Isn’t this like asking why society doesn’t collapse, when the software that drives it is filled with bugs? My impression was: any result in modern mathematics

Isn’t this like asking why society doesn’t collapse, when the software that drives it is filled with bugs? My impression was: any result in modern mathematics critically depends on another result, and that result depends on some other result... This is like how most large software systems depend on various 3rd party libraries. I guess the answer for both questions is that the things we build, whether they be mathematics or software, work well enough most of the time that you don’t notice the problems unless you’re paying attention.