Afternoon Discussions (contd.)

0:00 Or maybe as a book, as a book, unparallel table, I mean, the book. Oh, yeah, unparallel table, I agree. Almost as unparallel table as EGA. Well, I mean, you can say this in a correspondence, too, that this is terrible writing. Bayes is just hard to approach. I mean, no, to me, EGA I can read because it makes sense. Bayes foundations I cannot read because they don't make sense to me. But EGA is longer by a long shot. And EGA doesn't get to anything like the Theorems. You don't have to go to SGA, you know. Whereas Vail's approach, you know, does get you to the Theorems. Well, in fewer pages. In fewer pages. But it didn't get you to the Theorems in the Bacon lecture. Does this reflect a general attitude on Bale's part towards abstraction? Did he, was one of the reasons that he distrusted the Grand Equest because he saw it as attempting too much of a way of generalization and conceptualization? Did he believe... I'm just asking... Nobody here thought he could do both in the 1930s when he was younger. Obviously, he must have felt that it was possible to do both, I mean, when you start from scratch, when he was younger, you could do both. Hilbert, after all, managed to do this sort of thing more or less. In his old age, he then worked on foundation, relatively old age. You know, it's possible if you have the energy to go on to, to do these things. I mean, Hilbert, I think, had a considerable influence. I mean, the act of the Hilbert School surely had a strong influence. It wasn't really a nerd school. Of course, a nerd school is a lot out of Hilbert's approach to mathematics. And that must have had an enormous, very strong impact on Bay and on the early Brevard. But of course, Hilbert never taught anything. There was nothing mathematical that was alien to him. But Bay said it was never through Connevar. Yes, yes, sure. It's not everything Hilbert ever did. No, no, of course not. But Hilbert did take foundations very seriously, and he made an heroic attempt, you know, to produce a foundational theory, just that by the time he got there he was not solving. Key terms may include, for example, quantum mechanics and physics. Speakers include, for example, quantum mechanics and physics.

2:30 Well, that's my question. Did he see that? Did you see him dealing seamlessly with a general foundational system? Or did he think of foundations as something which would crystallize, change into bogus piecemeal from within mathematical development? You mean in the early days? Yes, it's clear from many statements by Ray that the model was Van der Waal and the model, the motivation was what Van der Waal and Kant was the motivation. So there's no objection to abstraction or anonymity. There is an objection to 3,000 pages before the first page. Okay, exactly. So pedagogical is an expository issue. Probably. The conceptual difference of the nature of foundation. And I think it was misplaced because I think those 3,000 pages are easier to read than any 600 pages of that. Well, possibly because they get essentially... But now, after all, Colin, come on, there's not quite fair to compare what an enormous machinery has been developed later. I also attended to it. I have a first time. No, no, no, no, what I mean is that, you know, by the time Groton did writing, it was an enormous elaboration of machinery, you know, 30 years on, from what Bay and the Brouwerichians were trying to do in the 1930s. It was enormous. I mean, expansion of machinery, and so, yes, so ways have been found, but I think in the 1930s, no, it was the right line. I think America would read the book. You know, well, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know, you know. Well, I think one of the motivations, I mean, the base debate, stated, repeated, I want to do it for the rest of mathematics.

5:00 What I mean by that is to include the geometry of the capital in mainstream mathematics with the same level of rigour as... But one time there was a need for algebra to put it in those foundations. We have to put it at the top of the list. And finally, I mean, when Bobacki published his series on the ego of each one, I think it's a part, a fulfillment of this implicit promise. And there were many more chapters, an account of Levin and geometry, many more things. And I hope that the fight will be over some day. Why don't we promise? Because, you know, that's the thing. They're all kind of prolegomena. They were prolegomena, you know, just some huge thing that's going finally to come. And that was indeed the intention. It's all very clear, it's all very beautiful. Of course, it doesn't matter to me, but you're waiting, you see, for the culmination, finally, of this enormous project. This is not a criticism, because the actual foundation is already, you know, it is a foundation. They had to supply a foundation to the foundation of mathematics, which I call the Theorie des Enseignements. But what they're writing, you know, the Topology Générale, the Algebra... These are, this is really regarded as a kind of foundation for actual mathematics. And they, you can see them in the algebra, they're beautiful, because I've learned a lot of mathematics from them. But there was this great culmination. I agree, but there are so many other things you realize that they might get to. Geometry, but differential geometry in particular, I don't... But the point is, according to the exacting standards of writing, I mean, it was so painful to write, to publish, I mean, to publish until it was published.

