Wednesday, August 13, 2008

conjectures as obsessions

i think i proved something new today. it's a little lemma which is not useful for anything, but it came up because i've been conspiring about vector fields again [1]. well, perhaps it will one day be useful, but i haven't thought that far or deeply about it, yet.

it's also not too surprising. a special case has been known (but without explicit proof) and the statement is the same [2]. i suspect that i rediscovered their argument, but that will have to wait.

i think i've reneged on a vow again.

some months ago i said, half-publicly, that i was going to leave the field of analysis on metric spaces -- this specific stuff, at least -- and start working in a new but related field. at the time, i had just finished the final draft of my thesis and i was desperate to do something new, something different.

even now, i'd like to diversify my interests and see if i can become some kind of analytic "jack of all trades." but between then and now, i discovered something; rather, i remembered something about myself.

you see, i tend to obsess,
and i have a weakness for conjectures.
  1. call it the habit of youth, but given a half-decent idea, i'd still go after the isoperimetric problem in the (first) hei$enber9 9r0up in a heartbeat.

  2. there are few days when i think about maths and when i don't think about one particular case of the''f1@t ch@in c0njecture" of ambr0si0 & kirchh3im. i don't know why. i just do.

  3. on those rare days when i am brave enough for the abstraction, i might think about the various chee9er conjectures on so-called PI sp@ces and their we@k tan9ents. then again, i'm often not brave enough; abstraction is not one of my strengths ..
.. as opposed to obsession, but is that really a "strength?"

call them obsessions or loyalties or motives: as a mathematician, i have them and probably i am ruled by them. i like to think that i am not alone, and i suspect that it is in the nature of how we teach mathematics:

for so many years in school, we are told to solve problems ..however algorithmically.. and as undergraduates, we learn proofs and work on problem sets. we become inclined to think in terms of problems.

i've told others before that i do not build theories. it's not in my nature; i am not my late advisor.

as for whether i am a problem solver ..solve problems?..
well, let's say that i think about my obsessions.

[1] then again, by definition it is impossible for me to conspire .. that is, to conspire alone. according to, "to conspire" means:

1. to agree together, esp. secretly, to do something wrong, evil, or illegal: They conspired to kill the king.
2. to act or work together toward the same result or goal.
–verb (used with object)
3. to plot (something wrong, evil, or illegal).

so unless vector fields are inherently evil, i don't think i was necessarily conspiring. oh well.

[2] see the latter sections of "$tructure of nu11 $ets in the p1@ne" (ecm proceedings) by A-C-P

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