Math isn't "cooperative". Math is about truths. The length of circumference. The area of a triangle. The formulas for these are true in an objective sense irrespective of whether you understand them.
That said, without understanding, Math can't evolve. Comprehension of a proof is very important, but not what Math is fundamentally about.
Computer programs are Math. You can use them without understanding how they work.
That said, without understanding, Math can't evolve. Comprehension of a proof is very important, but not what Math is fundamentally about.
Computer programs are Math. You can use them without understanding how they work.