it took me countless hours of work and checking .. but i've submitted my own preprint and posted it on the arXiv. it includes a proof of the same (stronger) result, but by completely different methods ..
.. so i suppose that's worth something.
that said, i harbor no ill will towards that other author. in fact, it's inspired me, led me to prove a new stronger version of one of my previous results .. but that's beside the point.
this other work is great stuff. i mean that honestly .. and as for why:despite all of this though, i was depressed for the better part of a week. it never occurred to me that in my super-small field, somebody else would be working on the same thing(s) ..!
it's the first instance in this business where someone actually builds measurable dιfferentiable structures from the ground up, i.e. from the very geometry of a metric space. everything else i've seen uses non-constructive existence arguments [1] and i've always felt that such structures "come out of nowhere," almost immorally so.
that's all i'll say, for now. i need to read that paper more carefully before i say more. maybe i'll interrogate the author, at some point ..
nobody owns a problem --- i believe that, wholeheartedly --- but i still felt that i lost something, throughout all of this ..
if i'm feeling better, then it's because of two reasons:
friends. maybe i need lessons in self-confidence, but it really helped to get a second opinion or more from colleagues who are regularly following posts on the arXiv.
the oddly reassuring thing about mathematics is that sufficiently different proofs of the same result are perfectly accepted [2], provided that the later proof is shorter or clearer. the fact is that this field gets very technical very quickly, and any additional means to understand something tends to be welcome. not being a scientist per se ..
.. but (a little) more on that later ..
.. i wouldn't know how it goes for physics or chemistry or biology. that said, i guess this is thanks to those friends who believe in me .. so thanks, guys!
distractions. the paper's done, so it's time to move on. i have another conjecture on my agenda now, and i'm terribly excited. it's like having again something to live for and, as i've said before, to fight against a worthy opponent with a real chance of loss.
it's having a clear, cutthroat purpose for waking up in the morning,re-reading what i just wrote, i think i'm a little crazy. (maybe you think so, too.) that doesn't matter, though: i'm excited, i'm not harming anyone, and it's up to me to see if the world is really my oyster or not.
automatically putting the coffee water to boil,
and heading straight to work because, now being awake,
you can't stand to wait another moment before setting to work!
[1] to be fair, one could say that my own work is of a different vein from these. the approach relies heavily on functional analysis, though, and as for its weaknesses: it's actually rather hard to check whether or not an arbitrary space supports these so-called derivatiοns.
[2] as for credit, it's who publishes first: fair's fair.
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