Gracie, I can’t reach out to you online, but this is my response as a mathematician. I hope it helps someone.
These kinds of questions you are asking are what drive us as a profession. It doesn’t matter if your example is Pythagoras or whoever. At some point, for every piece of mathematics that we know, someone asked “how?”, or “why?”, or “why not?” and then just let the ideas take them where they would. Literally some of the things that make a stack of technology work came from someone saying “what happens in 3d instead of in 2d?” and then he ended up graffitiing the answer on a bridge when he finally figured it out. No one asked him that question, he asked it himself. No one told him the answer either. It took some hard work, he tried a lot of things, he failed a lot, but he persisted. People had arguments for decades over whether that was the right way to do it. This was 150 years ago. Today I’m pretty sure most 3d animations you see today use that little idea. But he just wanted to know “why?” He wanted to know “can I do it?”
Sometimes it was people just thinking about walking around a town and across bridges. Sometimes it was a fun puzzle. Sometimes it was bets and duels. Sometimes it was a guy who did maths in prison. Sometimes it was a girl who did maths at night when her parents didn’t know and didn’t want her to. But everything we know in maths started with someone asking “why is it like this?”
Please keep asking “how?” and don’t take any nonsense when people don’t realise they don’t know either and never even thought about it.
(Via Jordan Ellenberg via David Butler on Twitter.)
theHigherGeometer 