Genuine question, from someone with a non-math background - at what point does the constraint become the number of unsolved conjectures remaining, instead of the ability for LLMs to actually solve for one?
Not entirely following the question, but there are an infinite number of conjectures, the blinding majority of which serve nearly no purpose to humanity. Consider that for every executable program one could create a conjecture, and therefore a mapping exists from executable programs to conjectures. Now, consider the infinite possibility space of executable programs…
Anyway, unless you mean conjectures that humans have already posited, or ones that are particularly famous, that list is much shorter, but also contains conjectures that I’m not convinced can be solved before the heat death of the universe using all available compute power. P != NP is a conjecture, for example. Also a lot of prime number conjectures that are extremely computationally expensive.
Math is very hit-or-miss; the complexity of a question does not give much of an indication about how complex the answer will be. Look up the formula for solving a degree-4 polynomial equation to get a purely visual idea how this can look (and then degree-5 suddenly forces you to use complicated new functions). And there are problems (like the Collatz conjecture or P vs. NP) that there doesn't seem to be any promising angle of attack for over at least decades.
I would wager that this is a fundamental part of the structure of math that has been a constant from ancient Greece till LLMs. There are even some formal results, similar to Gödel's theorems, that say that the maximum necessary length of a proof grows arbitrarily fast (e.g. more than exponentially, double-exponentially, or any function with a formula) with the length of the statement being proven.
Point is, math will most likely never suffer from this particular problem.
