Re: “Math 2.0” will need to value mathematical progress more holistically

I'm a lot more skeptical. I'm not a mathematician, but from my use of LLMs a very clear pattern of what they are good and bad at has emerged. They are extremely good at combining large amounts of information, and it seems this is what the current AI results in mathematics are. There are so many subfieleds of math with ties to each other, so many papers and niche results, that no human could ever read, comprehend, connect and organize that information in their brains. Pretty much all of it was created by humans. And there is real value in doing this and creating new results from what we've already discovered.

But there also is another type of discovery that requires taking a step back and looking at the problem from a different angle. If you are an engineer, how often has an LLM told you (without you explicitly prompting for it): Wait, what you are doing here doesn't really make sense, there exists a much more elegant abstraction that nobody has thought of, let's remove all that code, let's tackle the problem in a different way by thinking from first principles. Pretty much never. But in science a lot of the biggest discoveries have come from this kind of first principle thinking, questioning existing work and approaches and going against what already exists, not combining all existing data which is likely to be just a local optimum.

loveparade, 6 hours ago