7:30 In the final, Robert Gersh-Durratt, which were not intended to be published, it was just for circumscription and preparation for something to be published, and to transform them into something published according to the exacting standards of writing could have been a normal task, and, I mean, the historical fact is that of exhaustion of steam. I mean, the project started with great enthusiasm in the... These diving courses like Monterey Ray, Newton, and so on, all first made mathematicians with a lot of useful energy. Then there was a second generation. A second generation you can include myself and a few others. And then you have a second generation. After the necessary compromise, we decided to concentrate on two series, one on so-called commutative algebra, which was agreed that it should be us. I mean, we would not have overlap. So we had a discussion about that. I'm a Swiss. I'm a Swiss. I'm a Swiss national character, my lady. I'm a Swiss national character, my lady. And we've got a lot of energy and so on and a lot of knowledge. And good, I mean, little people like us. Little people like us. So he forced me and said, well, we have to get out of this impasse. It makes no sense to rewrite everything starting from the point of view of calculus. I agree that it would be better, but at the moment, I mean, Liebhoop is not yet in a satisfactory state, and with all the people there are at some point six or seven world experts, and when you have enough discipline, self-discipline, and with six or seven or eight world experts in the field...

10:00 The reason has been that if you had to rewrite all of today, the name of it wouldn't complete something. It's a completely normal problem. Especially when there's a chapter about the old system and the development. So that was basically pretty different now, but because they are the problem.

12:30 So many developers. And in a sense, Bobacky, that's what's happened to Bobacky, the first generation, all these things were assimilated and became common practice among the practice. Then there was another step, which is both the... And, as I said, at some time we had the best world experts in all space. So, we wrote what was at the time, maybe slightly more than that. Forgive me for that. Ah, we are ready. Ah, forgive me for that. You are forgiven. We'll edit that later. And that's the end. What has happened to whom like this and there was a third generation with some well-specified goal and to a large extent there was a second generation, more or less, and then we had a loss of aim, a foundation of action because the steam was out and something which had been successful for 50 years, the steam was out and the period was different and we had been too successful. So, I mean, we had to bring something new. I mean, something new we brought.

15:00 So what has happened is that in the Gospels and in the eighties and during the seventies we had a very, very painful. The lead group book and Foundations of Alphabet. What is called, what is called, what is called, I mean. And that you've actually negotiated a dividing line on Poinsettia. Exactly. So, but now of course, and then we had this lawsuit and I devoted a lot of energy for this lawsuit, not only me, it was this lawsuit, and I don't think I've got much sympathy for it. And you put it in one sentence. I think both Bobacki and his publisher were the losers, and the lawyers were the winners. Well, we usually are. Can I just ask one quick question, Kev? The date of this informal agreement on the partition of labor with the Great Indy, on algebraic geometry, roughly. The 1960s. The 1960s. It provides a rather natural start. The 1960s. And to study what happened from that point onwards in Rotterdam and in your other lecture, I mean, 1960, and on the other end, yes, and about the beginning of the 80s.

17:30 And of course, you have to understand that Germany was a sky for Bobakie. We came to sky for Dürer, not for Dürer, but for Bobakie. And, you know, the importance of giving a name in the writing of each of these. So, do you remember at all what principles were used for Devani? I mean, you can look at the works and see what they were, but what principles they had in mind? Oh, yes, we have the principles. I would say the raw culture has the raw culture. In a sense, I mean, as long as we can sew up without gluing, because cohomology could not appear because it would not cause my blood to grow. I mean, we know that in algebra and geometry there are five models, topology, cohomology, chromatography, which is sexism, and theorem A and B of theta in this version, I mean, theorem B and gamma in this version. So, I mean, it was clearly stated, as long as... As something is understood even in pure algebraic terms, without taking seriously into account the Zeiss key topology and the Geometrical Insights, it's for us. As soon as it really begins geometry, it's for you. I don't have more as a divider, I only respect it more. And it was easier because this guides myself to find myself, myself, and also some of themselves. The writing team was more diversified. I would say, basically, Dixnier, Samuel, Serre, myself, and to some extent, Bobbie.

20:00 Was Titz involved in all of this? Well, Titz was an advisor. I mean, Titz was the one who used many documents. He was never appointed formally a member. And we did seminars and so on extensively. And we discussed many things with him, discussed many things with him, but it was clear that it was a temporary problem. Tich was interested in the project of LIGO but not in the actual discussion about LIGO. We would invite him to participate. And we would, I mean, put Argenta in a such a way that he could participate. Concerned, it was clear that he would not participate. He was not interested and we did not ask him to be. A member properly should be interested in everything. That was the basic. The member who was really a member, I mean... And also, when we wrote the chapter on what is really probability in the decision-making process, we had a lot of advice from, again, I mean, there is conditions, you are in a specific project, we advise from you, we manage our agenda so that you can participate to some discussion, you can write to us and so on, but we don't provide to you, we don't provide to you.

