But is it a computational problem then?

Try doing a calculus problem. E.g., integration. Even if you do it on paper, your approach is probably wildly different than a computer integration algorithm. An algorithm that does it symbolically, ala Mathematica, is a pretty difficult thing to write for an arbitrary mathematical expression. People solve those problems largely through intuition, with a sprinkling of procedures that they remember.

> People solve those problems largely through intuition, with a sprinkling of procedures that they remember.

Without making the claim that LLMs have intuition (and certainly not inspiration), what you describe sounds analogous to an LLM with function calling.