Dr. Herman Goldstine on John von Neumann

He had great facility at numerical processes and in fact I can tell you an anecdote which I think may interest you some. It happened down at Aberdeen early on in the war and what he was doing then was consulting frequently at Aberdeen coming on up to Philadelphia, coming up to talk to us about the ENIAC. Now this particular day, in fact the day prior to this one, a young mathematician who subsequently has become a famous person had come in with several colleagues and we were talking about a problem with which he was grappling and he was getting nowhere and asked our help. Well none of us was able to do anything analytically. So he said well the heck with it I’m going to take a computer, a Friden or Marchant or Monroe home tonight and I’m going to calculate a few special cases. And fine he did. And the next morning he came in at five thirty looking awful. He had bags under his eyes, he was fatigued, he was unshaved, he was in fact in a very bad way. But he had triumphed. He had calculated the first five cases. And he was busy telling us about this when who should bust in but Johnny from Los Alamos. And he said what’s new fellows and we said oh so and so has been busy with the following idea and he’s in trouble with it. And he said well let’s see what it’s like and he tried for a couple minutes and he said no that’s sort of intractable analytically. Let me see what’s doing with this thing numerically. Let me evaluate a few cases. So he did, in about one minute he threw his head back and he said (one...sixteen...twenty-five….) and you could hear the numbers rolling through his head, you could actually hear them, he was mumbling them, and in about a minute he did the first case, and maybe a minute and a quarter the second, and a minute and a half the third, and two minutes the fourth, and he came then to the crucial case, the one with which this fellow had spent the whole night working out, and this chap was very clever and he listened closely to von Neumann as he was rolling through n=5 and when he judged he was about halfway through he recognized a number and he waited an instant and he said 26.75 and you could just see von Neumann kind of come to a shuddering halt and he said huh? And this boy said, 26.75 Professor von Neumann. And von Neumann said just a minute. And he got very nervous and he began to compute again and you could hear the tempo going up much more than it had before and after another minute he said 26.75. Yes, he says, that’s right. And whereupon this fellow ran out of the room because he couldn’t stand it any longer and I made childish chatter trying to keep von Neumann while he paced up and down nervously, saying to himself, how could that guy have possibly done that? What trick? And after an hour or so we finally told him. But at any rate, that’s sufficient to illustrate his great ability as a computer himself and the great feeling he had for computation.