My point isn't just that they are really weird, but that people think about mathematics in an extremely heterogeneous way
Heterogeneous compared to what? It's a lot more homogeneous then how people think about nearly any other subject.
I suppose I will defer to your expertise on how people think about everything, Eugene.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.