I want to write a proof. But I also want to save time. And so I miss nuances and make false assumptions and often think the answer is simpler than it is. It’s almost certainly motivated cognition, rather than inadequate preparation or “stupidity” or any other problem.
At least based on personal introspection, the part of my mind that comes up with proofs feels very similar to engaging in motivated cognition. This is in some ways ok because if a proof is valid then counterarguments aren’t something that need to be thought about. But yes, this can lead to the problem of constructing apparently valid proofs that then don’t work. One thing that seems to help is to engage in more or less motivated cognition to make a proof and then go through that proof in close detail looking for flaws. So essentially, use motivated cognition to try to get something good, and then use motivated cognition to try to poke holes in it. If you iterate this enough one will generally have an ok proof.
At least based on personal introspection, the part of my mind that comes up with proofs feels very similar to engaging in motivated cognition. This is in some ways ok because if a proof is valid then counterarguments aren’t something that need to be thought about. But yes, this can lead to the problem of constructing apparently valid proofs that then don’t work. One thing that seems to help is to engage in more or less motivated cognition to make a proof and then go through that proof in close detail looking for flaws. So essentially, use motivated cognition to try to get something good, and then use motivated cognition to try to poke holes in it. If you iterate this enough one will generally have an ok proof.