I think you are taking it a bit out of context here. Obviously, I assumed in that phrase, that mathematicians are stacking suitable methods and proofs. If some factors are too large to not fit in some bound, then obviously that's not something you would stack. But once you have suitable proofs and proven correct and suitable methods, you can stack, and correctness does not go out of the window. Correctness remaining, you will be able to get to a proven correct result.

Of course proving things in mathematics is also a lot harder, usually, than computer programming, and it is probably still easy to make mistakes.