as you've no doubt noticed, i do not spend the bulk of my time here recounting what's happened in my life. the way i see it, this is of far less interest to my viewing personnel -- half of which knows about it anyway and the other half of which doesn't really know me personally -- than what i actually put here is, or so i think. what i actually put here usually has a starting point and then digresses into general philosophical thoughts or whatever half-assed theory i've come up with recently. this viewpoint is why my links page is organized as it is, for instance.
thus it is that i don't talk much about mathematics. math is my job -- i'm a math grad student. i'm not sure i've talked about it once here, though i probably have. why does it come up now? because of my frustration with the world on one issue.
there's this area of mathematics called algebraic geometry, and it's a bitch. this is the second official time i've taken a full-year course on it (same material, more or less), and i've also sat in on two other semesters (one half-assed, one eighth-assed or so, admittedly.) i've probably spent more time on it than i have on any other area of mathematics, because it is wicked hard. this semester i'm putting a lot of effort into actually learning it, but even with this i fall behind. part of the problem is that going to class is both in the morning and boring, and so doesn't happen much.
right now i have an algebraic geometry problem set due thursday. i don't know the material -- admittedly this is because i've fallen behind over the last week, but this particular thing is also the epitome of the field: it's really difficult, completely unintuitive (or at least no intuition for why these concepts exist is presented either in the book or in class), and seems to have no obvious cool implications. the bottom line is that i don't think i want to do anything that really requires this, but because so many other people (including my advisor) are deeply tied up in it, it's "necessary" that i know the material.
now, i've always been one to balk at these necessary things, which perhaps explains why i'm having so much trouble learning it (since i really don't care.) but this one in particular is unbelievably frustrating. i'm not the only one; everyone in the class is having the same problems i am, and while the support group i founded is helping some, there's no getting around the fact that this seems to basically only be difficult (and not pretty, or going anywhere, or whatever.)
it's not a coincidence that this is hard and that there are so many people tied up in it. basically whoever started this field (bear in mind that the most foundational algebraic geometer i've met, robin hartshorne, is exactly the sort of person who would spring this cruelty on the world) figured that the best way to get people involved was to make it so utterly general that the framework could apply to every area of math. they did a good job of that, but are people's lives -- mathematicians' lives, since it has few real-world implications -- really better for it? a method for attacking things is nice, but i can solve things without it.
right now i am extremely irked. i see no way in which doing this problem set will benefit me, aside from making other people happier about my "progress." tonight i spent 30 minutes and (i think) solved a pretty neat, publishable conjecture, and i think that's damn good. but i still have this problem set hanging over my head. i have plenty to do without it, and i'd be way more productive in terms of actually producing research that would make other people happier if i didn't have to do it, both short-term and long-term.
interestingly enough, this rant -- my first here? -- is not coming at one of my particularly chagrined moments. this issue is compartmentalized off of the rest of my life -- ignore it and it will go away, which is what i did on another attempt, with "unsatisfactory" as the result. i'm not reminded of it like i am of the fact that my roommates fill the sink with dirty dishes or my "love life" or allergies or a thousand other things which are intrusive. but it's symbolic of the excessive structure of modern life -- we have all these things that people must do (car insurance, public schooling, prohibition against underage drinking, etc..) because they're good for the vast majority of people. but we turn a blind eye to the me who doesn't really want algebraic geometry (prove me wrong, field, prove me wrong), or the farmer who doesn't need public schooling, or the underage but mature (or overage but immature) imbiber.
i had what might have been the best dream of my life last night from a purely novelish, observational standpoint. it was so well designed -- i'm amazed at what my unconscious can come up with. and the character played by me was so clever. i woke up and envied it. the other item of relevance is my inane chatter theory, which i came up with a few days ago, and which pleases me, but which i've already told quite a few regular readers of this column, so i will not recount in detail here.
but if you want a proof that all acyclic unique-source, unique-sink orientations of d-dimensional cross-polytopes are linearly inducible, i'm your man.