four years have passed since my ph.d. you'd think i'd have become competent at judging what is good work, what is bad, and what work is worth pursuing.
i still don't have the hang of it .. not even close. i depend on a lot of people for advice, i bounce ideas off of people whose opinions i trust (at least, when i can get a hold of them), and sometimes i try to sabotage my own work [1] by repeatedly asking:
if you weaken the conditions enough for a definition, then you can always prove something. the point is whether there's any sport or surprise in it.
there's also something to be said for clean statements. i've thrown away dozens of pages of highly technical special cases to "theorems" that i wanted .. saving only the crucial pages that i need to rebuild everything else, if i need to. (it still adds up to a lot of paper, though, which is why i seem immune to the risk aversion of throwing work away.)
on the other hand, this sounds elitist. maybe i'm not being quite fair.
it's hard for me to appreciate, for example, an elementary proof to a hard-sounding result. it feels like cheating, like you've been tricked .. like you should have known all along and how could i have been so stupid not to see it?
when someone shows me a seemingly effortless argument, it's hard for me to step outside myself and think how long it took to find and shape this argument into simplicity.
so i think i've come upon the end of another project: this time a short one. maybe it will be a 15-page note, depending on how much detail i'll show.
i can't tell how interesting it is. i like the result(s), but the proofs aren't that illuminating. the techniques seem a little too simple. it feels like the same game; part of it involves generalised calculus on the plane again, something that i know how to use with some competency.
i feel like i should take time off from it before writing it up, see it with new eyes. that way, i can judge it more objectively, decide if it's worth writing up.
..
..
that said, i'm going on holiday this week.
i'm leaving the office and the country, joining up with an old friend to see new places. there should be internet, where i'm going, so if any random maths thoughts come up ..
.. then stay tuned. (-:
[1] it might also be career sabotage. it's not like i have many published papers or preprints. every successful project is rather crucial, so it's a fine line to walk .. \-:
i still don't have the hang of it .. not even close. i depend on a lot of people for advice, i bounce ideas off of people whose opinions i trust (at least, when i can get a hold of them), and sometimes i try to sabotage my own work [1] by repeatedly asking:
is this actually interesting?it's an unfortunate fact that the answer is no, most of the time.
do i get excited when i work on it?
does this answer a question that i want to see answered?
if you weaken the conditions enough for a definition, then you can always prove something. the point is whether there's any sport or surprise in it.
there's also something to be said for clean statements. i've thrown away dozens of pages of highly technical special cases to "theorems" that i wanted .. saving only the crucial pages that i need to rebuild everything else, if i need to. (it still adds up to a lot of paper, though, which is why i seem immune to the risk aversion of throwing work away.)
on the other hand, this sounds elitist. maybe i'm not being quite fair.
it's hard for me to appreciate, for example, an elementary proof to a hard-sounding result. it feels like cheating, like you've been tricked .. like you should have known all along and how could i have been so stupid not to see it?
when someone shows me a seemingly effortless argument, it's hard for me to step outside myself and think how long it took to find and shape this argument into simplicity.
so i think i've come upon the end of another project: this time a short one. maybe it will be a 15-page note, depending on how much detail i'll show.
i can't tell how interesting it is. i like the result(s), but the proofs aren't that illuminating. the techniques seem a little too simple. it feels like the same game; part of it involves generalised calculus on the plane again, something that i know how to use with some competency.
i feel like i should take time off from it before writing it up, see it with new eyes. that way, i can judge it more objectively, decide if it's worth writing up.
..
..
that said, i'm going on holiday this week.
i'm leaving the office and the country, joining up with an old friend to see new places. there should be internet, where i'm going, so if any random maths thoughts come up ..
.. then stay tuned. (-:
[1] it might also be career sabotage. it's not like i have many published papers or preprints. every successful project is rather crucial, so it's a fine line to walk .. \-:
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