So, I didn't really think about logic much; with one very very big exception, and that is this: I liked number theory and high school the first year of college I read a book by Claudian Wright, the Theory of Numbers, a lovely book, and um, I particularly like the part about partitions, uh, decompositions into squares, and you get the feeling that Jakobi and those early people had developed almost a calculus of infinite power series expansions, from which they deduced many of these wonderful results. So the thought began to occur to me, what is the calculus of power series, which could reduce every question of this type, in the same sense that there is a divisive procedure for polynomials. And I had *thread* almost no logic. So I thought about it and I was very, I thought I was making progress, but I essentially was doing was rediscovering how to formalize number theory elementary types of ***** functions, and I was very happy with myself. And I came to the University of Chicago and told people this was my dream. Uh, well the only type of students that were in to logic, that and there was nobody in faculty, with the exception, perhaps of Saunders Mac Lean, who had written a *capricious* logic ******* having kept up with the subject for many many years. And some of the students said "Well we can make this *by the way, it's Gödel's theorem." I said "What's Gödel's" I said "No. Gödel's theorem is a theorem of philosophy. It has nothing to do with the county and province of number theory." I just couldn't believe it. So they said well *Cleamy* is going to come and give a lecture at Chicago. Uh, why don't you ask Cleamy. So Cleamy came, and there was a **** professor *** you only saw him at tea time. And so there was a tea, and I walked up to him, basically "I want to ask you a question." He said, "Well, what is it you want to do?" And I told him. And then in a very firm voice he said "No! That's impossible."
...theory, so I... purpose theory... so I got these... of mathematics and read it and I mean, I had to read that section. And I still had the impression that nobody could prove something about number theory by reasoning about general things, about what is true, what is a proof. And so I read it... and for a few days I was convinced it was wrong and I went up to one of the older students and I said, "Look, I found a mistake," and he was very contemptuous, and after a few days of course I realized that his proof was right. Um, but it wasn't, it was almost, uh, it may be at the same time, almost, almost, uh, depressing, to think that this man was so superior to me that by thinking in the most general terms he could derive the result which, which had tremendous implications for number theory, at least the kinds of things I want to do, so he was my master, I mean.. very like me, I, I, I didn't, I wasn't, still wasn't, to.. for the logic, "Please look," then somebody can correct me, had very little about set theory, and uh, I couldn't even find a reference to his thinking, to his result on constructable sets other than the Princeton... reference, I was talking to Pilking Putnam; he's notoriously oblique, and, ooh, one of the minor offshoots of my work is I felt that people lost their fear of that monograph and so when you can actually work with this stuff. But, it was very difficult for me, uh, actually some of them in the collective works discusssed this,
The professor being referenced seems to be "Stephen Cole Kleene" according to the web. Some edits:
0:07 I liked number theory and in high school, the first year of college
0:32 So the thought began to occur to me, Was there a calculus of power series
0:38 there is a decision procedure for polynomials
0:42 and I had read almost no logic
0:50 I thought I was making progress--what I essentially was doing
0:53 number theory of *all* recursive functions
1:01 well there weren't any students who were into logic then, and there was nobody
1:10 [capricious] logic, in the sense of having kept up with the subject in many, many years
1:38 there was a U/I [unintelligible] was very afraid of the professor, you only saw him at tea time.
Forgive me for overlapping so much with someone else's work in what follows--I didn't see the continuity from the first section at first, and by the time I realized I was already heavily into the transcription. Anyway, I did go on from there.
~1:50 That [would imply?] Godel's theorem. So I thought it was time to read Godel's theorem. And I still was very dubious. So I got Kleene's book, Introduction to Meta-Mathematics, I read it, and I mean, I had, had started to read that section, and I still had the impression that nobody could prove something about number theory by reasoning about general things about what is true, what is a proof. And so I read it, a sketch of it, and for a few days I was convinced that it was wrong, and I went up to one of the older students and said "Look, I found a mistake," and he was rather contemptuous, and after a few days of course I realized Godel's proof was right. Uh, but it wasn't, it was almost, um, invading, and at the same time, almost, almost, uh, depressing, to think that this man was so superior to me, that by thinking in the most general terms he could derive the result which, which had tremendous implications for number theory, at least the kind of things I wanted to do. So he was my master, I mean, he didn't even appear to [U/I]. I, I didn't, I wasn't, I still wasn't too much with logic. Kleene's book, maybe somebody can correct me, had very little about set theory. And uh, I couldn't even find a reference to his complete, to his result on constructable sets other than the Princeton monograph, which, I was talking with Hilary Putnam--he's notoriously opaque. And one of the minor offshoots of my work was I felt that people lost their fear of that monograph, they saw, when you actually worked with this stuff. But it was very difficult to read. Uh, [actually] Sullivet [PH phonetic rendition] in the collected works, discusses why he thinks Godel wrote it in such an incomprehensible way, but so he was. He was a very meticulous person.
3:34 So I was lying in bed, not being able to sleep, still suffering from jet lag, and I thought, well I need some jokes, I need some literary references. And some thoughts came back to me in my, in my bed, in my strange state, and I remembered, I had an English teacher in New York City, Mr. Seligman, who was a great admirer of the essays of Francis Bacon. I think Bennie [PH] grew up from Anglo Saxon background, so even though he crossed the essays of Sir Francis Bacon. And he wrote one of his essays called, Of Truth. And what does he say? What is truth? said Pontius Pilot, and would not stay for an answer. So that was the discussion of truth. But there was another concept of truth which occurred to me, and that is, another one of my heroes in my late teenage years was the novelist Marcel Proust. He said, What is memory? The truth of memory, you know, something is God, [all/the wrong?] God, but is memory the truth of what happened? And I feel that way about Godel, when I heard that music, it actually made me feel quite emotional, and uh, I thought well he heard this music, I bet he really liked it, and I never discussed music with him, that's--I think it was said it was his favorite piece. And s-so suddenly this image came back to me. The other weird feeling I must tell you, uh, there's a lovely exhibit on Godel, I will say something perhaps I shouldn't, my wife is probably shaking her head right now, I think it's a lovely exhibit with one, one very bad exception: I don't think references to his wife were at all appropriate and I think they should have been omitted completely. Anyhow, I was walking down the steps. And suddenly I saw a marker on the steps, it said, in German, On this spot was murdered Professor Schlick [PH]--I forget his name. And it sort of sent chills up my spine, partly because I'm Jewish and I thought, well, he was murdered by the Nazis. It wasn't quite correct. But also there was a weird similarity that I had a colleague who was murdered by a deranged student also, called Lou, and so that also gave me a very, a very strange feeling. So the question is what kind of tr--what do you mean by truth? Well, w-one thing we discussed at the panel the other day was how many people were formalists, how many people were realists? Realists all those that believe that the abstract world of sets exists, and every statement is either true or false. I want to propose something which I'm sure will be hotly, uh, poo-pooed by people like Hugh Wooden [PH] that I think in my work we have an alternative thing, we have many universes, and they're very rich, and they involve mathematical complications. Uh, Si [PH] Friedman referred to the fact that Godel's work on set theory involved mathematical technique. Well I'm teaching a course right now on set theory, and I've found it hard to remember some of the details. So my work really did get into some tricky points, and so now we have to reconstruct all these universes, and some sense I'm very happy with that. I don't claim that this, in itself, [viciates? initiates?] the program. People who want to, uh, who want to describe it. 6:42