i never learn, do i?

i stayed up late last night and at the end of my travails, i wrote this.

there's no point in doing mathematics when it's too late at night -- at least, not for me. by the time i set down my pen and paper, either of two things happen:

1. i'm no longer awake or sharp enough to prove anything rigorously, no matter how much i really want to prove something;
   
   
2. i think i've proven something, but the late hour makes me sloppy. experience tells me that when morning comes, i'll find a mistake and then curse my idiocy.
   

at the time i wrote those words, it was 3:52am.
i think i'm obsessing again.

on the other hand, this morning [1] i looked through my work again and it's not all paper to be recycled. i did make an implicit hypothesis and only did a special case last night, so the work remains technically correct.

it looks promising, but when i think about it, the setting is somewhat specific and the tools i have in mind don't address those specifics.

so my suspicions remain: the tools don't seem to be strong or sophisticated enough to prove what i want to prove. i think i'm wrong in some way ..

after all, i am always wrong in some way..

but i don't yet know which way. this reminds me of a passage that descartes writes in his discourse on method:

I cannot help deriving extreme satisfaction from the progress which I think I have already made in my research into the truth and in conceiving such hopes for the future that, if among the occupations of men, simply as men, there is one which is surely good and important, I venture to think it's the one I have chosen.

However, it could be the case that I am wrong and that perhaps what I have taken for gold and diamonds is only a little copper and glass. I know how much we are subject to making mistakes in what touches ourselves and also how much we should beware of the judgments of our friends when they favour us.

anyways, time's up: that's enough for "new math." i should get back to writing up my dissertation again ..

.. otherwise i will never finish it .. \:

[1] technically, it was still morning: i woke at 11:15am or so, though i felt rotten.