:up:

However, math is infinite, and any number can be conceived, so there are an infinite number of possible thoughts. is this a problem for reductionism? — RogueAI

Not all numbers can be conceived distinctly and discretely. Any number can be conceived, but not any number of numbers can be conceived. There is a limit to the number of numbers a human can think of, name, and conceive.

But if math is just a rules game, how did we come up with innovations like imaginary numbers, which have real-world applications? Doesn't that require understanding of math on a conceptual level, rather than something that's just rules-based? — RogueAI

Thisi is a diversion from the original topic. It diverges from the claim that the mind can contain more data elements than what the brain can hold.

any number can be conceived — RogueAI

But not all integers can be conceived by a single brain. By conceiving I mean just simply naming them. Integers are simple numbers. But you (or any other human) can not name more than a finite number of integers, all different from all others,
in their lifetime.