[kxyvr]

Well, I suppose it's a philosophical thing, but I don't subscribe to the discover point of view. However, to be clear, I don't think there's anything wrong with this viewpoint.

For me, math is a set of rules that we know to be consistent. Based on these rules, we put together new constructions that obey this framework. When I prove a theorem, I don't really internalize it as discovering something that was already there, but as putting together a new creation based on a set of tools that I already have. As the author of the result, I have the flexibility to be as creative as I want in how I prove the result and that creativity has an affect on how people view and internalize the theorem. I mean, if someone writes a narrative story we could say that the story was always there and that they just discovered it in a sea of words. Again, there's nothing wrong with that point of view, but I prefer to say that the person created the story.