Tall, Dark, and Mysterious

5/15/2005

Everything I ever needed to know about grad school, I learned the hard way

File under: Righteous Indignation, No More Pencils, No More Books. Posted by Moebius Stripper at 2:30 pm.

Over at Toilet Paper With Page Numbers, a new-to-me blog that’s going straight into my bookmarks, some advice on picking your poison - that is, selecting an advisor for grad school. TPWPN’s taxonomy of advisors (Micromanager, Ambitious Geek, Absentminded Professor) is geared at science students, but anyone considering studying math at the graduate level should read it, too. Now. Seriously, git; TD&M will still be here when you’re done. If it were up to me, which it isn’t, that post would be included in every science grad student orientation booklet. I don’t remember what was in my orientation booklet way back when, but it wasn’t as useful as, say, this:

The Creative Genius: An older researcher who, at one point in the past, struck a home-run or two and is now flush with cash. Usually has more than one sub-group, and misuses time switching his or her attention back and forth between them as fancy strikes. Usually gives students a lot of room to pick their own projects, and has the money to let you develop your ideas. That’s great if you, yourself are creative, but a nightmare of a 7-year Master’s degree if you are not. (For real. I know of at least one 10 year Master’s). Be honest with yourself, and if you are just not that creative, go for the Micromanager.

Advantages: Money, money, money, and room to run free.

Disadvantages: Has a lot of ideas to start you out with in your first year. No one in the history of the lab has ever gotten any of them to work in the advisor’s entire 20 year career, so find a new idea quick, or prepare for Master’s hell.

Ah, that brings me back. Which reminds me, what is a certain student of my former advisor’s doing these days? Last we spoke, he was wrapping up his seventh year as a grad student and celebrating his 34th birthday, ostensibly making some progress on his thesis. Lifelong Student’s (15 years in postsecondary education and counting) graduate career had seen him switch departments twice, make enemies out of more or less everyone in all three of above, postpone his quals until Year 6, and finally get our mutual advisor (hereafter “Eccentric Genius”) to just solve his research problem for him so that LS’s Ph.D. thesis was reduced to a paraphrasing of someone else’s work. If Lifelong Student actually did manage to defend, then that would make him EG’s second graduate. In fourteen years. I lost track EG’s refugees sometime into my second year: in my three year stint in grad school, a good half dozen students had signed up, or seriously considered signing up, to work under EG and then came to their senses before I did. The other student of EG’s who obtained her Ph.D., did so just before I arrived; I heard through the grapevine (LS, in particular), that she hadn’t understood any of the first sixty pages of a paper she’d cowritten with EG, and that she had understood only approximately half of the last ten. After finishing her seven-year graduate school career, she took an unrelated job in industry.

But that’s beside the point I was planning to make, which is this: if you’re a Master’s student, it’s nigh irrelevant whether or not your supervisor is a leading expert in their field. In fact, I’d advise against working with leading experts, as I’d wager that they’re probably less likely than non-leading-experts to be able to communicate effectively with amateurs. Master’s students do not need leading experts. Master’s students need supervisors who are solidly grounded in their subject, yes, but nearly everyone with a Ph.D. in the appropriate discipline can be counted on for that. What Master’s students really need, and what are in considerably shorter supply, are advisors who can advise. Master’s students, particularly ones who’ve never done any thesis-like research before, need advisors who can identify, to the uninitiated, the steps of the research process and guide their students through them.

I wish someone had told me that when I was assigned to Eccentric Genius, a world-renowned researcher in Impenetrable Geometry; knowing that would have saved me more than two years of grief. Actually, I didn’t even need to be told that I didn’t need to work with a world-renowned expert; I would have settled for not being told, repeatedly, from professors and peers alike, that I was so lucky to be working with EG, that so many other students would kill to be in my position, that I would be insane to even consider working under anyone else, yadda. When other schools saw that I’d worked under EG, I was told repeatedly, the academic world would be my oyster, and this was truly the opportunity of a lifetime.

People kept telling me this, and I believed it. I believed it when, after our very first meeting during which EG told me to study up on a certain invariant, I read a paper and an appendix on the subject and tried, to no avail, to compute some examples myself. During our next meeting, I reported on my lack of progress, and asked EG if he could show me an example or two. For the next - no lie - FOUR HOURS, EG paced back and forth in front of the blackboard trying, and failing, to work through a handful of examples. “I haven’t done this in years,” he explained, “usually I use computations other people have done. But you can probably figure out from these papers…” Later that week, I pored through handful of papers he’d given me. Each used a different formula to compute the invariant; none of the formulas worked for the examples in the other papers.

