Leonhard Euler (1707 - 1783) and John Von Neumann (1903 - 1957) are, in terms of memory, calculation, and quick thinking, two of the most intelligent people to have ever lived. There are numerous stories about Von Neumann's lightning calculation and extraordinary memory, but I will tell some lesser known stories that show he was also incredibly fast with higher level thinking:
The statistician David Blackwell told the following story in an interview:
"Also, I got a chance to meet Von Neumann that year. He was a most impressive man. Of course, everybody knows that. Let me tell you a little story about him.
When I first went to the Institute, he greeted me, and we were talking and he invited me to come around and tell him about my thesis. Well, of course I thought that was just his way of making a new young visitor feel at home, and I had no intention of telling him about my thesis. He was a big, busy, important man. But then a couple of months later, I saw him at tea and he said 'When are you coming around to tell me about your thesis? Go in and make an appointment with my secretary.' So I did, and later I went in and started telling him about my thesis.
He listened for about ten minutes and asked me a couple of questions and then he started telling me about my thesis. What you could have really done is this, and probably this is true, and you could have done it in a somewhat simpler way, and so on. He was a really remarkable man. He listened to me talk about this rather obscure subject and in ten minutes knew more about it than I did. He was extremely quick. I think he may have wasted a certain amount of time, by the way, because he was so willing to listen to second- or third-rate people and think about their problems. I saw him do that on many occasions."
Eugene Wigner told this story in an interview:
"He [Von Neumann] wrote no articles on number theory. But once I told him - this is a story which is perhaps of some interest - that I was much impressed by a new theorem about which I had read. He said, 'Did you read the proof?' I said, 'No, but the theorem itself is really amazing.' He said, 'Well, would you like to have a proof?' I said, 'Yes, if you can give me one.' Then he asked me six questions: 'Do you know this theorem?', 'Do you know this theorem?' ... six theorems. I knew three and I didn't know the other three. And he gave me a wonderful proof, never mentioning the theorems which I did not know and using the theorems which I did know. He was amazing in this respect."
This story is ridiculous. Constructing a mathematical proof is not an easy undertaking in general, but Von Neumann not only came up with a proof on the spot, he wrote Wigner a custom-made proof.
However, Von Neumann did have limitations. Wigner also wrote:
"I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed.
But
Einstein's understanding was deeper even than von Neumann's. His mind
was both more penetrating and more original than von Neumann's. And that
is a very remarkable statement. Einstein took an extraordinary pleasure
in invention. Two of his greatest inventions are the Special and
General Theories of Relativity; and for all of Jansci's brilliance, he
never produced anything as original."
Paul Halmos wrote something similar in his memoir about Von Neumann ("The Legend of John Von Neumann):
"He [Von Neumann] 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 impossible to be unclear in thought or in expression. His insights were illuminating and his statements were precise."
Jacob Bronowski was a friend of JVN - and also a mathamatician. He rated JVN's intellectual gifts very highly, and that potentially he ocould have been one of the all-time greats, a first-rate world historical genius.
ReplyDeleteBut Bron. believed that JVN wasted in talents by pusuing other goals (politics, money, power, glamour) - and therefore never left behind the great work of which he was capable.
In other words, JVN lacked the inner motivation and concentrated fascination with 'his problem' that, for example, the young Newton possessed in abundance.
This may be perhaps explicable - in terms of this post - in JVN being too much of an all rounder, too 'normal' - lacking in the lopsidedness that genius level attainment requires?
I think Bronowski may have been right. I have heard that Oskar Morgenstern was also concerned that later in life, Von Neumann was too impressed with people from the "military-industrial complex."
Delete"In other words, JVN lacked the inner motivation and concentrated fascination with 'his problem' that, for example, the young Newton possessed in abundance.
This may be perhaps explicable - in terms of this post - in JVN being too much of an all rounder, too 'normal' - lacking in the lopsidedness that genius level attainment requires?"
That is a good suggestion. Since Von Neumann could make some sort of contribution to almost anything he chose to work on, it was hard for him to pick a few things to focus on. And he was willing to work on anything rather than try to discern "his problem."
There is a great quote about Newton that I think sums up Newton's attitude towards his studies:
"Newton's goal was incomparably more vast than the discovery of the 'mathematical principles of natural philosophy.' Newton wished to penetrate the divine principles beyond the veil of nature, and beyond the veils of human record and received revelation as well. His goal was the knowledge of God, and for achieving that goal he marshaled the evidence from every source available to him: mathematics, experiment, observation, reason, revelation, historical method, myth, the tattered remnants of ancient wisdom. ... one result of the restricted interests of modernity has been to look askance at Newton's biblical, chronological, and alchemical studies: to consider his pursuit of prisca sapientia [ancient wisdom] as irrelevant. None of those was irrelevant to Newton, for his goal was considerably more ambitious than a knowledge of nature. His goal was Truth, and for that he utilized every possible resource."
Betty Jo Teeter Dobbs, The Janus Faces of Genius: The Role of Alchemy in Newton's Thought (2002)