★★★★☆ A nonlinear mathematician

Adventures of a Mathematician

S.M. Ulam

Have you ever heard of Stan Ulam? If you're a normal person (by which I mean, mostly, not a scientist or a mathematician), the answer is probably no. If you have heard of him, what you have heard, most likely, is that he played an important role in the development of thermonuclear bombs. ("Thermonuclear" means roughly the same thing as "H bomb", as opposed to fission bombs such as the ones detonated on Nagasaki and Hiroshima.)

If you're a mathematician, you have probably heard his name in connection with an impressive list of mathematical thingies like theorems, conjectures, numbers, etc. Wikipedia lists a dozen such things. In fact, the breadth of this list is more impressive than its length. His contributions range from analysis to number theory via topology, etc. He was one of the most important mathematicians of the twentieth century. If you're a mathematician, Ulam's work has probably been relevant to your own. It certainly has been to mine.

Adventures of a Mathematician is not like G.H. Hardy's A Mathematician's Apology. G.H. Hardy's job is to explain to Jill-on-the street what mathematics is. Ulam assumes you already know. What's more, he assumes he can discuss things like function spaces without explaining what that means.

Ulam is a refreshingly nonlinear story-teller. Although he does begin his first chapter with his childhood in Lwów, Poland, he immediately diverges from the story of his youth to the nature of his memories of childhood and to speculations about the way memory works. This sort of thing continues throughout Adventures. These digressions are often occasioned by the appearance in his narrative of some well-known scientist or mathematician. He has a great deal to say, for instance, about "Banach, Fermi, and von Neumann, ... the three great men whose intellects had impressed me the most."

Lwów had an important effect on Ulam's way of doing math. There was a vibrant mathematics culture there. Lwów mathematicians met in coffeeshops and talked for hours about math. His whole life Ulam remained a mathematician who made progress by talking with other mathematicians.

Now, about the H bomb. The most complete account that I have read is Richard Rhodes's Dark Sun: The Making of the Hydrogen Bomb. Edward Teller initiated the Super project, as the H-bomb was at first known. Ulam's first, and terribly important, contribution was negative. He (with John von Neumann) showed that Teller's idea would not work. The obvious implication was that thermonuclear weapons were not possible -- they were not out there in Platonic reality waiting to cast a shadow on this universe. (Russian physicists working independently also failed until the Mike Shot proved it could be done.) Then, one day, as recounted by Ulam's wife Françoise in a Postscript

The technical and political debates were raging when Stan, mulling over the problems, suddenly came upon a totally new and intriguing approach. Engraved on my memory is the day when I found him at noon staring intensely out of a window in our living room with a very strange expression on his face. Peering unseeing into the garden, he said: "I found a way to make it work." "What work?" I asked. "The Super" he replied. "It is a totally different scheme, and it will change the course of history."

It did. The Mike Shot was the successful test.

Teller did not take all this well. He was not happy when Ulam showed his original idea would not work, and he was not happy to share credit with Ulam when Ulam figured out how to make it work.

Adventures of a Mathematician is, I'm sorry to say, not suitable for general audiences. If you're a mathematician you may enjoy it. I learned a lot.

Adventures of a Mathematician on Amazon

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