I think the rule would also be bad for math research: looking for a proof is, mostly, a better use of your time than trying to articulate the mathematical intuitions which lead to a conjecture.
Having been a mathematician, I want push back on this a bit. Often the hard part of coming up with a proof is understanding a problem in a way that permits a solution, and that’s all about intuitions. Further, I often find the limiting factor for people wanting to do math is not the ability to read or write proofs but to manipulate mathematical concepts in ways that suggest proofs.
Doesn’t have much bearing on your broader point, but this is an idea I feel is overly popular, especially among mathematicians, where lots of knowledge gets transferred only by talking to folks because of norms against describing mathematical intuitions in writing in favor of proofs.
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.
Having been a mathematician, I want push back on this a bit. Often the hard part of coming up with a proof is understanding a problem in a way that permits a solution, and that’s all about intuitions. Further, I often find the limiting factor for people wanting to do math is not the ability to read or write proofs but to manipulate mathematical concepts in ways that suggest proofs.
Doesn’t have much bearing on your broader point, but this is an idea I feel is overly popular, especially among mathematicians, where lots of knowledge gets transferred only by talking to folks because of norms against describing mathematical intuitions in writing in favor of proofs.
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.