Grant Sanderson: evaluation

Transcript context

…Yeah. That will be the main incentive. Or the incentive would have to change, not just in mathematics but in other areas of science, from proving things about the world to consolidating proofs into problems or higher-level insights. We were having a discussion earlier at lunch about a recent talk you were giving on design and how it helps us understand things. In the limit, is there really a difference between the conceptualization of an idea and the idea itself? If you think about special relativity and spacetime diagrams, and Minkowski spacetime, this is a way in which we illustrate why there’s length contraction and time dilation. But that is the reality… So, the exposition does seem to be the explanation in some sense here. There’s a couple of interesting things there. One is that there seems to be a really strong correlation between the people who come up with genuinely novel insights and the people who are actually quite clear in their communication of it. You might imagine the opposite, given that the experience of a university student is often that the expert teaching them is not necessarily the best explainer of that topic, because they’re so spoiled by their expertise. But what seems, at least in some cases, to be the case is that the people who are really coming up with something quite novel—you’ve got Einstein or Claude Shannon or someone—you read their papers, and they’re really lucid. It doesn’t feel like this is just for the experts and you have to chop through it with a machete. They’re very good expositors. Feynman has this characteristic too, he’s a very good expositor. Maybe the same part of the brain that comes up with the correct new way of thinking about it at a research level also has this knack for good explanation. I think this is pertinent to AI. I used to think that AIs would become these automated theorem provers, but the role of mathematicians was going to shift towards my job, explaining these things. Now I suspect that actually they’ll also be quite good at doing that, probably better than most humans are at explaining and distilling. So digesting and explaining what was going on is probably actually not what’s left for mathematicians, by the nature of how these things are going. We can talk about ways this might not be it, but probably the same thing that comes up with the really good new idea that solves some new problem is also just good at explaining it. That’s a way my beliefs have changed. What’s the last thing you think you’ll be doing? Both you and also what the human mathematical community will be doing.…

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