doubts and demons.

sometimes i wonder if i should be a mathematician.

sometimes it feels like i'm not cut out for this. i'm too error-prone and too neurotic, too often like this namesake, a "frustrated over-analyst." too often i worry about my work, wonder if i've bungled another proof, made another error, and convinced myself of something wholly erroneous or unfounded.

sometimes i believe i can't do anything right, and sometimes that belief is justified when i find another error or inconsistency in something i've written months ago, an idea that i've run off with and imagined grand, shining towers ..

.. only the foundations are faulty and though imagined, the towers nonetheless fall into a collapse.

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for some reason today, i feared there was an error in one of my proofs, and i read through my write-up. sure enough, i found one: a flaw.

i thought about it last night, lost my nerve and couldn't sleep well, a half-sleep. i "woke up" this morning at 8am, jotted something down ..

.. and it seems like it works. there might be something wrong with how exactly to say it, but it's clearer now, and the result is still true ..


.. i think,
but i've been wrong before.

it's a terrible thing when a mathematician loses his nerve. at the moment, i can't bear to look at it anymore, but i've been told that i'm finishing soon ..

.. and there's a lot of work to be done,
if that's really the case ..

.. and i haven't even gotten anywhere near writing up the schoenflies stuff (read: salvage from the first thesis problem) or doing professional things, like cv's and teaching/research statements and fellowship grants and the like!

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i don't know anything; i don't think so, at least.

all these hours, all these days,
is this really research that i've been doing?
valid, careful arguments?

what if it's all wrong, and i've simply not found the one error that i cannot fix? what's to say that i haven't convinced myself of something stupid once again and wasted days or weeks or ..ye gods.. months?


when you don't believe in an afterlife, then the time you have remaining is what matters most. i don't mean moments (because one has to get on with living life and not watching clocks) but i mean longer times that you can forget but still count, like days and months.

yet i'm wasting all this time ..