“The Legend of John Von Neumann”, 1973-04 (; backlinks):
John von Neumann was a brilliant mathematician who made important contributions to quantum physics, to logic, to meteorology, to war, to the theory and applications of high-speed computing machines, and, via the mathematical theory of games of strategy, to economics.
…The heroes of humanity are of two kinds: the ones who are just like all of us, but very much more so, and the ones who, apparently, have an extra-human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue. Von Neumann’s greatness was the human kind. We can all think clearly, more or less, some of the time, but von Neumann’s clarity of thought was orders of magnitude greater than that of most of us, all the time. Both Norbert Wiener and John von Neumann were great men, and their names will live after them, but for different reasons. Wiener saw things deeply but intuitively; von Neumann saw things clearly and logically.
What made von Neumann great? Was it the extraordinary rapidity with which he could understand and think and the unusual memory that retained everything he had once thought through? No. These qualities, however impressive they might have been, are ephemeral; they will have no more effect on the mathematics and the mathematicians of the future than the prowess of an athlete of a hundred years ago has on the sport of today.
The “axiomatic method” is sometimes mentioned as the secret of von Neumann’s success. In his hands it was not pedantry but perception; he got to the root of the matter by concentrating on the basic properties (axioms) from which all else follows. The method, at the same time, revealed to him the steps to follow to get from the foundations to the applications. He knew his own strengths and he admired, perhaps envied, people who had the complementary qualities, the flashes of irrational intuition that sometimes change the direction of scientific progress. For von Neumann it seemed to be impossible to be unclear in thought or in expression. His insights were illuminating and his statements were precise.
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