[MrManatee]

I think there exists a separate skill for classifying problems by difficulty, apart from being able to solve them. This skill can be developed from both directions by learning which problems have been solved and which haven't been.

If someone asked me to find solutions to these example equations, there are three complications that I would immediately notice:

1. We are looking for solutions over integers. 2. There are three variables. 3. The degree of the equation is 3.

Having all three is a deadly combination. If we were looking for solutions over reals or complex numbers? Solvable. Less than three variables? Solvable. Degree less than 3? Solvable. With all three complications, it's still not necessarily hard, but now it might be. We might even be looking at an unsolved problem.

I haven't studied enough number theory to actually solve either of these problems, but I have studied enough to know where to look. And because I know where to look, it only takes me a few seconds to recognize the "this might be very difficult" vibe that both of these have. Maybe LLMs can learn to pick up on similar cues to classify problems as difficult or not so difficult without having needing to solve them. (Or, maybe they have already learned?)