English Script Request

Twenty-four year old Paul Cohen went to Hartley Rogers, the well known MIT logician and asked him "what's the best problem in logic?". Of course, Hartley without hesitation said "the undecidability(?) of the Chuman(?) hypothesis". I don't know if this story is true, but I do know that a few years later, Paul Cohen did succeed in proving the undecidability(?) of CH, one of the landmark results, and perhaps most famous result of logic after Godel.
The technique that professor Cohen developed to do this, the method of forcing(?) is today then the second of three most important techniques in said theory.

It's with great pleasure that I introduce Professor Paul Cohen, who's ...(?) "My interaction with Kurt Godel, the man at work"

"Hello, is this working?"

Audience members: "yes"

"Well, let me apologise, then, since this is not a standard talk, I'm not going to present
any astounding ...(?) predictions(?) of a future, uh, analogies with the, with the right ...(?), or anything like that. It's a personal talk, and I must say that I was rather moved last night, especially when they played Hoffmann: Tales of Hoffmann the barcarolle, and to think that Godel enjoyed that music. And as I was explaining (have explained?) it was a great pleasure for me to have sitting at the table ...(sir?) Hilary Putnam(?), who I knew about at the time I did my work, and he jogged my memory about things about Godel that I... that I... I will come back to this. What he said about Godel's interesting... I think would be universally agreed... Godel was a fragile person, and the people who knew him sort of took care of him. They felt... one definitely felt responsible almost for him, but for me it was a tremendously emotional thing, for me to be able to show him my results.

Twenty-four year old Paul Cohen went to Hartley Rogers, the well known MIT logician, and asked him, "What's the best problem in logic?" Of course, Hartley without hesitation said, "the undecidability of the continuum hypothesis". I don't know if this story is true, but I do know that a few years later, Paul Cohen did succeed in proving the undecidability of CH, one of the landmark results, and perhaps most famous result of logic after Gödel.

The technique that professor Cohen developed to do this, the method of forcing, is today, then, the second of the three most important techniques in set theory. It's with great pleasure that I introduce Professor Paul Cohen, whose title is "My interaction with Kurt Gödel, the man, at work".

[Paul Cohen:] Hello, is this working?

[Audience:] Yes

[Paul Cohen:] Well, let me apologize, then, since this is not a standard talk; I'm not going to present any astounding claims, predictions of the future, analogies with the, with the Wright Brothers, or anything like that. It's a personal talk, and I must say that I was rather moved last night, especially when they played Hoffmann — Tales of Hoffmann the Barcarolle — and to think that Gödel enjoyed that music. And, as I was explaining, it was a great pleasure for me to have sitting at the table professor Hilary Putnam, whom I knew about at the time I did my work, and he jogged my memory about things about Gödel that I — I will come back to this. What he said about Gödel's interesting, I think would be universally agreed. Gödel was a fragile person, and the people who knew him sort of took care of him. They felt — one definitely felt responsible, almost, for him, but for me it was a tremendously emotional thing to meet him, to show him my results, and I want to apologize for my talk because I think, in the ultimate analysis, it will be incomprehensible to people who aren't at least mathematicians at minimum, and not set theorists. I will try to explain the feeling of the time, the emotion, because no other word suffices to explain it: it was a deep emotion that I saw, heard, and told him my result.

As I said in my abstract, his work was so well-known, especially in the beautiful collection — the collected works, which was edited — chief editor was my colleague, Solomon Feferman — which was done at Stanford, which has not only his collected works, but autobiographical material and wonderful notes giving the origin of each paper. So there's no point in me discussing that. This talk will be personal, and it'll be about me at least as much as about Kurt Gödel, so I'm not sure if I want to take questions at the end of this, since I don't want to talk about personal things more than I intend to in the talk.

So one of the points I want to mention was that — okay, so how did he influence me? So I have to tell you a little bit about how I got interested in set theory, These stories, for example, that you say, "Huh, may be true", but I can't deny that some people came up to me and actually said that form — that story in a slightly different form, and we were talking about truth, and I said, "What does it matter if the story is true? You're gonna continue to tell it, aren't you? And, uh — no matter what I say, so go ahead and you can do it at my expense. It's a good story, so keep telling it. It's possible that I said that. When you say it to me, it does ring a very, very dim bell. It's possible that something like that happened."

[Paul Cohen:] Uh, Okay, so I want to tell you a little of my history, which is well known to most people who know me. I wrote my thesis at the University of Chicago under Professor Anthony Sigmund, and as fate would have it, I wrote my thesis on the very topic which George Camden was interested in when he discovered set theory, namely through the expansions(?) in trigonometric series. But I had no real interest in set theory. I do remember Sigmund posed as a problem to me, a technical problem that she thought would be of a theoretical(?) nature about the union of two sets of uniqueness. Not being a set of uniqueness if they were closed that was no.

....about the union of two sets of uniqueness not being a set of uniqueness if there were cloze that was known but he had a feeling that sets more complicated than cloze sets might needn't count [swallows and mumbles], I really had no idea how to do it so I essentially never really worked on it.

[4:43] So I worked in analysis and my interest really was to a great extent analysis and number theory and I achieved some success, I guess one of the privileges of age and having to give these talks I can brag a little bit so before this work that was a wonderful achievement for me when I got the Bôcher prize in analysis and a letter from a wonderful English mathematician, Harold Davenport, if I may be, he didn't know who I was and I had made an announcement of this little projection result and he asked an Englishman sooner to die than visit Chicago, "Do you know this fellow?" and he said "yeah I've met him, he seems to be an accomplished student" but I'll never forget the letter he wrote to me, he said "Dear Professor Cohen if your result is correct" or something of that effect, "you have the satisfaction of knowing you have solved a problem which has defeated a generation of English analysts" and that was a compliment, which I never forgot, this wonderful feeling

[5:39] So I didn't I didn't really think about logic much which....