This is my office Brady, full of beautiful memories, full of actions, full of work and
also full of some maths curiosities.
See this, for instance, it looks like a plain doughnut.
Let's see, it separates into two Möbius bands which are intertwined.
This required quite some skill at the, you know, 3D printer.
This is the famous Möbius band in wood, you know, just one side and just one boundary.
This is Pythagoras, we know, we're not even sure that Pythagoras existed; for all that
we know he may be a myth, but so important myth.
I bought this in Athens, one of the places most important for us mathematicians; the
place where, you know, mathematics was upgraded from a set of recipes to solve problem into
a way to access some eternal truths.
One of the most important books ever – The Elements of Euclid, here in the beautiful
English edition.
Look at these colours... (Brady: Wow)
Here there was an effort to bring the very notion of reasoning to life.
Look at this.
This is a memory from my teaching in the Aims Cameroon Institute.
You know I go teaching in Africa every year at least couple of weeks and it's important
for me and I get a lot of joy from that.
And this is a memory from there and this is the symbol I love so much – the integral.
You know, this is like an S elongated.
I work in analysis, I draw integrals all the time, so much that whenever I start working
on a problem, the symbol 'integral' flashes in my mind.
You know it was Leibniz who invented this notation – it's an S like summation.
And we know the exact year and even the exact day on which he thought of this notation – one
of the most successful ever.
When you think that this flash of Leibniz now is used by hundreds of thousands of people
around the world - everybody learns it in school, and reminds us that notation is so
important, and so...S is a dear letter to me because S is the symbol of entropy on which
I worked for years of my life and S is the symbol also of integration.
Look at that.
This was knitted for me.
This is hyperbolic crochet – it's constant negative curvature.
It's like a little bit of the hyperbolic plane.
Now we know since Hilbert that there's no way to represent the hyperbolic plane in its
entirety in our limited 3-dimensional world.
If you try to continue it, it will break down - at some point it will be impossible to continue.
And still, that little bit you can touch, and it has the property that any point, any
little bit has exactly the same geometry as any other little bit – constant curvature.
I'd like to show you one of the jewels of this collection.
This is the Gömböc.
This took ten years to the guy who discovered it.
A solution to a big and simple problem at the same time.
Is it possible to make a shape that will be convex, homogeneous and have only two equilibrium
positions, only two – one stable and one unstable.
If I let it go from any initial configuration, it will go back to its stable position.
(Brady: Your office seems very busy, seems very full of things.
What should I read from your office?)
From my office, first read that I am a busy guy and that I receive lot of things.
Books arrive here almost every day, reports, letters, so many many things.
And also, I travel a lot so everywhere I travel there's something for me to take back.
Many of these objects are associated with memories for me.
(Brady: Do they help you work?
Like when you're, when you want to think, when you want to work things out, when you
want to do mathematics, is this environment like, good for you, does it stimulate you
or does it distract you, like, where do you do your best thinking?
Is it in an environment like this?)
I think what is around you when you think doesn't matter so much.
What you feel matters – sounds, how comfortable you are, the desktop, your chair – that
really matters.
And I think supplies of paper, having blackboard, that also matters.
And when you think deeply the rest just vanishes in some sense.
But I may have the feeling of being at home.
In some situations however, when you are deeply with your problem, you feel at home anywhere
just thinking about your problem.
Some of my best work was done in hotels, on the train, and there's no rule.
More important when you think is what goes on inside rather than outside.
We have some enlightening texts by Henri Poincaré describing various illuminations arriving
randomly – sometimes crossing the street, sometimes during some walk – this also is
in my experience.
The best thoughts can be nearly everywhere.
Then, to do your systematic work, to work quietly and systematically, it's good to really
feel in your environment, like at home.
But the real (click) flash moments, they can occur anywhere.
Flash moment is most often when you are alone, that's for sure, but some of the most important
ones in my career occurred in conversation.
Actually my, in my book, “Birth of a Theorem,” first chapter is about how Clément Mouhot
and I start working on the so-called Landau damping, and there's a discussion between
us (click) and there's a flash with the two of us.
It's clear that me alone or him alone, there would have been no flash, and that determined
part of our life for the two years coming.