As much as this blog is about Maths, it's also about rants. So here's another one. This one doesn't come with an answer, just a question, and one I keep circling back to in lectures, problem sheets, and increasingly, in life. What does it actually mean to prove something? I'm sure this is a moment every budding mathematician hits eventually. You're sat there in a lecture, staring at a proof that's being written down far too confidently, wondering where the hell it came from. Not about how it works1, but why anyone thought to try that in the first place. I think that's the weird thing about proofs, once you see them, they often look inevitable, obvious, even. And yet, before you see them, they feel like they've appeared out of thin air.