system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What makes mathematics factual?
gpt
The ELI5 answer is that math is more or less like a game. Mathematics is carried out by a predefined set of rules on a predefined set of objects. Because the game never changes, the allowable moves never change, and so the possible outcomes never change. Any situation in which the rules of the game are allowed is therefore subject to the outcomes mathematics applies to. So things like basic physics which work on just adding and multiplying numbers representing physical quantities are essentially universal because they are a situation in which you are playing the game, just using different words for the same things.

&#x200B;

Sometimes, the rules of the game do change. This can happen because we find out the game is broken (as in e.g. the crisis of naive set theory), and sometimes it happens because we find out that some other games are also cool or useful, or less controversial. Not all mathematicians agree that we *should* be playing the game that we are, and so they play slightly different games, but this doesn't effect the main allowable moves of the game. The basic things like + and x are still the same, it's that there are some weird edge cases involving things like ungodly huge infinities and what you can and can't do with them that some people object to.