Morning Discussions (contd.)

0:00 Sheremov and Sheremov was minister of physics and then in scientific term he was at that time he was appointed a professor of political technique and so his mathematical life was more or less devoted to the teaching of political so most politics so just to explain that he more or less left. Then at about the same time Verdi died too early. Verdi was dead. Verdi died too early. He was 14 like that and he died in a crash. He had a summer house somewhere in the mountains, lost some of them and he remembered over and over that access to space was quite dangerous, almost quite dangerous. Yes, sir. It's near us, old Saint-Jean, I think. I've been visiting him from time to time and he always advised me to be careful of all his difficulties and dangers. And some evening they missed the great thunderstorms. They left. Yes, exactly.

2:30 The reconstruction of the academic system after 1968, the change in mood. The shadow police of the world. The new zeitgeist, right? It does. I hate to say I'm okay with watching you decide. Independently.

20:00 Most of the change certainly was Rashi's lines. As Tom Sip found it, he claimed later to be a rather beleaguered figure. He said he later on claimed he was a philosopher, he wasn't really part of the trend. I swear, I'm your A.G.S., you know. And here I will hide places.

22:30 Exactly. Philosophers, historians, and sure, ideological propagandists of one kind or another, rather than scientists or mathematicians. That's where I would differ with Novat's dissertation. He sees his confrontation with Brody and Tom, and he writes it as how Tom really had the vision of mathematics that would carry on in Brody's campus. You know, it was a dead end. He says that? Well, not that sharply, but that's the direction he wants to take. No, of course, nobody is a supporter of him. I have my own reservation. When it comes to the fact, he's quite accurate. When he describes the fact, he's quite accurate. In his judgment, I don't agree with him in his judgment. He's a video supporter of Tom. He claims that the main asset of IHS was Tom. And he says enough of the facts of Tom's work that I think you could conclude this wasn't the future. He does say it, but it's not his direction. Which book is this? The dissertation was never published. It's a Princeton dissertation on the history of science. I wrote to him and I said, first of all, you need to make it two books. You need to make it a Grote-Viton book and then a Ruel book, because the whole last half of it is on Grote-Viton. You know, but they were both good enough work, you know, even if I disagreed with them. Could you write down the title, you know? But also, to finish, since you mentioned Ruel, that's right. I mean, the I.H.S. wasn't there. You have to also include Ruel.

30:00 It's so powerful that it's themselves that are lost. Then into the 60s, he is suddenly this public figure, a public figure who is allowed to be on national TV, and he's praised for that, because he believes in himself. So Grotendieck was saying, well, this success came from the combination of speech. It's not just what's the constraints related to the mood in the case of Grotendieck or Tom.

32:30 Yes, they somehow exploded. You can see, I mean, when he retreated to Montpellier, I mean, I visited him from time to time, but he still had the mathematics, still had the absolute mathematics from time to time. There was no milieu. I mean, Montpellier University is a university, but it's not the first thing. No, it's not. I mean, it's inflated. And if you look at the shows, they are honest people, they do their jobs, they teach, they exhort.

35:00 It seems a strange place. Well, I don't think it seems a strange place for you to go back to in any way. At least that was my... People go to Las Vegas. I had to go to University of Nevada in Las Vegas, light teaching load, buy a nice house 20 miles out of town. Yeah. More per year, because he agreed to take it. And, uh... Yes, I forgot not to describe. As soon as you... As soon as you come... Well, there was some modest bonding from the... I think it was just a personal reason of the defense at the time of the state and the state university and the American university and you see, okay, this man was there, he disappeared, this man was there, he disappeared, but where are they?

37:30 It's really, interestingly enough, it's only recently that the key is indeed an example of a centralized state.

52:30 We might not do a function, but if I did a function, it would be a function of a song. Grutendieck spent most of his time talking about science as such, and it seems that most of the actual calculations and the nitty-gritty of it was actually at the level of the science.

1:02:30 I mean, the arena within which all this stuff is really going on, right? I mean, as I say, you have the same phenomenon of commutative rings with groups and everything else. You have the invariant notion, which is helpful in general. Right, right. But to get at a particular case, you need presentations. Right. Unnatural presentations, in a way. Right. Maybe just to construct the appropriate topos. I think it's an interesting statement, you see, because, well, dramatically, I think there's some content to it, but once you've constructed it, you've already got the thing, because there's so much involved in constructing a particular example that you're simply, you're really encoding the solution at the same time as you're giving the invariant statement of the problem.

