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Notes -
The classification of Finite Simple Groups is the largest I recall hearing of, off the top of my head. Looking it up now, it added up to over 10k pages, so in the same ballpark as 1.6M lines, and probably a significantly larger proof when you consider how much more verbose formal proofs have to be. I wouldn't call the classification something any human, singular, has written, though; it's essentially the combination of several hundred proofs of intermediate steps written over decades by around 100 mathematicians.
Looks like there's work in progress to simplify it, but it's only getting cut down to several thousand pages?
I guess the follow on to the other comment here is what is the length of the FSG in lean, in this Lean 4 Mathlib library? I think the FSG being the compilation of hundreds of proofs over decades by 100 mathematicians, and it be comparable to this Navier-Stokes proof in length/complexity(?) is reinforcement to my belief that LLM-AIs are very good at the sort of thing that is just too large in scale for human's to perform at. Assuming this is the solution to the NS, then it would have taken 100s of mathematicians decades to solve this, just by the shear scope of knowledge and effort required.
Good question! Right now the answer is "mu"; it's not in there. We might try to extrapolate from the English proof - if around 20 pages of English turns into 250K lines of Lean and around 1000 pages of English turns into ~13M lines of Lean, I'd guess we'd be in the ballpark of a billion lines in total.
Well, the trouble is that we might not yet know what the scope of knowledge and effort required was, only what the scope that was sufficient was. The same theorem can admit scores of different proofs, of greatly varying difficulty levels and lengths. Human mathematicians tend to find proofs uglier the longer they are, counteracted by the extent to which they can be broken into intermediate lemmas (or in the FSG classification, whole-paper-worthy theorems) that look interesting on their own. But AI mathematicians so far appear to just be trained to Do The Task and get to any proof. My wild-ass guess is that without any AI assistance it'd have taken us decades to get a solution here, but it wouldn't have been a thousand man-years of effort on this problem, it would have been hundreds of man-years of effort on other related problems that eventually made this one look more tractable.
Nobody will ever try for a better non-AI-assisted solution, though. At this point the fastest way to get to a nicer proven counterexample will be to train (or at this point maybe just task) AIs with finding shorter+simpler+more-interesting proofs.
I think "too large in scale" has always been computers' strong suit vs humans, but the scope where we can actually employ that scale has greatly changed. It used to be that computers were good for tasks where describing how to get a solution was simple but actually executing that process was incredibly tedious. It feels like we've cracked the next level, tasks where describing how to verify a proposed solution is simple but actually figuring out how to get to that solution is incredibly tedious. There's still one level left, that of problems where we can't cheaply verify/score a proposed solution so we have to actually get AI to learn efficiently rather than just self-playing with a billion artificial problems before tackling a real one ... and then that's pretty much it.
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