I don't think I've worked on any problems that took more than a couple days to solve. And yeah that feels intuitive. But I suppose I would have thought these long-unsolved general case math problems were mired in emergent properties at large numbers that made these kinds of approaches impractical.
Well, "these kinds of approaches" isn't really a binary thing. When you're looking at a problem, you try a big mix of lots of different approaches - maybe you try making the problem smaller, and you get something that you could possibly crack if you made this extra assumption, and then your friend talks about their own unrelated work and you think "hold on, there's a bit of an analogy there", and you go back to your books and discover that a handy missing piece is actually Lemma 3.6 of some famous text, and you take a lot of showers, and eventually maybe the walnut shell has softened enough that you can peel a bit of it off.
My record for one I've actually solved is like 6 months working on a problem (on and off). I'm actually more of a physicist than a mathematician (although my work is all about proving theorems and lemmas), so the objects I work with tend to be at least possible to play around numerically with for special cases.