1:05:00 The way I put it sometimes, and I don't know what you would think about this, is that you create a universe in which virtually all that exists is the problem you want to solve, so that what the solution will turn out to be will stand out here, because virtually all there is is the problem. Contradiction between problem and solution is solved in the medical speeches about universes of code and the connective holistic perspectives and the like. Is this the reason why you notice, when you read presentations of algebraic geometry, he says quite a bit of meaning. He's not going to get involved with the topologies at all. He's going to look much more at the more specific kinds of construction. My impression is that presentations of algebraic geometry, I mean, of the results, of course, that were achieved by the Grotendieck, you know, by Grotendieck and his followers, are not often presented. You see how they try to avoid the whole language at times. It's quite explicit. Okay, I can say, well, I mean, my impression, I've looked at many such treatments, and there's no treatment of algebraic geometry which uses properly even the most elementary aspect of it. The one that you began to translate there. Yes, the two chapters. That comes closer than any. And luckily it's from Gabriel. And luckily it's from Gabriel that I first learned some of the tales about what tokos theory is. I think his point of view is more advanced than many others in that direction. That all these books don't use it because they don't understand it. It's evident from, well, you also noticed that in Eisenbud's most recent book, I think it might have the great geometry, he has a, you know, he does it in the way with the prime ideals and all this.

1:07:30 And then he has an appendix where he says, well, really we should have done this with functor, like the, he kind of described the tangent model as a functor of all this. And he gets a number of things quite wrong in this, you see, demonstrating that he doesn't really think that way, that this isn't internalized. And so, and again, I give this sort of general explanation of things that, you know, we, you know, starting with me and Tierney and then all the rest, we have drastically simplified all that so that people would only pay attention, they couldn't learn it, and they could properly use it in elementary. But all that they have is still SGA, which is this other thing that only Grotendieck could understand. He had such a tremendous mental power that he could actually take these complicated layers of definition and think with that. This would be where most of us have difficulty to have some abstract definition here that we can rest on. So, in some sense, it's only going to be could understand it written that way. And D'Auligny. Maybe D'Auligny as well. Maybe D'Auligny. Yeah. But it's very few and, you know, what we need is an exposition which does this. I mean, in complex analysis also, it's tremendously, they still do things in a tremendously complicated way, which can be drastically simplified. As Freud liked to put it, the trivial aspects of the trivial, so they're real content, but there's a vast analysis based in that way. You look at textbooks on economic cohomology, and because they're going to do it, they have to talk about these things, but they'll all say, we're not going to talk about topologies. We're all going to propaganda that is too difficult. That's the underlying thing. For each site, the category of abelian sheaths on that site, they name the category of abelian sheaths on that site, they talk about sheaths and sets on that site, they treat that category, but they don't name it, somehow you can name the category of groups, but you must not name the category of sets, the set sheaths, that which they dare not name.

1:10:00 And it's true that in Tom's book, which I looked at in some detail this way, you would actually have to add a couple of pages to chapter two and a couple of pages to chapter three to introduce the topos. Which I think is out of print right now. You'd have to add a couple of pages to each of those two chapters, but you'd cut lots of pages. But yeah, it's just this bizarre idea that you can... We can talk about shapes of groups, talk about shapes of sex, name the category of shapes of groups, deal with the category of shapes of sex, but not name it, because then we'd be talking about a tale about a songbook, an actual book. Well, yeah, that's the reflection of this general. That something is difficult leads to the propaganda that's difficult, which leads to it being even more difficult, rather than any attempt to simplify or take advantage of some of the things that we're talking about. How about spaces versus shapes, I mean? I just want to mention that you have to go over and select a question and then you have to go through this. So, if you want to use that practically, you need to think about it completely, which mentions our work, but consigns it entirely to this scrap heap of logic.

1:15:00 So this is a very super point with us, because the theory is all about logic. We think logic is important. We should learn about it. We see the topos as geometry, direct question if there's all these rumors and propaganda which said, oh, it must be logic, it must be logic, didn't you work on the independence of the continuum hypothesis, didn't you introduce intuitionistic logic, and all these kind of things, as though these were standards.

1:17:30 I don't understand them. Topos theory is the synthesis of geometry. It's a big synthesis of all these things. If you emphasize it, it's true that on purpose you might emphasize the logical facet of it, and for others, if you like, the more specifically geometric. But it goes anything that smacks of logic, you know, at all. You see, mathematicians, the whole... I know, so I thought...