Devlin's Angle

April 2009

Stanislaw Ulam - a Great American

This month (April 3, to be precise) marks the 100th anniversary of the birth of one of the most remarkable and influential men of the twentieth century: Stanislaw Ulam.

Ulam was a brilliant Polish mathematician who came to this country at the start of the Second World War, became a leading figure in the Manhattan Project at Los Alamos, New Mexico, the top secret project to develop the nuclear weapon that ended that war, and, together with Edward Teller, worked out the design of the thermonuclear weapons that were at the heart of the Cold War. But inventing the H-bomb was just one of many remarkable things he did.

He was one of those amazing people who did important work in many areas of mathematics - number theory, set theory, ergodic theory, and algebraic topology.

But his real strength was in his incredible ability to see things in a novel way. For example, during the war, when he was at the University of Wisconsin, his friend John von Neumann invited him to join him on a secret project in New Mexico. But he wouldn't say what it was. So Ulam went to the university library and checked out a book on New Mexico, and looked at the book's check-out card. It listed the names of all the scientists who had mysteriously disappeared from the university, and by looking at what they were experts in, Ulam was able to figure out what the project was probably about. He himself then joined the Manhattan Project. That was in 1943.

At Los Alamos, Ulam showed Edward Teller's early model of the hydrogen bomb was inadequate, and suggested a better method. He realized that you could put all the H-bomb's components inside one casing, stick a fission bomb at one end and thermonuclear material at the other, and use mechanical shock from the fission bomb to compress and detonate the fusion fuel. With a further modification by Teller, who saw that radiation from the fission bomb would compress the thermonuclear fuel much more efficiently than mechanical shock, that became the standard way to build an H-bomb.

It's a little known fact that Ulam and Teller applied for a patent on their design. I'm not sure if the patent was ever granted, but if it was and you want to build an H-bomb, you'd better make sure you get a license on the patent.

Another Ulam invention at Los Alamos was what we call the Monte Carlo method for solving complicated mathematical problems - originally the integrals that arise in the theory of nuclear chain reactions. The method gets its name from the fact that you use a computer to make lots of random guesses, and then use statistical techniques to deduce the correct answer from all the guesses. It's a great idea. These days the Monte Carlo method is used all over science and engineering to solve problems that would take too long to solve by other methods.

Perhaps the most amazing of Ulam's many suggestions was something called nuclear pulse propulsion. This is where you detonate a series of small, directional nuclear explosives against a large steel pusher plate attached to a spacecraft with shock absorbers.

Yes, you heard me right. Don't be fooled by the fact that this is the April column. This was not only a serious proposal, but it was taken seriously by the US government, who instigated the top-secret Project Orion to build such a spacecraft in the late 1950s and early 1960s.

In theory, such a propulsion system would generate about twelve times the thrust of the Space Shuttle's main engine. The spacecraft would be a lot bigger than the Shuttle, mind, and could carry over 200 people. It would get to Mars and back in four weeks, compared to 12 months for NASA's current chemically-powered rocket-craft, and it could visit Saturn's moons in a seven-month mission, something that would take about nine years using current NASA technologies.

A lot of progress was made during the course of the project, particularly on crew shielding and pusher-plate design, and the system appeared to be entirely workable when the project was shut down in 1965.

Why was it shut down? The main reason given was that the Partial Test Ban Treaty made it illegal.

Some people in the know have since suggested that President Kennedy initiated the Apollo program not only in response to the launch of Sputnik, but also to buy off the people who wanted to continue working on Orion.

Another Ulam idea that attracts a lot of interest these days is one of a number of so-called Singularity Events that have been contemplated. The one that tends to get the most press coverage these days is the supposed date when computers surpass people in intelligence, but Ulam's singularity is different. In a conversation with von Neumann that Ulam wrote about in 1958, he speculated that, because the progress of technology - and changes in the way we lives our lives - is constantly accelerating, there will come a point when we cannot keep up, and there will be what mathematicians call a singularity. But this time, it won't be a singularity in a physical system but in human history. So human affairs, as we know them, could not continue. You and I probably won't experience this. But our children might.

Ulam died in 1984. I never met him, but I did once occupy his office. In 1965, Ulam became a professor at the University of Colorado in Boulder, and in 1980 I spent the summer there. Ulam had remained a consultant at Los Alamos ever since the war, and used to spend part of each year there. That's where he was when I arrived, so his office in the Math Department was available, and they gave it to me.

So what sense of the man did I get from occupying his office? None whatsoever. It was completely empty apart from a single calculus textbook that I assume he had used to teach a course. But on reflection, maybe that does say something about him. When the subject of the invention of nuclear weapons comes up, the names that get bandied about are Oppenheimer and Teller. Ulam is rarely mentioned. Yet his contribution was no less than either of the two others. He was, it seems, a man more interested in the ideas themselves than the public recognition his work could bring him. Certainly, my Boulder colleagues who did know him speak warmly of him. In an era when Britney Spears and Paris Hilton are two of the most famous Americans on the planet, I'll vote for Stan Ulam as one of the greatest Americans of all time.

Devlin's Angle is updated at the beginning of each month. Devlin's most recent book for a general reader is The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, published by Basic Books.
Mathematician Keith Devlin (email: [email protected]) is the Executive Director of the Human-Sciences and Technologies Advanced Research Institute (H-STAR) at Stanford University and The Math Guy on NPR's Weekend Edition.