So I was hanging out in my professor's office on Friday, playing maths, and I asked, "Couldn't I have a small problem to work on over the weekend?" So he thinks for a minute, and then he says, "If [itex]f[/itex] is a continuous function such that [itex] f: [0,1] \to [0,1] [/itex], then there exists a fixed [itex] x \in [0,1] : f(x)=x [/itex]. Prove this" (I'm in his elementary proofs class.) So I take it in for a brief moment (too brief) and I smile and say, "easy, it's one of those basic calc function theorems, they're all in my book.....Rolle's? no.......ah yes! Intermediate value theorem will do the trick! I just have to look up the definition to be sure, then it will be simple." And he looks at me and says, "I'd like to give you a hint but it would then be obvious." And I shoot back straight away, "Hint? What you have said is already more than sufficient! This will take five minutes. I got this." I. Got. This. I so don't got this. I first had a twinge of doubt when I opened my calc book and under the intermediate value theorem where I expect to see a proof I see instead: "This proof is given in more advanced books on calculus." Uh oh. Okay, I think, this is a rather abridged book, I've completed the entire thing, I can probably do this. They just don't want to put it here because it's like, chapter 1. .... It's only a matter of minutes before I realize this isn't the theorem that I need at all. I discover that I need a "fixed point theorem". Such a thing is definitely not in my calc book. So here I am on Saturday morning thinking, "omg, this is going to be very hard for someone at my level." But I better do it, because I said it was a cakewalk! Anyone else said something to a prof they later regretted?