How do math geniuses understand extremely hard math concepts so quickly?

I don't know if I would call myself a "math genius", but I've written a type-theory paper so that at least involved reading the work of legitimate math geniuses...

In my experience, you have to go at a concept from multiple angles, and work with it by hand. A lot. You can't just do repetitive problems, it's the variety of perspectives combined with the quantity of problems worked-out that eventually makes it click and allows your brain to form an intuition of what this thing really is and how it behaves.