Let me say a couple things about now Newton and my picture of him, then we will look the rest of the class at the specific readings for today. My picture of him, I've already given you. He had the capacity when he worked on a problem, to concentrate on it at very substantial length very effectively.

When you actually look at problems he worked on versus other people, and I'll give you one later tonight. Keith and I don't know how else to describe this, it's obviously something I can't do, myself, or I'd probably be a mathematician. He had a capacity to identify where the difficulty in any problem was, pretty, almost right off.

The rest of us try things, trying to sort of search out where's the hub of the problem. He an ability to identify the hub of the problem, and then all of the effort goes into it, goes under the real difficulty. He sometimes resorts to approximate methods for that.

He sometimes resorts to really a genius roundabout ways of doing it. But he's constantly focusing on that. Once he understands, and gets control of the real problem, things start falling into place for him. So as a result, he does things in far fewer pages, than other people at the same time did.

And it's that capacity, the satisfaction he got working on problems, the capacity to stay with them and constantly to succeed, that I tend to think of is what's peculiar about him. With one other feature, my Jerusalem talk was entitled something to the effect of The Next Question Beyond.

Once he gets a solution to anything, he then starts asking, almost invariably, what's this telling me? What further can I learn from this? And he goes, the Principia grows out of nine handwritten pages, asking questions, what's this telling me. It becomes 500 pages 20 months later because he keeps asking further questions.

We'll start seeing that in the next two weeks. It's the combination of being able to solve problems and then, once he solves them, asking the next question asking what it was about this problem that is important, or something like that, and building on it. He does that is such a sustained fashion, that it's rather spectacular time and time again.

When he finally hits a problem in the Principia, the three body problem that he can't solve, he really seems shocked that he's hit a problem that he can't solve. You almost have the feeling he's never had a problem in his life, mathematical problem, that he hadn't been able to solve.

That's my picture, but I'll end this before break with John Maynard Keynes's picture. Keynes became a Newton scholar. He bought a large fraction of the alchemical papers when they went on sale in the 1930s. He was in King's College. King's College is almost next door to Trinity College and he ended up in, I can't give you the date from this, I think it's 1943, writing a biographical note on Newton, that I think originally appeared.

I never quite remember this, whether it originally appeared on BBC, or someplace else. You can look this up. I'll give you the reference at the end, but here's what he says. Remember I just told you that this is about him, about Keynes. I just told you what I described about Newton is about me because of course like to think of myself as a problem solver.

And wish I were half as good as Newton. Well here what Keynes says. I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection. Anyone who has ever attempted pure scientific or philosophic thought knows how one can hold a problem momentarily in ones mind.

And apply all one's powers of concentration to piercing through it and how it will dissolve and escape and you find that you are surveying a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him, and that's as good an account of him as I've ever read.

He seemed to have had unlimited powers of concentration on a single problem without any outside thoughts intruding. And I trust none of us can do that for more than a matter of seconds, particularly if the problem's hard. Okay? And Keyne's just guessing, we don't know. We know that Newton, while working on the Principia, his meal brought to his quarters in Trinity College would be at the door the next morning.

We know that often happened. We know that when he solved the problem of the path to fastest descent, his niece tells us he was up until well into the middle of the night when the next morning, when she asked him why he was up so late, he made some remark about, we can't let these foreigners outdo us.

That's, she quotes it. So, at any rate, from here on, we're gonna be looking at individual problems of Newton. I've said what I want in a survey of him. And I can't stress too much, don't take too seriously anything I or anybody else says. Because he's a very difficult to fathom individual.