There's been a question going around the #MTBOS this past week -- succcinctly stated by @Trianglemancsd: "Also the original question is an important one. Why does watching a sports performance inspire while watching a math performance intimidate?"
And there's a lot of good thinking out there about it.
One key difference is the external/internal dimension -- watching a sports performance, even a novice can have some basic understanding of what is going on because a large part of what is going on is visible. I can't run that fast, spin that fast, release that fast, hit as accurately, etc., I might say while watching Stephen Curry, but I know how to improve every one of those pieces, and at some level at least, I can understand why those moves are important. A professional basketball player watching basketball will have more insight than I will, but I would still be able to have a conversation with them about what is going on, and I could still go out and try to make that move or hit that shot and feel a connection with Curry even if I will never be able to do exactly what he does.
But if I watch a math performance, someone solving a mathematical puzzle, how much of the "action" can I really see? If I don't know why any of the moves were made, how can I improve my ability to make any of those moves? If I sit with a mathematician and discuss what we are seeing, will I even be able to follow the color commentary?
I'm reminded of my favorite Feynman quote, about figuring out the universe being like watching two masters play chess. We might be able to figure out the rules, but we will have a very hard time figuring out why any of the moves are being made. When we are watching math being done there is very little that I can grab onto, and thus very little that I can use as inspiration to improve myself.
So how do we make the mathematical game more external? How do we connect the moves being made to a story that students (and ourselves) can understand?