lmao I'm in tears how on earth was this perceived
anyway here goes potentially pissing off three perfectly respectable fields
any idealising romanticising proselytising about math, about what math is, will end up with the idea of "ultimate truth", right? the promise of order and a pristine reality that exists, outside of meagre human existence. and it really is there!! all sorts of patterns and connections and don't you find it breathtaking that humans will pick up a symbol or two and if you play around with it enough there's actually laws acting behind it all?? like, there's actual understanding!! it's not all just obscurity and chaos!! fucking incredible. and I mean it's no wonder people would think math is some sign that god exists, you know? (#teamleibniz)
but then you think a bit more and realise. hang on. something isn't right. For one reason or another, I don't think this 'thing' I'm thinking about actually exists. the idea of an infinite all-good all-powerful god is absurd, isn't it? and no fucking way infinite dimensions or "two intersecting parallel lines" (or even real numbers) actually exists. I mean Plato thought there's some other 'world' where the perfect ideal triangle hangs out with the perfect ideal tree, but obviously he's on crack, right? but what the hell. if they don't actually exist what have we been talking about? everything that's been written are just hanging in air. how do we justify the investigations that continue despite fundamental scepticism?
and then you think. maybe it's impossible to get away from that scepticism. maybe we can never prove that there's some whole 'truth' out there. maybe there is no complete truth. and there isn't. math says this. because we (Gödel) figured out a way to talk to math about math and asked "hey, do you know all the truths about numbers out there" and it said "no". (and that's fucking insane. isn't that so fucking insane??)
math is incomplete. it can never be fully known or defined. but that doesn't mean it's not there, still constantly being revised as we find out new things about it every day. there is no truth but there are truths. math doesn't really exist independent of us. in some sense we did make it all up. any concept or label we use are ultimately only for the moment, for us to better understand the world and the worlds we've created. tomorrow we might find something new. another perspective, another set of concepts and theories. but that's exactly what it's meant to do.
math is fucking queer.