Terence Tao: evaluation

Transcript context

…And even the meme applies broadly. The universality to the meme. Yes, you can go meta if you like, but there are many, many processes. For example, you can take lots of independent random variables and average them together in various ways. You can take a simple average or more complicated average, and we can prove in various cases that these bell curves, these Gaussians, emerge, and it is a satisfying explanation. Sometimes they don’t. So if you have many different inputs and they’re all correlated in some systemic way, then you can get something very far from a bell curve to show up, and this is also important to know when [inaudible 00:49:55] 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 if a population of a hundred thousand Americans with mortgages ask what proportion of them would default on their mortgages, if everything was de-correlated, it would be an asset bell curve, and you can manage risk of options and derivatives and so forth, and there’s 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… You need both, but mathematics can help, because for example, these central limit theorems, it tells 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 and things are fine. It tells you where to look for weaknesses in the model. So if you have a mathematical understanding of Szemerédi’s theorem, and someone proposes to use these Gaussian [inaudible 00:51:32] 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 economist, “How much of a risk is that?”, and then you can go look for that. So there’s always this synergy between science and mathematics. A little bit on the topic of universality, you’re known and celebrated for working across an incredible breadth of mathematics, reminiscent of Hilbert a century ago. In fact, the great Fields Medal winning mathematician Tim Gowers has said that you are the closest thing we get to Hilbert. He’s a colleague of yours.…

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