What makes mathematics factual?
In: Mathematics
Mathematics takes arbitrary claims about the world in, and reasons about them. If you reason about unicorns, the math probably has less of a grounding in real world than if you reason about physics, say. Math sincerely doesn’t care how you choose your starting point for your reasoning. It just takes it in, and allows you to draw conclusions.
And as it turns out, many times we’ve only later found out that things that we reasoned about just due to mathematical curiosity, actually have some counterparts in reality. Like for example, non-euclidean spaces were thought to be fanciful nonsense for a very long time, until people realized that actually surface of a sphere can be seen as a non-euclidean space, so all that fanciful unicorn math actually relates directly to say, maps of the world and navigation.
Math doesn’t care. Cartographers might. Or physicists. Or electric engineers. Or programmers. Or locksmiths. Or doctors. Or whoever just so happens to start from somewhere and wants to start reasoning about where they are.
Or, you can go the other way around, start with facts and try to figure out where you are located in the world of math. For example, Newton thought that if you’re sitting in a train moving forward at 50mph, and on the next track you see a train pass you by at 30mph relative to you, you could tell how fast the second train moves relative to the ground is simply 50+30=80. Einstein then showed that that math, while totally okay math, does not describe reality. In reality, the second train moves slightly faster than 80mph relative to the ground. He located a better math that more closely aligns with the reality.
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