John Von Goddamn Neumann

VON GODDAMN NEUMANN

“You know, Herb, Johnny can do calculations in his head ten times as fast as I can. And I can do them ten times as fast as you can, so you can see how impressive Johnny is” Ñ Enrico Fermi (Nobel Prize in Physics, 1938)

“One had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch.” Ñ Eugene Wigner (Nobel Prize in Physics, 1963)

“I have sometimes wondered whether a brain like von NeumannÕs does not indicate a species superior to that of man” Ñ Hans Bethe (Nobel Prize in Physics, 1967)

“One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.”

“The four Budapesters were as different as four men from similar backgrounds could be. They resembled one another only in the power of the intellects and in the nature of their professional careers. Wigner […] is shy, painfully modest, quiet. Teller, after a lifetime of successful controversy, is emotional, extroverted and not one to hide his candle. Szilard was passionate, oblique, engag, and infuriating. Johnny […] was none of these. Johnny’s most usual motivation was to try to make the next minute the most productive one for whatever intellectual business he had in mind.”

“There was a seminar for advanced students in Zrich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. von Neumann didnÕt say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann”ÊÑÊGeorge Plya

“At a mathematical conference preceding Hilbert’s address, a quiet, obscure young man, Kurt Gdel, only a year beyond his PhD, announced a result which would forever change the foundations of mathematics. He formalized the liar paradox, “This statement is false” to prove roughly that for any effectively axiomatized consistent extension T of number theory (Peano arithmetic) there is a sentence ? which asserts its own unprovability in T.

John von Neumann, who was in the audience immediately understood the importance of Gdel’s incompleteness theorem. He was at the conference representing Hilbert’s proof theory program and recognized that Hilbert’s program was over.

In the next few weeks von Neumann realized that by arithmetizing the proof of Gdel’s first theorem, one could prove an even better one, that no such formal system T could prove its own consistency. A few weeks later he brought his proof to Gdel, who thanked him and informed him politely that he had already submitted the second incompleteness theorem for publication.”

“The only part of your thinking we’d like to bid for systematically is that which you spend shaving: we’d like you to pass on to us any ideas that come to you while so engaged.”

Excerpt, Letter from the Head of the RAND Corporation to von Neumann (Poundstone, 1992)

“Most mathematicians know one method. For example, Norbert Wiener had mastered Fourier transforms. Some mathematicians have mastered two methods and might really impress someone who knows only one of them. John von Neumann had mastered three methods: 1) A facility for the symbolic manipulation of linear operators, 2) An intuitive feeling for the logical structure of any new mathematical theory; and 3) An intuitive feeling for the combinatorial superstructure of new theories.”

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time, a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover?

There are two ways to answer the problem. One is to calculate the distance the fly covers on each leg of its trips between the two bicycles and finally sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly an hour after they start so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: “Oh, you must have heard the trick before!”

“What trick,” asked von Neumann, “all I did was sum the infinite series.”