I cannot say, math research isn’t my domain of expertise, I’m just trying to follow along :)
replyBut I find it interesting that Lean, a validator/compiler made by humans, is what enables those discoveries. But somehow all the praise goes to the models
I mean we don't instantly fall into ASI, hopefully. The problem with humans is every problem we solve the goal posts get kicked further down the road until they are reaching relativistic speeds. It starts around "well, the AI hasn't solved a novel problem" then moves to "well, they didn't write the validator" and suddenly humans are at the point of saying "Well AI hasn't rewrote the constants of the universe, what good are they".
replyOf course another way to look at this is, the people that wrote the validator got praise for that years ago. Now and up and coming actor is solving problems that took us 100s of years to create in insanely short time periods so of course it's going to get a lot of attention as it well should.
To be clear: I’m aware the LLMs are solving problems. I’m just saying that what enables that whole research revolution is Lean. We wouldn’t be seeing all those results without it. I would like to see it acknowledged when people are talking about LLMs solving maths. The same way I think we should acknowledge the humans who are guiding and prompting the LLMs. I don’t think that necessitates to move a goal post
replyI don't think so. People have been trying things like this with evolutionary algorithms for a very long time already. LLMs can interleave symbolic manipulation with empirical experiments and simulations and charts and thinking/reasoning text, and an LLM will much more efficiently search the space of candidate ideas than any handcrafted mutation algorithm. Any task with a cheaply verifiable goal that requires fanning out across a massive search space is ideal for contemporary LLM technology to make progress with.
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