Terence Tao

But I developed what's called a gauge transformation.

So the equation is kind of like an evolution of heaps of wheat, and they're all bending back and forth, and so there's a lot of motion.

But if you imagine stabilizing the flow by attaching little cameras at different points in space, which are trying to move in a way that captures most of the motion, and under this sort of stabilized flow, the flow becomes a lot more linear.

I discovered a way to transform the equation to reduce the amount of nonlinear effects, and then I was able to solve the equation.

I found this transformation while visiting my aunt in Australia.

And I was trying to understand the dynamics of all these fields, and I couldn't do it with a pen and paper.

And I had none of the facility of computers to do any computer simulations.

So I ended up closing my eyes, being on the floor, and just imagining myself to actually be

this vector field, and rolling around to try to see how to change coordinates in such a way that somehow things in all directions would behave in a reasonably linear fashion.

And, yeah, my aunt walked in on me while I was doing that, and she was asking, what am I doing doing this?

It's complicated, is the answer.

Yeah, yeah, and she said, okay, fine, you're a young man, I don't ask questions.

A lot of pen and paper.

One thing you pick up as a mathematician is sort of, I call it cheating strategically.

So the beauty of mathematics is that you get to change the rule, change the problem, change the rules as you wish.

You don't get to do this for any other field.

Like, you know, if you're an engineer and someone says, build a bridge over this river, you can't say, I want to build this bridge over here instead, or I want to build it out of paper instead of steel.

But in mathematician, you can do whatever you want.

It's like trying to solve a computer game where you can, there's unlimited cheat codes available.

And so, you know, you can set this, there's a dimension that's large, I'll set it to one.