Saturday, June 28, 2008

weekend indulgences.

lately i've been splitting up my mathematical pursuits into two kinds:
  1. mathematics that i promised to do;
  2. mathematics that i want to do, right away.
this can't possibly be healthy. i blame this on my habit of making promises too easily, and having no sense of how long it takes to do anything mathematical.

this weekend i am indulging myself.

these past weekdays i've attempted -- sometimes succeeded -- in writing a first draft of a paper, as derived from the results in my frustratingly long thesis. admittedly, most of it involved cutting and pasting, second-guessing, rewording, summarizing, and other under-handed tricks.



so what is the indulgence?

i get to think about new math, sort out a new idea of which i am still suspicious. the last time i met my math sibs, i sketched this same idea for them and persisted that it was only an idea, not a proof.

they thought i was being modest;
they thought it was a sketch of proof.

well, i think i found a gap -- something subtle, nothing serious -- but it requires careful thought. i tell you: nobody ever takes me seriously. i don't say that i'm worried, for nothing!



anyways, a gap is a gap. i tried an idea and it's not perfect, which means a new idea is in order.

this reminds me. my late advisor had this manner about him:

when he was alive and well, a year or more ago, i'd walk in for our weekly meeting. he ask how things were going. i'd often say i thought about this, i think it's close to a proof, but something doesn't quite work.

he would want to know. he would want to know how close i was. he would get excited about it. i think little gaps in proof were like riddles to him: among other things, it's probably why he was a good mathematician.

to me, this gap is a weird little riddle, and the ultimate endgame doesn't worry me so much. i have to say, it's just a weekend indulgence, but i'm excited about working it out.

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