conjectures

last week the advisor made a conjecture which seems on-target, but i wasn't sure what to think of it.

i suppose it's a natural reaction. if i knew how to think of it, i'd have proven it, and it wouldn't have been a conjecture now, would it?

today i made a conjecture which encapsulates the advisor's previous conjecture, though i wasn't thinking of it at the time.

more accurately, i made it last night over a glass of white port wine. then i realised that i was indeed drinking port and thus could not be trusted with conjectures, so i labelled the page i wrote on:

crackpot conjecture

and then happily continued with my whimsical speculations.

doing so is like giving free license to be wrong. sometimes i write "scratch paper" on a recycled page and then start messing it up with scrawls and diagrams and cross-outs. when there are enough ideas, then comes the good paper and the process of clarifying the ideas.

even to this day, i feel like i can only do mathematics, draft by draft; some habits do die hard.

the weird thing is that the conjecture still sounds plausible when i'm sober, and it would relate these metric co-tangent bundle and exterior differential notions with geometric measure theory.

the cool thing is that the advisor also thinks it's plausible.

the worrisome thing is that Weaver's notion of exterior differential may be rather rigid, and it mightn't be as interesting an object of study.

then again, it could be my paranoia: after you've killed one thesis problem (for the worse), there's always the fear that you'll do it again. who'd have thought that it would be so worrying to be right, for once?