it's a strange thing. whether classes run or not, my mornings have been as they always are ..
.. so why is it so hard now, to work diligently and accomplish something for my week's mathematical endeavors?
today i was distracted by too many things: the recent humidity (and a relative warm day in an non-air-conditioned apartment), a promise to play basketball in the afternoon, and another commitment in the evening.
i entertained an idea today, but it doesn't seem right. for one thing, it's not quite well-defined, but it's temptingly close ..
.. and it's the only thing that i can think of, which seems not unreasonable to prove. a month or two ago i had formulated a rough conjecture
(rather, i'd call it a claim;
it's not grandiose enough to be called a conjecture.)
now i'm close to something, but i can't quite formulate what the new form of the claim/conjecture should be.
perhaps i should explain that.
over these past months, we've encountered plenty of instructive examples and cautionary non-examples which show that, as i would have stated, the old conjecture is false.
however, interestingly and frustratingly enough, all the non-examples the advisor and i have considered are not that far off from that initial claim.
it's almost as if we need a magic word or a password, and then the gates will open. if we had the right claim -- if we could formulate what seems true and fits the phenomena we see in examples -- then i could set out and try to prove it.
i cam mumble or scribble something, but it wouldn't be precise .. yet. but i'm working on it.
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