Adam Brown: prediction

Transcript context

…Whenever our future AI civilization does come up with more and more unified theories of physics, or deeper theories that make better predictions, do you think that humans will be able to keep up? Once this step is taken, will we actually be in a position to understand what our AI civilization understands? I don’t know that we’re going to be able to keep up entirely, but I think we’ll keep up much better than pessimistic forecasts would suggest. Let’s take mathematics as a simpler example than physics. Many mathematicians are worried that these LLMs are just going to turn into proof machines. Terry Tao has this phrase, “indigestion”, he uses, in which these LLMs will produce billion-line inscrutable Lean code that will serve as a certificate that a particular theorem is true without providing any insight as to why that might be true. Wouldn’t that be a depressing world, say the mathematicians. I think that is a possible future, but I actually don’t find that to be a very likely future. Because as well as being superhuman provers, we also expect these large language models to be superhuman explainers. Maybe they’ll do the exact opposite of that. Maybe they’ll take proofs that are very hard to understand, and by doggedly trying and trying and trying, they will be able to come up with ways that are human comprehensible. They will take proofs that are difficult to understand and make them easy to understand. I think the empirical evidence, it’s early days, but it’s pretty supportive of that more positive vision. There was an Erdős problem that was proved a few months ago now, and it wasn’t just an incomprehensible set of Lean. In fact, it wasn’t even proved in Lean at all. It was proved informally. There was a follow-up paper by some human mathematicians that took these new, human interpretable ideas that the machine had come up with to prove this Erdős conjecture, and used them to prove new theorems. So that was the exact opposite of that case. It came up with a very human interpretable idea, and then humans were able to fully comprehend it, comprehend it so well they were able to deploy it in a new scenario. We’ve seen that throughout. The unit distance conjecture, I think, is a good example here for a number of the themes you’ve been discussing. One is that it’s totally comprehensible, the disproof of the unit distance conjecture that it came up with. To you, perhaps.…

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