Comment by omnicognate
14 hours ago
> demolished software and mathematics because those have well-developed verification that's easier than doing the thing itself
They are proving useful for the parts of those things that have that verification, but in neither case is that the whole of the field. In maths, for example, we have seen LLMs find answers to some interesting problems/conjectures, but haven't yet seen them pose any similarly interesting problems/conjectures themselves because the criteria for a "good conjecture" are unclear whereas the criteria for a resolution of an existing conjecture are usually supplied by the conjecture itself.
Did anyone ask? i.e. did anyone with enough background to be able to judge whether a conjecture is "good" just point it at the repo of solved problems and ask it to formulate new conjectures based on the results/proofs? Or ask it to propose new structures to study? Or to identify a previously unknown general technique/tool that it had used in a proof?
It was asked to do a specific thing, and then its brain turned off/was reallocated to something else entirely (e.g. CRUD programming or answering celebrity trivia). It doesn't just idly think in its downtime. If we want it to do something else, we need to ask.
> Did anyone ask?
Given how... motivated the major LLM manufacturers are for good press? I've zero doubt that they have.
This is just moving the goalposts, yet again, all of mathematics has been hyper optimized on solving problem, proving theorems getting results and writing papers.
Only now that their job (the elites) has been automated was it really about explain results and theory building all this, despite those actions getting explicitly rejected from all the top journals (sans maybe math journals intended for a undergrad/high-school readership). People who weren't in the club and genuinely enjoy math are having the time of their life proving results. There is just a lot of groupthink and silent majority effects due to said elites running departments.
I use "theory-building" separately to Gowers since what he's talking about is field creation that solves tons of problems at once (Grothendieck, FTC, etc (I'll add AI itself here as a meta theory)) not making connections after the fact for the benefit of the lesser humans' understanding.
I have literally no idea what you're on about. All I said was we haven't seen LLMs produce any new conjectures/problems of a similar level to the ones they've been solving (and I even said "yet"). Have you seen any? What does this rant about "elites" have to do with my comment?
> Only now that their job (the elites) has been automated
I’m sorry, are you seriously referring to mathematicians as elites?
> People who weren't in the club and genuinely enjoy math are having the time of their life proving results
If they couldn’t do so before and they can now, it sounds like they don’t understand what their LLMs are producing anyways. That doesn’t sound very fun to me. If they genuinely enjoyed math, maybe they would want to understand it instead of prompting an LLM to do stuff for them?