i felt a little proud of myself mathematically.
- i didn't say anything deep,but i was glad to have discussed some questions about p-harmonic systems with tomasz, a student of tadeusz iwaniec. in fact my understanding of that particular theory is superficial; what little i understand, however, does fascinate and tempt me.
if i didn't have to complete research for a thesis, i'd sorely wish to work on such problems. this is not to say that thesis work is going poorly -- the opposite, really -- but i am too tempted by greener grass on the mathematical lawns of others! - my understanding of elliptic complexes is equally poor, but some recent work of derek (another student of iwaniec) reminds me of a theorem of d. jerison. i told him this, and he actually wrote it down. he knows his research better than i would, of course, but i hope this reference will help him.
that diminished, however, after i tried to warm up to work again. having lost my copy of a particular paper, i browsed through an electronic copy and started reading a paper (to appear) which the advisor has written.
it's 92 pages long, and having reached page 52, i feel humbled again and slightly depressed. its breadth is astounding, and today, like some days, i feel as if the advisor knows everything and i can essentially say nothing of consequence.
if someone asked me what a mathematician often feels, i would say, in decreasing order:
- frustration: every good mathematician knows a few claims that (s)he cannot (yet) prove.
- humility: to each mathematician, there is always a wiser or cleverer someone, who has produced work which that mathematician can appreciate, but does not fully understand.
- add almost everything else here, but ..
- joy: because, every so often, one proves something at long last, or stumbles onto a proof which is a pleasant surprise.
anyways, it's time to get myself back together, so that i can accomplish something by tomorrow!
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