impasse.

in one of my research projects, i'm at an impasse. there is a claim that, to make any progress, i either have to prove or disprove.

i'm not sure which one should be right.

if it's true, then i'll get a surprising result. logically, there's no reason to suspicious of it, but the human, intuitive side of me has trouble believing it.

if it's false, it means that i'll have to turn back to a paper and reprove things for an analogous (yet logically different) case .. with the risk that, perhaps, it won't work out. so the obstruction is that of mental laziness; i'll run all my options before having to "re-invent the wheel."

when i was an undergrad, i thought that all of mathematics was rigor and logical steps. the older i get, the most i appreciate intuition, geometric or otherwise.