam worked with physicist Edward Teller in Los Alamos on the hydrogen bomb. Ulam was able to detect an error with Teller’s model of the hydrogen bomb. Compression of the thermonuclear fuel within the bomb was one area of redesign suggested by Ulam. Teller successfully restructured this component to involve radiation implosion from the fission bomb within the hydrogen bomb model. See Figure 2.

Figure 2

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- It is said that he developed something called a “Monte Carlo Method” for examining complicated mathematical integrals that are involved in the theory of nuclear chain reactions. What exactly is a Monte Carlo Method and how does it relate to nuclear chain reactions?

To understand complex physical or mathematical systems, statisticians use the Monte Carlo Method. This process randomly generates numbers for input into those systems to generate a wide range of solutions. Once data is collected, one can determine the likelihood of each solution by dividing the number of times a particular solution was generated by the total number of trials. Since accuracy is imperative, larger numbers of trials will make the likelihood of the solutions more precise.

Ulam initially contemplated the probability of winning a game of solitaire and found that by merely playing numerous games of solitaire and recording the outcome of each game, he could determine the answer to his question. Next, Ulam thought that a similar approach could be utilized for the production and diffusion of neutrons in radioactive material. The Monte Carlo Method proved useful in predicting what might happen in atomic chain reactions, thus aiding in solving many of the multifaceted problems in producing an atomic bomb.

- During World War II and following it, President Truman suggested the U.S. develop a hydrogen bomb. How was Ulam involved?

According to his own calculations, Ulam determined Edward Teller’s design of the hydrogen bomb would certainly not work. About a year later, Ulam produced a new innovative design. Apparently, his solution was inspired from a dream. Ulam proposed a configuration in which x-rays emitted by the fission initiate the fusion of the hydrogen atoms. Ulam and Teller used this new design when they developed Ivy Mike, a staged fusion bomb. See Figure 3.

Figure 3

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- It is said that Ulam was one of the first mathematicians to use, and promote that scientists and mathematicians use computers for scientific research and experimentation. How original was this idea, and why is it important that we acknowledge this?

Ulam saw the advantage of computers when he developed the Monte Carlo Method. After all, computers are capable of generating a lot of data in a short time, compared to manually deriving solutions. Ulam was able to advance the flexibility and overall usefulness of computers.

- A book entitled “Adventures of a Mathematician” was published a while back- what does it contain?

Ulam’s autobiography, “Adventures of a Mathematician” describes the numerous, foremost mathematicians and scientists with whom he worked. Ulam discusses his childhood, education, and contributions to the field of mathematics and science. In particular, he discusses research that resulted in the development of the hydrogen bomb.

Ulam’s book contains some amusing anecdotes. Following are a few notable quotations from the book.

“*It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.”*

“*It is most important in creative science not to give up. If you are an optimist you will be willing to “try” more than if you are a pessimist.”*

“*The story that Dick Feynman could open safes whose combinations had been forgotten by their owners is true.”*

“*As one sharpens a knife on a whetstone, the brain can be sharpened on dull objects of thought. Every form of assiduous thinking has its value.”*

- He seemed to think that math could be applied to biology and other scientific fields…What were his contributions in this field?

Ulam returned to pursuits of research, education, and scholarship when he accepted a position as professor and Chairman of the Department of Mathematics at Boulder, Colorado. While there, he began conducting research in the field of biology, and soon became involved in the field of Biomathematics through the University of Colorado’s School of Medicine.

Ulam read about new discoveries in molecular biology. Those discoveries made him curious about a theoretical role, in which mathematical ideas could relate to biology. Ulam published a report with a Los Alamos associate, Robert Schrandt, about numerical modeling of evolutionary processes, which related his previous ideas about branching processes to biological inheritance.

Another collaboration resulted in a report about biometrics, which is the science of measuring physical properties of living beings. Some of the advantages of biometrics may include ease of use, security enhancement, no password required, and difficult to fool biometrics systems due to trait stability. There are different types of biometrics in use today involving either physiological (face, fingerprint, handprint, iris, and DNA) or behavioral (keystroke, signature, and voice) markers. Sensing machines are the result of biometrics. See Figure 4.

Figure 4

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Other examples of how biometrics is used can be seen in Figure 5.

Figure 5

https://pbs.twimg.com/media/DPYcfBfXkAA2yZs.jpg

- In the big scheme of things, why is his work important?

It is safe to say that Stanislaw Ulam’s work with thermonuclear weapons changed the world. Ulam’s work highly influenced additional fields of study such as, set theory, logic, topology, and other topics in mathematics. Some of his breakthroughs in one area resulted in solutions for other disciplines. Ulam credits luck and extremely good colleagues for his accomplishments.

- What have I neglected to ask about this great mathematician?

Although Ulam authored numerous books and reports (over 150 papers), his wife alleged he did not enjoy writing words down on paper due to the fact that he suffered from myopia on one eye and presbyopia in the other. Perhaps if he had been willing to wear corrective lenses, his mindset might have changed.