Yeah, I overstated this due to the point I was trying to make. I’m not sure quite what I should say instead, but...
Clearly it would be bad for math to monomaniacally focus on original reasons for believing things; likely worse than the current monomaniacal focus on proofs.
There’s a use-case where it is better to look for proofs than to look for your true original reasons. The use case has to do with communicating. Your point about the problematic nature of putting only proofs in papers is well-taken, but there’s also a good reason why publications have focused on that. Proofs are the extreme end of a spectrum of gears-y-ness.
Yeah, I overstated this due to the point I was trying to make. I’m not sure quite what I should say instead, but...
Clearly it would be bad for math to monomaniacally focus on original reasons for believing things; likely worse than the current monomaniacal focus on proofs.
There’s a use-case where it is better to look for proofs than to look for your true original reasons. The use case has to do with communicating. Your point about the problematic nature of putting only proofs in papers is well-taken, but there’s also a good reason why publications have focused on that. Proofs are the extreme end of a spectrum of gears-y-ness.