ADVENTURES OF A MATHEMATICIAN by S.M.Ulam

University of California Press, 1991. ISBN 0-520-07154-9

Ulam was born in Lwów , Poland, of an assimilated middle class Jewish family. In todays parlance he was a maths nerd, but at the same time part of the flowering of intellectual and artistic life of Cracow-Lwów in the interwar years in that part of the old Austro- Hungarian Empire.

He was influenced by Banach, Kuratowski and Mazur among others with the Scottish Café keeping a large notebook on hand so that they could write down new problems and results as they occured. This became the famous "Scottish Book".

Banach and Kuratowski knew von Neumann, and Ulam's correspondence with him led to a visit to Princeton in 1935. He stayed in the U.S. becoming a junior fellow at Harvard in 1936.

By 1943 he was at Los Alamos (again with the help of von Neumann), as a mathematician rather than a physicist or mathematical physicist but in the company of a unique group of individuals that included Bethe, Fermi, von Neumann, and Feynman.

The virtue of the book is the window that it opens on the scientific life at the creative level. His old professor and friend Steinhaus said that Ulam was the best formulator of problems in the world and it is interesting that it was him and not the physicists that devised the way to make the A Bomb work. He and his colleague Everett also showed that Teller's idea was a non starter (all done by slide rule with the MANIAC computer result later confirming it). (top)		 The portraits of the scientists are very good:

John von Neumann:

It was his feeling for and knowledge of the details of mathematical knowledge systems and the theoretical structure of formal systems that enabled him to conceive of flexible programming... By suitable flow diagramming and programming, an enormous variety of problems became calculable on one machine with all connections fixed. Before his invention one had to pull out wires and reconnect plug boards each time a problem was changed (? what about Flowers - see review of "The Secret War").

Enrico Fermi:

At the same time he had decided in his youth to spend at least an hour a day thinking in a speculative way. I liked this paradox of a systematic way of thinking unsystematically. Fermi had a whole arsenal of mental pictures, illustrations, as it were, of important laws and effects, and he had a great mathematical technique, which he only used when necessary. Actually it was more than mere technique; it was a method for dissecting a problem and attacking each part in turn. With our limited knowledge of introspection this cannot be explained at the present time.

The last chapter of the book is entitled Random Reflections on Mathematics and Science and it is easily worth finding the book for this chapter alone. He looks in an original way at the aesthetic character of theories, language, simulations (he invented the Monte Carlo technique), biology and much else.

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