Looking back on my three years at CMI, and looking forward to five years of solid research in mathematics, I am currently trying to gauge: what is the skill set that I need to push myself through in mathematics, to see my ideas through (as I mentioned earlier), and to, in general, do well and survive?
Many of those things, I probably already have (though there’s always scope for improvement). For instance, I definitely have an ability to persevere with stuff, to concentrate for long hours. I also have a general propensity to document and organize ideas, to handle huge masses of information and ideas, and to come up with searching questions and search for answers to those.
Probably one of the things that I lack (not really lack, but could get more of) is the ability to do research alongside others, viz, to collaborate, to learn from senior people working in the area, to be able to work under another person’s guidance. I somehow feel (as I probably mentioned earlier in this blog) that I have too much of an independence trait, too much of a desire to do what I want, that may be it gets in the way of following what others say or advise.
Interestingly, I still do seek advice often; only I don’t usually implement it! I also often get started, half-heartedly, on a number of projects, and while I do tend to persevere on a few of them and see them to completion, I don’t usually close, or discard, the other projects.
Apart from being able to collaborate with people on an intimate basis, and take advice, i also need to get more on the social network of mathematicians. I think there’s quite a lot of sub-networks within mathematics students wherein the students share not just mathematics, but a lot of other things, and getting into these networks will help me feel part of a bigger community. Not having been able to do this much hasn’t really been my fault — on the other hand, I think I could have done better if I really wanted. It’s also something not unique to me.
I remember right from the time I was part of the Indian contingent to the International Mathematical Olympiad, that there were so many peopel from other nationalities whom I could have interacted with, but didn’t. It’s the same story out here, in France, four years from that time. Probably it has something to do with reverting to one’s familiar shell, doing the things one is typically used to (including both work and fun) rather than exploring what is new.
Another skill that I need to pick up is my presentation skill. As such, i am fairly good at giving mathematical talks, but presentation skills mean a lot more than just giving talks of mathematical content — it means presenting oneself to anybody in such a way that one can bring that person to one’s point of view! For instance, it may mean convincing a professor to back my research project, it may mean convincing somebody to sponsor me, it may mean a whole lot of other things!
Also I need to be a bit smarter about what the requirements at a place are, what it takes to convince the people of my sincerity as well as of my overall appropriateness. In CMI, I did suffer a bit initially because there were certain courses that I did not take seriously. At that time, I did not think that the knowledge I gain in them is of much use (which was probably true, but now I realize that coursework is an opportunity to gain a relationship with a teacher which could be useful later). I plan to be much smarter now. (In general, being smart about what counts and what doesn’t is an ingredient for success in any endeavour).