There's a dimension of task-sets that's something like: how much is it the case that solving tasks like this basically boils down to "crunching the numbers"?

We could call this "combinatoricness" or "algebraicness". Algebraic things are soulless, calculative. More to the point, compared to more structure-rich tasks, it's less the case that being a mind implies being good at algebraic tasks, or vice versa.

Examples:

• Small-world games tend to be algebraic. E.g. chess, Go, etc. Think of a Zachtronics game like SpaceChem. Or tetris.

• Similarly, a lot of problems in number theory or analysis have this quality. Think of doing a complex integral that involves applying a number of "tricks", or generally doing complicated algebra. Constructions in axiomatic geometry also have this quality. I think the IMO problems that this AI solved have this quality in contrast to at least problem 5, though not sure. (The boundary here is much more jagged than just subareas of math, though.)

• Fairly extremely algebraic would be computing a complicated chaotic system; you just have to do all the detailed computations.

• Among the most extremely algebraic would be average-case hard computations. E.g., reversing a one-way function with non-tiny probability absolutely requires large amounts of compute.

• It's definitely not the case that "AI only exceeds human capability in very algebraic task-sets". LLMs and stable diffusion image generation both seem like they exceed humans at some aspects of their respective task-sets that are not very algebraic, though everything is a mix to some extent. But a reverse statement might be true: If a task-set has a high degree of algebraicness, and an AI can pass a minimum threshold of possessing the structure to unlock the compute -> optimization pipeline, then AI exceeds humans at that task-set.

• Most normal tasks humans do aren't very algebraic.

Humans tend to find it fun when there's a continuum of combinatorics/algebra in a domain. In chess, very crudely speaking, you could look one move ahead, two moves ahead, etc. (That's not really how it works, but there's a similar spirit that does hold true. Stronger players will tend to deal with longer, more complex, more contingent, more counterintuitive combinations. Even Karpov would, I assume without knowing, be playing strategically/positionally in response to an environment with such calculating opponents, tuned to shut down such tactics.)

We can ask different things. We can ask "how much explicit structure is there to be recognized in the world of this task-set"; this could range from 0 up to the whole cosmos. We can also ask "how much explicit structure is there, relative to the less thing-like combinatorics". That's an ambiguous question, but for example we could be asking "if there's an agent that performs at such-and-such level when predicting / manipulating / planning / designing stuff in this area, what would tend to be the ratio of explicit-structure to combinatorics?". A fuller analysis would tease these things apart more.

See sophistication.