If someone has a very, very high IQ...

Your typical IQ test is based in pattern recognition and acquisition of information that is in front of you or stored in your memory.

People who are able to solve problems quickly do so because they have an intuition for how the solution may look like, and they’ve compartmentalized methods of solving, such that they may access it quickly. You do the same thing once you feel very comfortable with a given type of problem.

Give someone 1000 integrals to do. I’m sure, at the end of it, they’ll be pretty fucking good at integration, and they’ll be faster than you.

Center left?

Middle left has a rather weak pattern behind it in a way that each column has 3 of one color and 2 of the other. Now going columnwise, you get 3 empty, 3 filled, 3 empty, 3 empty, so one could guess 3 filled would follow in the next 2 collumns forcing it to be middle left.

As I said, though, it's a pretty weak pattern.

If this were true, math would have been developed to its current level millennia ago.

No, high IQ does not guarantee high proficiency in math. Such proficiency is more or less a roll of the dice genetics wise. However high IQ highlights better ability to notice patterns.

can you count without learning numbers first?

Middle left

...

That does not explain the second column.

The right three blocks are a function of the left three. There is no pattern where the rows depend on the ones above.