This is the wrong way to think about mathematical (or any other kind of) creativity in my opinion. In the extremely high-dimensional space of "ideas" (whatever that means) there are almost certainly profound ideas that are the interpolation of existing knowledge, i.e. the curse of dimensionality. It's not at all clear that you need to extrapolate from existing knowledge to be creative.

I really don't think that's true. Of course after the fact a counter example looks easy. Because look at it, it's obviously that it doesn't work. But that disregards the process of finding it. That requires great creativity(or computational resources if the problem is tractable at all).

>GenAI is great at combining existing things in new ways (interpolation). It's terrible at creating new things from scratch (extrapolation).

I think you believe a fallacy about how human cognition works if you think we actually do something different than interpolation