Sunday, August 12, 2012

work-in-progress, part 4 of 4: triumph!.. i guess?

so this is the last of this series. maybe there will be others like it in the future, but i've told my piece for now .. maybe more than that.

honestly, this should be part 5; then again, why restrict ourselves to integers?

on a more serious note-- had this story ended otherwise, then i like to think that i'd still have told it .. but that's what i'd like to think. the truth is that i don't know. the most i can say is that i'd have written noticeably less, if only not to dwell too much on one failure and start something new right away.

some of you are students, graduate or otherwise, and perhaps this account just shows you that nothing ever goes smoothly, even years after the ph.d. .. but on occasion, that things move along well enough. (i could say the same about this blog as a whole.)

for those of you who know me, though: i still don't know why you trust me with anything ..

// initially written: mon, 30 july 2012 //

i patched the proofs and my old theorem's back from the grave. i feel pretty good, like not only have i dodged a bullet or two ..
.. but disarmed the bad guys, saved the day,
all the while muttering, "i'm getting too old for this sh-t" [1].. q-:
so if i may indulge in a little shameless gloating .. i feel like i really understand what's going on now, in the sense that my intuitions have become rigorous. along the way, i dare say that i've developed a few new techniques ..

.. and strangely enough, for Euclidean spaces!

it's either that, or i don't know the literature well enough so that i'm ignorant of previously similar constructions.

this has happened to me before; i thought that approximating Hölder functions by Lipschitz ones was novel,
but semmes has done it before, more elegantly; my colleague rοger's observations had preceded mine, too.

in particular, i am proud to say that some of these ideas involve geοmetric measure theοry. to me, this is a stroke of good fortune!

you see, this is a field that i have always admired; if things had gone differently, then perhaps i would have specialised in it as a student [2]. these things are hard to say, of course.

// initially written: thurs, 2 august 2012 //

you'd think that finishing a project would make me feel elated, but then you'd be giving me too much credit. i now feel empty, like i lost a worthy opponent.

at this point i'm reduced to typesetting, checking citations, and other minor corrections: hardly anything worth regaling anyone.

sometimes i feel like i've taken the ascetic ways too far: there is this common advice to not worry about the destination, but enjoy the journey there. now that this journey is over and i see the destination, i cringe.

that's it?

these last few mornings i've been scribbling on the same conference legal pad as i've done before, back when i thought i might lose those theorems. most of the time it's picking up loose threads from proofs, seeing where it takes me. i'm slowly collecting a small list of problems to work on next.

every so often, though, i try to construct a counter-example for the theorem again.   you never know ..

[1] suffice it to say that, as a hot-blooded american boy, i grew up on all sorts of action flicks: ah, the 80s .. (-:

[2] i feel like that about a lot of topics. for example, sometimes i think it would have been better if i had really focused on optιmal transpοrt or in stοchastic games, when i was younger and could pick ideas up more easily; maybe even banach space theory. for worse or for better, i'm firmly a metrιc-space guy now.
.. "if things had gone differently" .. that's a dangerous direction towards which to ponder.

1 comment:

Rod Carvalho said...

Quoting Sylvain Cappell:

"When you start on a new problem, you always feel stupid. You might spend a whole day on a single paper, an hour on a single line. And you still don't understand it. When you get to a certain position in life, you don't want to feel stupid anymore. In mathematics, that's when you're dead."