I've been working on a math problem for months now. I had a really nice approximation for a while, but I wasn't happy with that, I decided I needed to check how good my approximation was. I'm not sure I actually figured out how good it was (I'm not really good with approximations) but I did manage to find an exact solution (which I guess tells me how good my approximation was while also making it obsolete) Yeah, I put a lot of research into my writing.