Terence Tao

And this is also important to know when a situation fails.

So universality is not a 100% reliable thing to rely on.

The global financial crisis was a famous example of this.

People thought that mortgage defaults had this sort of Gaussian-type behavior that

that if you ask a population of 100,000 Americans with mortgages, ask what proportion of them will default on their mortgages, if everything was de-correlated, it would be a nice bell curve and you can manage risk with options and derivatives and so forth.

And it is a very beautiful theory.

But if there are systemic shocks in the economy that can push everybody to default at the same time, that's very non-Gaussian behavior.

And this wasn't fully accounted for in 2008.

Now I think there's some more awareness that this systemic risk is actually a much bigger issue.

And just because the model is pretty and nice, it may not match reality.

So the mathematics of working out what models do

is really important, but also the science of validating when the models fit reality and when they don't.

I mean, you need both.

But mathematics can help because it can, for example, these central limit theorems, it told you that if you have certain axioms like non-correlation, that if all the inputs were not correlated to each other, then you have this Gaussian behavior, so things are fine.

It tells you where to look for weaknesses in the model.

So if you have a mathematical understanding of central limit theorem and someone proposes to use these Gaussian copulars or whatever to model default risk, if you're mathematically trained, you would say, okay, but what are the systemic correlation between all your inputs?

And so then you can ask the economists, how much of a risk is that?

And then you can go look for that.

There's always this synergy between science and mathematics.

There's certainly a lot of connecting threads, and a lot of the progress of mathematics can be represented by taking stories of two fields of mathematics that were previously not connected and finding connections.