Terence Tao

how the ancient Greeks were able to measure things like the distance to the Moon, the distance to the Earth.

Using techniques that you could also replicate yourself, it doesn't all have to be like fancy space telescopes and very intimidating mathematics.

Change of perspective is really important.

You say travel broadens the mind.

This is intellectual travel.

Put yourself in the mind of the ancient Greeks or some other person, some other time period.

Make hypotheses, spherical cows, whatever.

Speculate.

And this is what mathematicians do and some artists do, actually.

If you propose axioms, then the mathematics does follow those axioms to their conclusions, and sometimes you can get quite a long way from initial hypotheses.

I have worked on some equations, there's something called the wave maps equation, or the sigma field model, which is not quite the equation of space-time gravity itself, but of certain fields that might exist on top of space-time.

So, Einstein's equations of relativity just describe space and time itself.

But then there's other fields that live on top of that.

There's the electromagnetic field, there's things called Young-Mills fields, and there's this whole hierarchy of different equations.

of which Einstein is considered one of the most nonlinear and difficult.

But relatively low on the hierarchy was this thing called the wave maps equation.

So it's a wave which at any given point is fixed to be like on a sphere.

So I can think of a bunch of arrows in space and time, and yeah, so it's pointing in different directions.

But they propagate like waves.

If you wiggle an arrow, it will propagate and make all the arrows move kind of like sheaves of wheat in the wheat field.