Terence Tao

Or past observations, does it fit observed data?

So there's definitely a symbiosis.

I guess mathematics is unusual among other disciplines.

We start from hypotheses, like the axioms of a model, and ask what conclusions come up from that model.

In almost any other discipline, you start with the conclusions.

I want to do this.

I want to build a bridge.

I want to make money.

I want to do this.

And then you find the path to get there.

a lot there's a lot less sort of speculation about suppose I did this what would happen you know planning and modeling speculative fiction maybe is one other place but that's about it actually most of the things we do in life is conclusions driven including physics and science I mean they want to know where is this asteroid going to go what is the weather going to be tomorrow but mathematics also has this other direction of going from the axioms

What do you think?

Well, you need both, top-down and bottom-up.

Yeah, it's a really interaction between all these things.

So over time, the observations and the theory and the modeling should both get better.

closer to reality.

But initially, and this is always the case, they're always far apart to begin with.

But you need one to figure out where to push the other.

So if your model is predicting anomalies that are not predicted by an experiment, that tells experimenters where to look to find more data to refine the models.

So it goes back and forth.