Von Neumann's ability to instantaneously perform complex operations in his head stunned other mathematicians. Eugene Wigner wrote that, seeing von Neumann's mind at work, "one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch."
Paul Halmos states that "von Neumann's speed was awe-inspiring."
Israel Halperin said: "Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car." Edward Teller wrote that von Neumann effortlessly outdid anybody he ever met, and said "I never could keep up with him".
Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met", and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception.He was a genius."
George Pólya, whose lectures at ETH Zurich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle:
Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph 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? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their 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."
Von Neumann had a very strong eidetic memory, commonly called 'photographic' memory.Herman Goldstine writes: "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 The 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."
It has been said that von Neumann's intellect was absolutely unmatched. “I always thought Von Neumann’s brain indicated that he was from another species, an evolution beyond man,” said Nobel Laureate Hans A. Bethe of Cornell University. "It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived," wrote Miklos Redai in "Selected Letters."
Glimm writes "he is regarded as one of the giants of modern mathematics".The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the "most scintillating intellect of this century", and Hans Bethe stated "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man".
Until a man is twenty-five, he still thinks, every so often, that under the right circumstances he could be the baddest motherfucker in the world. If I moved to a martial-arts monastery in China and studied real hard for ten years. If my family was wiped out by Colombian drug dealers and I swore myself to revenge. If I got a fatal disease, had one year to live, and devoted it to wiping out street crime. If I just dropped out and devoted my life to being bad.
Hiro used to feel this way, too, but then he ran into Raven. In a way, this was liberating. He no longer has to worry about being the baddest motherfucker in the world. The position is taken.
I don't know whether the following is true or false, and whether it is good to spread it, but it is a telling lesson about not building your worth upon your "achievements": here is a description of Von Neumann learning about his own upcoming death:
"... his mind, the amulet on which he had always been able to rely, was becoming less dependable. Then came complete psychological breakdown; panic, screams of uncontrollable terror every night. His friend Edward Teller said, "I think that von Neumann suffered more when his mind would no longer function, than I have ever seen any human being suffer."
Von Neumann's sense of invulnerability, or simply the desire to live, was struggling with unalterable facts. He seemed to have a great fear of death until the last... No achievements and no amount of influence could save him now, as they always had in the past. Johnny von Neumann, who knew how to live so fully, did not know how to die.
To be absolutely clear: I am certain I wouldn't behave any better faced with my own upcoming death. I just think it's not too good to heroise famoous people and stories about them to the point they are no longer recognizable as humans at all...
And to be fair to the great man, here is a nice biographical article by noone else but Paul Halmos himself:
You can read that anecdote as telling you something extra about von Neumann, or you can read it as a reminder of how awful and terrible a thing death is -- an indictment of the way most people accept wrongness instead of fighting it.
I've always been fascinated with Von Neumann. Inventing game theory, developing the quintessential computer architecture, putting quantum mechanics on an axiomatic basis, having almost as many theorems named after him as Gauss... Few of us can even hope to develop his depth of mastery in one field, much less in the breadth and variety of fields in which he achieved.
Neumann didn't develop the Von Neumann architecture. He was one of many who worked on the ENIAC/EDVAC machine where it was developed. He summarized much of the work that was done, in the abstract (meaning that it was not classified), and his First Draft was distributed.
Years later, when John Mauchly was defending his patents on digital computers (after it had become declassified), the First Report was brought up as a public disclosure.
Does anyone know of a biography of Von Neumann? I've looked for one many times and never found any. It's like he was five different men – he revolutionized so many fields, any of which would have been an epic accomplishment. He was also the only one who immediately understood the significance and consequences of Gödel's incompleteness result, according to Goldstein's biography of that other genius.
Turing's Cathedral[1] is not a proper biography, but it's mostly all about Von Nuemann during the period where he worked on the early computer. I have read most of it while in the bookstore, and it's really good.
> George Pólya, whose lectures at ETH Zurich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
Today, a lecturer is grateful if the majority of students stops playing WoW for 5 minutes during the lecture.
When you look at someone like Neumann you learn to be humble. The gap between him and an average guy like me is so large that it seems silly to worry about wether I'm good enough.
But here's the thing: I often don't know who I'm comparing myself with.
Took some pictures, posted them and looked at other profiles, went back to the camera, worked harder, rinse and repeat. Turned out, the others were working for National Geographics and the like.
People don't start out as the greatest mathematician in the last few centuries. And how do you even differentiate between talent and hard work?
I'm not quite sure what point this is making. No one should feel any inadequacy compared to von Neumann - his intellectual gifts were handed down at birth, they were a fluke of genetics, a statistical outlier. Comparing your intellectual achievements to his is like comparing your wealth to that of David Tisch or Larry Ellison's kids.
The author of the piece, however, is pretty clearly comparing herself to peers - "kids that have had a computer since 1987". This is a valid mode of self-criticism; you can legitimately glean some insights from comparing yourself and your actions to those of people in similar circumstances. If this results in feelings of inadequacy, well, just waving it away is a disservice to yourself.
Another variant of the story has the series vs average reasoning as a trick to see whether JvN was a mathematician or a physicist. When he answers immediately, the questioner exclaims, "Aha, you must be a physicist". He replied, "but the series was so simple". (it's geometric IIRC)
In the case of the fly, von Neumann probably just calculated the length of the first and second trip and calculated the sum using the self-similarity of the series.
Von Neumann's ability to instantaneously perform complex operations in his head stunned other mathematicians. Eugene Wigner wrote that, seeing von Neumann's mind at work, "one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch."
Paul Halmos states that "von Neumann's speed was awe-inspiring."
Israel Halperin said: "Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car." Edward Teller wrote that von Neumann effortlessly outdid anybody he ever met, and said "I never could keep up with him".
Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met", and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception.He was a genius."
George Pólya, whose lectures at ETH Zurich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle: Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph 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? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their 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."
Von Neumann had a very strong eidetic memory, commonly called 'photographic' memory.Herman Goldstine writes: "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 The 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."
It has been said that von Neumann's intellect was absolutely unmatched. “I always thought Von Neumann’s brain indicated that he was from another species, an evolution beyond man,” said Nobel Laureate Hans A. Bethe of Cornell University. "It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived," wrote Miklos Redai in "Selected Letters."
Glimm writes "he is regarded as one of the giants of modern mathematics".The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the "most scintillating intellect of this century", and Hans Bethe stated "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man".