Adventures of a mathematician [Hardcover]

Ulam was a pure mathematician, like Banach or ErdĆs, not like Dirac or Einstein. Yet he had the ability to escape from formal abstract considerations to think about how other sciences could show him a path to new mathematical considerations. In this regard, the Monte Carlo method and all his proposals to non-linear systems and usage of computers for exploring them may be are his greatest achievements (his H-bomb papers are classified, and I like to think Monte Carlo is still more useful).

For that matter, this book is of the greatest interest for he who wish to deepen his understanding of links between mathematics and physics, that are usually discussed by physicists often having very poor idea of what mathematics really are about. The chapter "random reflections" is a jewel which by itself makes worth buying the book, explaining for instance how practical problems can lead to new mathematical concepts, how mathematic theories link altogether, or advocating the use of computers to help mathematicians view new spaces of new objects. Many aside jokes or peculiar reflections--like how mathematics change according to what language one is exploring them with (English, Russian, French, German...)--make the book very entertaining, seldom boring. This "mathematician's mathematician"'s overview of this century's science (he also had some contributions to biology) is thus highly recommended.

(caution to purists: the book has been edited by Ulam's wife from recorded tapes, he didn't write it.)

Stan Ulam was head of the math department at U. of Colo., Boulder, where I was a doctoral candidate circa 1970. I hardly knew him to speak to, but heard about his participation in the Manhattan Project, and that many of those connected with it considered him to be the "father of the H-bomb" rather than Edward Teller. Having already been put off by the dryness and lack of application of a great deal of the math I'd studied, I was intrigued on hearing that a pure mathematician could have played such a central part in that effort. That, and the book's title, convinced me to buy it, even though I was an impoverished grad student.

There are many reasons why I love this story, but I think foremost is the picture of a gregarious, open, and sometimes mischievous man who was also bright enough to hold his own with the leading scientific minds of the 20th century. The sketches of the many famous people he worked with are priceless -- for example, Enrico Fermi, Richard Feynman, George Gamov. And especially John von Neumann, possibly the most brilliant mathematician of that time, certainly the most diverse and prolific (he practically invented the computer industry that I now work in). Having tried to read his work on game theory, it's especially comforting to me to hear Ulam refer to him as "Johnny".

My struggles with some of the math mentioned in the book give it special meaning to me, but this is not a technical book at all, and I hope that aspect won't be off-putting to non-mathematicians. Ulam was simply trying to give an honest picture, through the lens of his own experiences and friendships, of how people become mathematicians, of how essential group efforts are to progress in science and math, and of the staggering accomplishments that can result when people push the limits of thought. This book is about history and humankind, by one of the brightest and most thoughtful individuals who ever lived.