An article I wrote in 2007 on life as a graduate student, for the Mathematics Society magazine at my alma mater, St Stephen’s College.
I am a currently a PhD student at the University of Illinois, where I have been for a very long time. (But I have my reasons — the principal one of which is about to have her second birthday. And I do have company — there are other students who joined with me in 1999, who are still here. We are the “nth year students”.) In the meantime, my batchmates from Stephen’s have all been building careers for nine or ten years now; they actually have incomes — wow! And they do things like buy houses — wow! And rent villas in Italy for the summer — wow! (Ok, that’s just one guy.)
So, why am I here, and what exactly am I doing? I will try to tell it like it is. Some version of this story applies to almost everyone who does a PhD in Maths, or Math, although the structure of the programme may differ. At first, of course, there are all the usual hoops to jump through — required courses, qualifying exams, foreign language exams to demonstrate you can read Mathematics articles in French or German. This part was hellish, but doable. I was used to hanging out at the Dhaba all summer and the Lawn all winter and starting to study in February. Now suddenly I found myself with serious weekly assignments — sometimes the problems assigned were hard enough that they were actually published results. And ever the perfectionist, I refused to turn in unfinished homework. So night after night I stayed up till 4 a.m., killing myself till I figured out every last problem. But as I said, it was doable — if I put in the sweat, I would solve it. After a couple of years of this, I chose an advisor and a thesis area, and then I had to take an oral exam to demonstrate comprehensive knowledge of my chosen area. It took six months of preparation, and it was quite stressful, but again, it was doable. Just another exam. And then it was done! Yay! At long last it was time to shrug off the drudgery of courses and homework and tests and get down to the real stuff — research — the whole point!
And ever since, I have been engaged in this exalted pursuit. Is it sublime, or delightful? Is it exhilarating? No, no and no. Well, that’s not quite true — there are exhilarating moments. In my case, one such moment so far. Let me describe it. I was trying to prove a result. I could do the very simplest case, and doing so had given me an idea I could carry forward. So I worked at it for weeks. There was a kink. Briefly I thought the result was false. I changed my mind. I worked some more. I banged my head against the wall. I stared at it and stared at it. I doodled. I fiddled. I wasted paper. But I kept coming back to the same problem. I talked to my advisor. He had no idea either (but he continued to be sure that this was doable.) I tried to fix it one way. I tried to fix it another way. Finally I had a thought which gave me some traction. What if I discard the problem sets in the right way? I worked at this new idea, and two days later, there came a moment when I was pretty sure I had it. There were still some details to check, but I really had it! That was the exhilarating moment.
On the bus on the way home, I checked the details. It was all okay. I told my husband, I have something! I emailed my advisor and told him I’d write it up so he could look at it. Over the next two days, I wrote it up with all the details — all the details — and in the process discovered something that … didn’t … quite … work. It was wrong! There was a mistake! I was disappointed, but luckily, everyone I knew and everything I had read told me that this was par for the course.
So I kept at it. I had to find another way. And two weeks later, I did. It was complicated and technical and each case was replaced by countably many cases, but this time it was correct. (And this time I was simply cautiously optimistic. So the total number of exhilarating moments is still one.)
Mathematical research, by its very nature, is hard and unpredictable. There are no experiments that will give you results, expected or unexpected. You have to sit by yourself and work in the dark. It is mostly drudgery and failure. On almost every day, you make no progress. But you keep at it because you want to solve it. You have lots of thoughts and very few real ideas — nine out of ten times they fail outright, a few times they fail only after a wild goose chase. Finding the idea that worksis like panning for gold, looking and looking for that metallic glint thatis the real thing. Luckily, you don’t need a whole lot of that gold — a few nuggets will do — and finding them is grueling but not impossible. One afternoon in my department’s coffee room, a retired professor in my department put it this way: you’re trying to solve a problem, and you spend days with it. Eventually you come to a point where you have thought every single possible thought there is to think about the problem, and absolutely none of them works. At that point, it’s as if God says, okay, she’s worked long enough. Let’s throw her a bone!
So far my one bone has led me to a solid, honest result. And the same process of getting up at six and eating my porridge and creeping out of the house before the baby wakes up, so I can get in a full day of staring at papers and having a string of unsuccessful ideas — this is going to get me another result, and another. It’s painful and not what I expected, but this too, is doable. I have a community around me engaged in the same pursuit, and they too go through the same process, with the same rewards. It’s hard — but that’s precisely what keeps me engaged. And the day will come when my advisor will say, Okay, you’re done. (Now, that will surely be exhilarating.)