Monday, April 02, 2007

pride and humility.

i'm back from a weekend grad student conference in syracuse. let it be said that the analysts of syracuse know hospitality and entertain well!

i felt a little proud of myself mathematically.
  1. 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!

  2. 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.
it is a fine thing to feel useful .. hence my rare bit of pride.



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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