22:30 I mean, the ordinary members, regular members, you know, stand there to sway on the Bible, sway on the Bible, to be tested, and people, some people are more interested in something and some people are less interested in it. Did you have a special match? The missions, the dreams, they struck me. It was a mission, yes. And what, I mean, the positive side, I mean, life is best when there's a bright side and a dark side. There is a sense of community, of cooperation in the work, and public service, I mean, that's a positive side of it, as I see it. When I want to pass, I have to join them. When I want to go over, I mean, session blanche, it means open meetings, meetings which are open to non-members, so I participate in them. But then, of course, I saw the positive side, and so, but that's always also the dark side. I mean, one day you made a fool of an academic who complains that when they take your problem from one, you are conforming everything in the French academic world, I mean in mathematics world, and then you immediately realize that when you see the official picture of the goal, you now have a very natural breaking point, which is...

27:30 Yes, I was just saying that this, as it were, treating a negotiation between the Bulwarki and Gromendieck in 1960, so it does take us very naturally into the exploration of the whole of algebra and geometry, and then the larger, as I say, the larger picture of his. I'm going to say what the significance of his legacy is for the overall shape and direction of quantum mathematics, which in turn leads naturally to what Bill was going to talk about, the law of the enchantment program. So there's a lot of ground to cover, but I think if you try and... I shall leave around 4 p.m. on Tuesday. Okay, so we're still happy for most of Tuesday. Okay. Which would be good, because Leo Curry will be here also for that. Absolutely. I will be able to share. I call my daughter, and she will be there around 7 p.m. in my home. So I'll have to be there. So we can keep doing that. Thank you for your attention. We had a very fascinating discussion on that today. We also had a study on what may have become the algebraic major results of a keynote. But there is no real answer to that. So let's not add a single word about the algebraic number.

30:00 No, that's exactly what I was trying to say. What the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, what the, Just before 1960, we've heard how Grotendieck came from the more general functional analysis considerations to do some very concrete things in the complex analytic situation, but we haven't really heard anything yet about his work, as opposed, say, to Serres on algebraic geometry at all, and nor have we really heard how, what the... What the emphasis was around the weight conjectures for the whole Burbecki group of the French mathematical community and exactly at what point Grotendieck got hooked on this particular thing. You know, Serre refers to some explaining this to Grotendieck, but I'm not sure if this is a vague fact. Excuse me, what? Is it, yeah? That's knowable. I mean, I don't know. I don't know that, but that's going to be worth it, that's going to be worth it, that's right. I see. Because, I mean, Sarah mentioned some of the enthusiasm with which Grotendieck received the ideas from him, as well. Oh, yes, absolutely. Straight from Sarah, only from Sarah. The other thing about... Yes, yes. But Sarah has always been a very good intelligent person, even if they didn't know how to speak English. Yeah, I agree. Sarah... Oh, one, two... He was involved with the filter of bridges, as you said. No, I mean, Sarah was very... I mean, as you speak, the influence you are so pleased with. But to talk more about that, I would very much like to ask you why... It's also the general question for me. The references that touch on these Alan Jackson articles are the very patchy nature of Brodendieck's knowledge of many things. His preparation was very inactive. But if you read the correspondence, you can see how important he was in that.

32:30 Yeah, yeah, yeah. Knowledge on both sides. But it's true that at some point, I mean, I hope already late, maybe in 55 or 55, something like that, But I mean, asking, say, whether there have been many, infinitely many zeros of the zeta-faxes, and the rims of the zeta-faxes. So he would not have had any systematic, very systematic, advanced knowledge of algebraic geometry. And, I don't know, the opacity of the meeting but it was enough to tell it's clear that what you have learned from me is it's a deep geometry problem but a matter of life. I gave you problems, my methods are, I'm exalted in, and you have to learn a new method.

35:00 And in a sense, I mean, as Merleforth stated, it's a method but no problem. Two or three days after that, on the position of logic with respect to... The idea of co-algebra is that you introduce a further structure, and in fact, it's a universal property, that is, among the symmetric and normal, and it's coming out of the law that we're given any potential effect. I cover all the best possible questions, and they're exactly the ones that go up in the books.

37:30 You need polynomial functions, but there's no specific formalism there for obtaining the polynomial functions. It's just very funny to me when I read the Tohoku papers, you know. Of course, since you've learned it, let's escalate it around. It's like having a zero over here in a Tohoku paper. But you didn't have to. They're right. They're reusable. But it seems as if they're not keen on it. That's the talk. The world is very consistent by linear or more general structures. And you don't need to talk about how it works. You can give a purely general model of a version of a certain kind of dimension theory that will make a point that's not here. I mean, you will end up with something like this. It may come heavily disguised, but it's true. And it comes out to be basically a mystical goal in this paper, but it does push us into a mystical course. We're going to try to give some very abstract... I mean, it's based on ideas that have been taken up by Brevard's program in which they mention considerations. You think this is... I recall I saw that paper. I don't say that's what I'm going to go on. I'm never here. I'm just going to go to any company in life, or wherever it is that I'm going to go to. But when we have any discussion with the faculty, we collaborate with them. Great. I'll talk to you later. Yeah, yeah.