Comment by dwohnitmok
Comment by dwohnitmok 2 days ago
> How do AI did it? Using already existing math. If we need new math to prove Collatz, Goldbach or Riemman, LLMs are simply SOL.
An unproved theorem now proved is by definition new math. Will LLMs get you to Collatz, Goldbach, or Riemann? Unclear.
But it's not like there's some magical, entirely unrelated to existing math, "new math" that was required to solve all the big conjectures of the past. They proceeded, as always, by proving new theorems one by one.
Yes, "new math" is neither magical nor unrelated to existing math, but that doesn't mean any new theorem or proof is automatically "new math." I think the term is usually reserved for the definition of a new kind of mathematical object, about which you prove theorems relating it to existing math, which then allows you to construct qualitatively new proofs by transforming statements into the language of your new kind of object and back.
I think eventually LLMs will also be used as part of systems that come up with new, broadly useful definitions, but we're not there yet.