Imaginary numbers are a perfect example of that. It’s basically just “Okay, in the common number theory, you can’t get the square root of a negative number. What if you could?”. And what do you know, you can build a consistent theory where square root of -1 exists, and it has surprising properties.

Intuitively, good luck trying to make sense of it. But it doesn’t matter, it works, and it’s useful to build other stuff. That in turn can be used as modelling tools in physics and all.

The comparison doesn’t work. Maths are abstract, you don’t “believe” in it. You build a consistent theory with minimum assumptions (axioms) and if something stops being consistent, it means some of your assumptions don’t work and you need to change them to build a better theory. Maths is an abstract tool, not a representation of reality.

Infinity is just a concept you can define. There are tools to demonstrate something is true over an infinite space and obviously, you need those for a lot of basic maths. You’re not going to go anywhere in basic arithmetic or geometry if you can’t prove anything works over the infinite set of numbers or the infinite space.

I love that game, but if you are not enjoying it at that point I am not sure I can see it getting better for you for the rest of it.

Though if you just beat Orochi, that’s more like a quarter of the game if memory serves. Ōkami is quite longer than your classic Legend of Zelda game, I’d say for me it took a bit more than twice as long to complete the first time compared to, say, Twilight Princess.

Its story is more like a series of legends rather than a unified storyline, which didn’t bother me since it fits the mythology theme.