delusions of grandeur are dangerous.

to put it simply, i thought i had a great idea .. about three days ago. i even wrote up what seemed a proof of a theorem ..

(whose existence i had suspected for weeks)

and after writing that, i thought of a corollary and "proved" that.

but then i developed doubts. [1]

if i have a proof of this case, then why doesn't it extend to this case .. which isn't true?

it took a few hours, but i settled that doubt, too.

then, yesterday morning, i thought to write down the argument, complete with the context, what is assumed, what it implies, and what it doesn't address.

my initial motivation was to write it well and settle it for good, so that i could be more productive and spend today thinking about something new. it was then that i realised that the object of my idea is not well-defined.

for the non-mathematicians out there, this can be the kiss of death for an idea.

so i today i found myself in a "dilemma-&-chase." i've just invented the term, and it means:

the method could still work, and the proof patched. maybe it will take just a little effort, and that it's worth chasing down.

then again, maybe it won't work. so here's the dilemma: should i keep going, or stop and do something new?

at any rate, i should have trusted my gut feeling. delusions of grandeur .. of having conquered something .. are never good signs, i say.

[1] when i was headed to the gym on friday and in the early afternoon, my officemate asked me why; i told him that i proved something that's a little too good to be true, and rather than getting emotionally invested in the matter, i had to do the opposite, and run away from the problem for a while.

he nodded in understanding.