OpenAI paired its Astra proof claims with Lean certificates and a public repository. That makes the results checkable, but it does not make the unreleased model or peer review disappear.
My understanding was that any hitherto success of LLMs in mathematics was in its trying approaches and information from different fields where they weren’t traditionally applied (within mathematics), they have surfaced potential links but haven’t created anything in any real sense. Still, a potential legitimate use for them that I personally hadn’t anticipated.
I mean that math is so far beyond me I have no clue if or how the proofs would “create anything” or lead to anything useful. I’m sure they do, besides adding a little bit to our civilization’s knowledge.
I do suspect that LLMs think very “broadly” with a very broad knowledge but can’t really reason very deep without training for a special problem. So rapidly trying different approaches does sound like how they do it. So maybe it is a little bit similar to a typing monkey except that it apparently did these proofs with a relatively limited budget.
My understanding was that any hitherto success of LLMs in mathematics was in its trying approaches and information from different fields where they weren’t traditionally applied (within mathematics), they have surfaced potential links but haven’t created anything in any real sense. Still, a potential legitimate use for them that I personally hadn’t anticipated.
I mean that math is so far beyond me I have no clue if or how the proofs would “create anything” or lead to anything useful. I’m sure they do, besides adding a little bit to our civilization’s knowledge.
I do suspect that LLMs think very “broadly” with a very broad knowledge but can’t really reason very deep without training for a special problem. So rapidly trying different approaches does sound like how they do it. So maybe it is a little bit similar to a typing monkey except that it apparently did these proofs with a relatively limited budget.