What Is Research?

March 28, 2007

A new phase of my life in the offing

Filed under: Regular updates — vipulnaik @ 11:01 am

Yesterday night, I was feeling extremely fatigued and worn, and when I stopped to think of what was causing this, I realized that I’ve just been going on and on for days on end without stopping and thinking of where I’m heading.

This semester has been rather light for me (in terms of course load: only five courses) but I have offset that my taking on a number of ambitious and tricky tasks, most notably the Group theory wiki. In addition, I’ve been involved with a teeny-weeny bit of work on things like CMI Spark, CMI Online Programming Contest, Olympiad teaching and training.

I’ve also been giving quite a few Student talks and have been trying to prepare lecture notes for some of my courses such as Lie-theoretic methods in analysis (I haven’t worked on that for a long time, but that’s a different story).

In addition, I’ve been trying to get started on some other wikis, particularly a Differential geometry wiki. And I also plan to get started on my Commutative algebra wiki. I’ve also been trying to work on developing a theory (which again hasn’t been working out, called APS theory, on a wiki devoted to that.

So in the midst of all this (attempted, and so far largely unsuccessful) activity, I have so far forgotten to face up to and think about the new life that lies ahead of me.

To set some background.

I am currently in the third and final year of my undergraduate programme at Chennai Mathematical Institute. Once I complete my B.Sc., I plan to join into a Graduate School (viz a place for Ph.D. in mathematics). Once in Graduate School, I hope and expect to work on research in some important problems in mathematics, probably make some original contributions that’ll earn me a Ph.D., and then, continue with mathematical research.

I’ll be starting on Graduate School probably some time in August-September, and I need to begin the emotional journey towards that. I need to figure out how it’s going to be different from the undergraduate life, what the new pressures and responsibilities will be, and how I can do well in Graduate School.

I also need to look at my more long-term plans and see how Graduate School will fit into them.

Unfortunately, I’ve been too caught up with the things I am currently doing to be able to stand back and stare.

But now, as I write this blog post, I am forcing myself to think hard.

One of the basic differences between my current undergraduate life and life in Graduate School, will be that in Graduate School, I’ll actually be expected to produce results. As in, there’ll be papers I have to read, results I have to create afresh or extend.

Right now, whatever little of papers I read or research work that I try acquainting myself with, I do of my own accord. And I always have the freedom to stop reading when I get bored or when the stuff gets too complicated or when I realize that this is not the right order in which to read things. So, because I don’t really need to get anything done, my efforts to acquaint myself with new research are sporadic and ad hoc.

On the other hand, getting a doctorate, as far as I understand, is not something that can merely be accomplished by knowing a bit about everything, reading a bit here and a bit there. One needs to take a specific problem and make definite progress on it that is worthy of publication somewhere. Trying to make definite progress that hasn’t been made by any person so far seems a daunting task. I mean, what guarantee is it that, however smart I am, I’ll actually be able to find something new and significant in the five or so years I am allotted for my Ph.D.?

From what I have observed of the research world and the way it operates, a crucial component of research is reading and thoroughly studying research papers. Unfortunately, I don’t think I have yet gotten the hang of it — also somehow I don’t seem to enjoy it (of course, it may be too early for me, considering that I am still an undergraduate, but the sinking feeling I get on seeing a long series of pages with abstruse symbols and claims and proofs does depress me). This is notwithstanding a post I myself put on this blog on
How to read research papers.

This is one of the things I need to look into to overcome. So far, I have looked at research papers, but it’s usually for something specific — a definition, a little claim, a particular theorem, etc. The first big attempt I made to study a research paper was under Professor Dipendra Prasad at the Visiting Students Research Programme at TIFR, Mumbai. This was the paper on Lie Group Representations of Polynomial Rings.

I got off on the paper with a good but not too good start — and it was really slow progress. By the end of the programme, I had managed to read and understand the proofs for only twenty of the eighty pages. Of course, that was my first experience, and there were many learnings I got from it which I feel will help me in future experiences (some of which are documented in earlier blog posts). Somehow, what I didn’t learn was to like deciphering a paper from start to end.

Another aspect of research and graduate life that frightens me as of now is the need to collaborate with others and work under people. So far, I have been working largely of my own initative, and most of my interaction with teachers is for learning specific subject material or clarifying doubts or general discussions. The notion of actually going through a paper with a guide, where I have to meet him/her on a regular basis and report progress, sort of scares me. The problem here is that it’s not just a commitment to myself or a personal choice, it’s based on and largely driven by the other person (particularly since as the guide, he/she is the senior and the one deciding the directions).

Of course, there are all kinds of guides and all possible arrangements one could have with the guide, and in fact, many research students have told me that the guides try to guide as little as possible and let the student decide the course.

Among other things that frighten me about my Ph.D. is that if I get too emotionally involved with trying to solve a particular problem, and if it doesn’t work out, then what do I do? And if I don’t come close to getting any new results within five years of getting started (or whatever the number of years is within which I need to complete my Ph.D.) How desparate will I get?

What happens if I have to abandon my favourite subject for a subject where I can get a result faster? What happens if the areas where I want to work turn out to be duds?

The other thing that’s bothering me about my Ph.D. is that it seems in some sense a final step — after that, I’ll stop being a student, I’ll be at the giving rather than the receiving end of knowledge (while doing a Ph.D. one is sort of at the interface between the two, one is trying to create knowledge while simultaneously attempting to acquire it).

So I want to utilize the time I spend in my Ph.D., to prepare myself as thoroughly as possible, for the road ahead. This is not just in terms of the mathematics content, but also the way mathematics and research is done, the various politics and administrative issues involved with research, the key to teaching and learning good mathematics, the various issues facing the mathematical and research community and the way they interface with other disciplines.

I’d ideally like to have a good network of people doing various parts of mathematics at various places, with whom I can interact and interface so that I can experience the feeling of doing mathematics in a community.

On the whole, it’s going to be an interesting and challenging phase, and the things I can do now (or perhaps over the next few months) are try to talk more to the people who are already doing it, and try to get over the mental block that I have (or think I have) with reading research papers.

I also need to wrap up, or reach a sort of logical point, with all the many ambitious projects that I have started and gotten underway right now. I don’t know how much time I’ll get to pursue these once I start out Graduate School, but I think there’s a fairly good chance it’s going to be far less than what I have right now. Which means I should go to Graduate School with these shelved aside (that doesn’t mean I won’t work on them — it just means that I won’t expect a regular output on them from my own side).

Let’s see how things unfold…

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