self-criticism.

now that the final version is about 6 weeks old, i think i'm allowed to say this:

      much of my thesis is mathematically pointless and unnecessary.

i could say that the whole thing is pointless, but that's either a modestly hollow exaggeration or a philosophical understatement. [1]

this is what i mean: i can point to many a lemma, each of which serves no purpose. i wrote it because i had a proof for it. such lemmas don't imply any bigger, more interesting results. they're just there, and i know why:

      i was afraid that my thesis would be too short.

looking back, i was a fool. that thesis is 145 pages long [2]; do you really believe that all of it could be wonderful and golden and informative and useful?

i suppose there were other reasons: those results don't imply anything now, but i might need them later. it's bad taste to cite a thesis and not a published research article, but if i absolutely needed them, then at least i could find them there.

in fact, those results are clues. again, they serve no purpose now, but i might forget them. if i ever go back to that tome (read: thesis) then maybe i will remember why:

      i was this close to answering one particular conjecture.

maybe i'll come up with something later, fill the gap, and nail it down for good. then again, maybe not .. but just in case ..


so for now, i'll retract my last accusation;
maybe i'm not a fool yet.

only time will tell.


[1] this is going to haunt me for a while: try searching for "mathematics is useless" under google search. hit#1 is, unfortunately, me. to find the same page on yahoo search, you need the full title of that blog post.

[2] of those, 7 pages contain no actual maths. they include the title page, dedication, acknowledgements, table of contents, and the bibliography.