Geometrical Thinking — Minimal Surfaces — Part 2

0:00 What I do here is to see if we can spot how to divide these kinds. I mean, are there joints that we can cut this up? Or are we going to say they're a kind of spectrum? And there are clear cases, but no, I mean, the amount of overload, I can take the last word, diminishes here. some other kind of thing, but I mean, do we have a spectrum of way of thinking? My whole thought was based on the unthought-out assumption that probably there are four or five characteristic ways, and I certainly don't want to see 40, but maybe I'm wrong, and we should settle for a spectrum, but nonetheless with, you know, extreme cases, as many things, it's all so I didn't want an example just to say that mathematicians do make these typically make these distinctions themselves and I think at every level I mean some mathematicians care and some don't some will spend a lot of time saying you know I want to purely algebraic proof this purely algebraic theorem others say I don't want to prove this theorem we haven't got one and i don't care where it comes but it's stupid even to care i mean the old is huge right um but i think at every level from the first year first term undergraduate teaching through to top quality research these distinctives are in the mathematics community in various forms so i started from the presupposition that we should try and respect that and make sense of it But what sense to make of it? I'm going to warm up back there. No, no. Certainly the problem he started with was very clearly out there because Benyamin Osegri, in fact, the whole lectures of modern geometry is about that. He's obsessed with the idea. Is there a geometric proof of this? Why isn't there? Certainly there is one, even if Helgas is not... from a formal logic point of view. You can do even a sequent calculus of this. For every N, you can actually write down the axioms that are there.

2:30 And there certainly is a proof for each individual N of that. We don't know it. And what we would like to know is obviously a uniform one that would work for every N. So whether we had it or not, it's out there. So, in a certain sense, there is no doubt that there is a geometric proof of this. In some sense. In some sense. In some sense, there's no doubt. You still sound a little like a dog in my home one day. Yeah, and then on the thinking question, I guess most of us are overlooking that there is a part of mathematics about that much about thinking, namely computational ones. In other words, you prove things by computing things and at least geometrical thinking can be distinguished from the rest that it's not by proving, by computing things. I mean we wouldn't call something geometric thinking if you got it by computing a few things and showing this is equal to that. I mean, equational thinking would definitely be something that is not geometric yeah but what if that's where our minds actually work I mean what if our minds aren't actually just computers yeah if we are that way I mean the the part that we're not that part is definitely to be considered not geometric right because everyone thought that well all of mathematics is proving well no before the Greeks there was mathematics then it was improving it was computing if it's really computational if you can do it if you can do it by just operations just well Well, no, that's the problem. We're calling in two, but it's not a two. These operations involve tremendously fatlocking. I mean, I have a very good piece of work who is Boilbang eventually proving some number was less than one. And that was a great deal of calculations, and Ban went one of the persons conjecture. So I want to box what you're saying. In other words, I didn't think of that one. Let's put equational thinking in there. I'm very happy with it. But again, it might or might not be part of a geometrical argument. you want to say it's like and it might occur within a box in inside so you

5:00 think about it might form the entire paper but you know i i i i'm not going to give up yet on there being some kind of overall story it has to do with this grand collection of inferences names as a way of getting a problem thinking so you allow computation inside the already painting in the morning. Thanks. And now a brief announcement. You've all been very patient, but my patience is worn in with the noise. So, Fabian has tried to find another room. That's gone. Yeah, because of the noise, we decided to change the building. And the remaining conferences will take place just near to the pizzeria where we just go right now. So we'll go for lunch Just need, just need to go on to book a pizza during the conference. Thank you. No, no, no. Sorry. Very good. Thank you. Well, you guys, thank you. Well, thanks for solving the problem.