Sunday, February 06, 2005

Something like a Socratic dialogue ..

It feels like I'm standing still .. or rather, sitting still. Anyways, you get the idea .. or wait, you may not. In fact, that's the point of this post: it's meant to convey the idea to you. Right. Yes.

"So what's this idea all about?" you may ask.

"Nothing big," I reply casually. "It's just that I've come to a point in my academic life that I should do something. In fact, I feel the urge to do something, to make progress towards some end."

"You're talking in riddles again," you point out, "and you're being vague."

"Fine, fine," I retort, "Lately I've realized the limitations of being a student who only sits in lectures, solves problem sets, and takes exams. It's a passive sort of learning, in that one must be given topics to ponder and ideas to entertain in a reasonably digestable form. Despite the frustration of understanding this matter or that, the efforts are temporary and the work not so motivating, because you have no inherent tie to it. It's just coursework that your instructor has assigned to you, or it's a topic decreed by a syllabus."

"Everyone feels that way at some point," you agree, "but what's the alternative? What's your alternative?"

"I'd like to come up with ideas of my own .. or learn ways of coming up with ideas. I think I see now why the structure of the graduate program has developed the way it has, here in the Mathematics Department. I'm not saying that there's nothing left to learn by sitting in classes, but I'm not growing as a mathematician if I'm not thinking for myself and letting others suggest to me what to think about and what is 'interesting.'

"I feel mentally restless, but it's a good sort of restlessness. It's the same sort which appears during the last week of holiday, when you've had enough good cheer and merriment and are ready to take on the rigors of the daily grind again.

"The course of the graduate program urges me to go and seek a thesis advisor, so that I may proceed to pursue academic research and write a thesis. I think I agree to that now."

"Well, were you ethically opposed to it, before?" you ask in jest .. at least I think it's in jest.

"Of course not, but mine was a neutral sort of opinion, simply because I hadn't thought much about it. Now I have, and I agree with the philosophy. I agree with it as an avenue for intellectual growth, but also as a realistic end.

"Regardless of whether I can learn all that I mean to learn and do the best that I can hope for, at the end of the day there remains a concrete objective. I have to take my oral prelims, I should do a bit of research, and I must write a thesis. Those goals cannot be argued, and taking this bare, concrete perspective, one could say that the rest is icing on the cake, so to speak.

"I think I'm ready."

"That's nice," you say.

"Thanks," I reply.

ps. I finally wrote to one of my profs. With any luck, we'll discuss matters of advising soon and with some more luck, perhaps this prof will be conducive to working with me.


Kevin said...

Hooray! Congrats on writing to the "prof". From the sound of your post, it seems like the research group thing we were discussing the other day is just what you are looking for. Marie expressed interest too, provided that she passes the algebra qual in May.

Kevin said...'d it go? Well, i'm sure.

janus said...

In response to the first comment: thanks for the good cheer, Kevin. It's a little progress on the advisor search, at least.

As for this proposed research group, I think it's an excellent idea; it'd be a fine thing to tackle problems on our own terms. Marie and others are happily welcome, though if the group is too "large" (for example, 10-12), it might be somewhat difficult to keep a single focus going.

Sounds like fun, though. (:

janus said...

In response to the second comment, it took me a moment or two to parse the tone of your second sentence! I was mentally waiting .."What is Kevin sure about?"

But yes: well.

Anonymous said...

Sounds you want to pursue someting a la Grothendieck--develop your own mathematics. Good job. Now, go out and do it!! :-)

janus said...

Grothendieck? Surely you're kidding; my ideas can't possibly compare to that magnitude.

Specifically I mean this: that I'd like to have a vision or develop my own program of investigation. More and more, it seems that I am motivated more by problems and phenomena which arise out of constructions or examples.

Perhaps this comes from spending too much time in classes and now I think in terms of problems and how to solve them .. mind you, this doesn't imply that I'm any good at solving them - only that I think about them.

At the very least, I know now that there are specific lessons I want to learn (as well those which I should learn but am unaware of, of course) and to do so, I must make progress as a graduate student: obtain an advisor and get to work!

Anonymous said...


Haha. I was just saying that you're developing your own direction and views on what you want to do....I dunno if you read Grothendieck's RC (there's a partial English translation available) but some of the themes expressed in your last post are, in many ways, just like his. Striking out in your own direction.

Regarding how good/bad you are solving these the end, reformulating the problem, recasting it in a new light, is arguably more important than anything else. After that, it's technical "know how" that matters...

but yah, Grothendieck was a freak...