The Mathematician's Office - Numberphile

This is my Brady

office

, full of beautiful memories, full of actions, full of work and also full of some mathematical curiosities. Look at this, for example, it looks like a simple donut. Let's see, it separates into two Möbius bands that intertwine. This required quite a bit of skill with the 3D printer. This is the famous wooden Möbius strip, you know, only one side and only one boundary. This is Pythagoras, we know it, we are not even sure that Pythagoras existed; For all we know, it may be a myth, but it is a very important myth.

I bought this in Athens, one of the most important places for us

mathematician

s; the place where, you know, mathematics went from being a set of recipes for solving problems to a way to access some eternal truths. One of the most important books of all time: The Elements of Euclid, here in the beautiful English edition. Look at these colors... (Brady: Wow) There was an effort here to bring to life the very notion of reasoning. Watch this. This is a memory of my teaching at Aims Cameroon Institute. You know that I go to show Africa every year at least for a couple of weeks and it is important to me and that makes me very happy.

And this is a memory from there and this is the symbol that I love so much: the integral. You know, this is like an elongated S. I work in analysis, drawing integrals all the time, so much so that every time I start working on a problem, the "integral" symbol flashes in my mind. You know that it was Leibniz who invented this notation: it is an S-type sum. And we know the exact year and even the exact day that he came up with this notation, one of the most successful in history. When you think that this flash of Leibniz is now used by hundreds of thousands of people around the world, they all learn it in school and it reminds us that notation is very important, and that's why...

S is a dear letter to me because S is the symbol of entropy that I worked on for years of my life and S is also the symbol of integration. Check it out. This was knitted for me. This is hyperbolic crochet: it is a constant negative curvature. It's like a bit of the hyperbolic plane. We now know from Hilbert that there is no way to represent the entire hyperbolic plane in our limited three-dimensional world. If you try to continue, it will break down; At some point it will be impossible to continue. And yet, that bit can be touched and it has the property that any point, any bit, has exactly the same geometry as any other bit: constant curvature.

I would like to show you one of the jewels of this collection. This is Gömböc. This took the guy who discovered it ten years. A solution to a big and simple problem at the same time. Is it possible to create a shape that is convex, homogeneous and has only two equilibrium positions, only two: one stable and one unstable? If I release it from any initial setting, it will return to its stable position. (Brady: Your

office

seems very busy, it seems very full of things. What should I read in your office?) From my office, first read that I am a busy guy and that I get a lot of things.

Books arrive here almost every day, reports, letters, so many things. And besides, I travel a lot, so wherever I go there is something I can take with me. Many of these objects are associated with memories for me. (Brady: Do they help you work? When you're, when you want to think, when you want to solve things, when you want to do math, is this environment good for you, does it stimulate you or does it distract you, like, where do you think best? Is it in an environment like this?) I think what's around you when you think doesn't matter that much.

What you feel matters (the sounds, how comfortable you are, the desk, your chair), that really matters. And I think the supply of paper, having a whiteboard, that matters too. And when you think deeply, the rest just disappears in a sense. But I can have the feeling of being at home. However, in some situations, when you are deeply involved in your problem, you feel at home anywhere just by thinking about your problem. Some of my best work was done in hotels, on the train, and there are no rules. When you think, what happens inside is more important than outside.

We have some enlightening texts by Henri Poincaré that describe various illuminations that arrive randomly – sometimes crossing the street, sometimes during a walk – this is also my experience. The best thoughts can be almost everywhere. So, to do your work systematically, to work calmly and systematically, it is good to really feel in your environment, at home. But true flash moments can happen anywhere. Flash moments usually happen when you're alone, that's for sure, but some of the biggest ones in my career happened during a conversation. Actually, in my book, “The Birth of a Theorem”, the first chapter is about how Clément Mouhot and I started working on the so-called Landau damping, and there is a discussion between us (click) and there is a flash with the two. us.

It's clear that just me or him alone, there wouldn't have been any flash, and that determined part of our life for the next two years.