I believed it the next week, when, in passing, one of EG’s colleagues at the grad school told me that he was impressed that I was reading those papers, which were high-level research papers, didn’t I know, certainly not the sort of thing that most graduate students get weaned on. I pointed out that there was nothing impressive about being assigned high-level papers to read. If I were able to understand them, that would be impressive. Still, though, I blamed myself for not living up to what I foolishly thought were reasonable expectations.

I believed it when I finished the summer research term with nothing to show for my work. I was lucky, I knew, to be working with Eccentric Genius. The reason I wasn’t making any progress was because I wasn’t smart enough. I just needed to work harder.

I started to grow doubtful a few months later, when I noticed that EG’s solution to my complete lack of progress and utter inability to make heads or tails of any of the papers he gave me, was to give me more papers to read. After a year I had some thirty high-level research papers in my office, and I’d started working with Lifelong Student on one of them. We were able to make some sense of it, but neither of us could see how on earth it applied to our assigned research topics. Still - I was lucky to be working with such an expert, and I knew I should be grateful.

I was frustrated and upset, but still grateful in some perverted way, when my questions about how the subject matter was motivated were brushed off. “That doesn’t matter,” he said, “just use the axioms.” It was true that those axioms had been developed in response to some other research problems, rather than being handed down by God Himself to his prophets in Impenetrable Geometry, but the fact of the matter was that I had a thesis in Impenetrable Geometry to write, and that it behooved me not to worry about what all of this stuff meant. There just wasn’t any time for that kind of thing. Meanwhile, had I managed to compute those invariants yet? I explained - again - that each of the research papers computed the invariants with a different formula that seemed to come out of nowhere, and perhaps I could make some sense of the formulas if I had some context, or something. None was provided; just trust the formulas, I was told, and don’t worry about where they come from.

It was at this point that I began to see clearly the roots of my frustration: I had decided to study math specifically because I thought I would never be expected to trust in tradition, to take any theory for granted. But I also knew that if I was going to accomplish anything under EG, it would have to be at his level, so far removed from the more elementary material that I couldn’t possibly learn all of the background in the time I had and that I would consequently have to start by accepting some results that I had neither the background nor the intuition to comprehend deeply. I had been working - or, more accurately, “working” - under EG for nearly two years at this point, and had gotten nowhere with him.

He realized it too, and decided to try something different. He started meeting with me and Lifelong Student together, and assigned us to dig through yet another collection of papers to see if there was anything useful there. I am not omitting details here: he handed us three hundred pages of mathematics with the explicit instructions, and I quote, “See if there’s anything useful here.” Anyone who’s ever taken a serious math course knows how absurd this is: getting through even a twenty-page pager will often take an entire weekend,

And I, beaten into submission and resigned to never being able to earn a Master’s degree, set to it with LS. We pored over the three hundred pages of mathematics, meeting periodically with EG. I couldn’t for the life of me tell what on earth anything in these three hundred pages of mathematics had to do with my research problem (which I still didn’t really understand, but whatever), but I plodded through (a subset of) them anyway. After all, I knew why it was that I wasn’t understanding anything: it was because I was stupid. And how could I squander the opportunity to work with a leading expert in Impenetrable Geometry?

A few months into this, LS commented in passing, “You know, I can sort of see what these three hundred pages of mathematics have to do with my research problem - however, from what Eccentric Genius told me, I don’t see what they have to do with yours.”

I suddenly felt ill. The next day, I composed an email to EG, asking, not in so many words, that question: how was the research problem I didn’t understand related to these three hundred pages of mathematics that I also didn’t understand? EG wrote back, calmly, “That’s a good question” (!!!) and then explained that it seemed I’d “lost interest” in my original research problem, so he’d taken it upon himself to give me another one, one related to what LS was working on.

He’d never bothered to tell me this.

This was two weeks before I was to take off for my summer job, which I spent variously distracted and in despair. I knew that I would not get a Master’s degree under Eccentric Genius. Classmates of mine who’d struggled through graduate level classes and had routinely solicited help from me, were getting their diplomas in two years. I didn’t know if I’d be done in three.

The next fall, fortunately, luck was on my side. Two things happened. One, I attended a conference of six talks, five of which I didn’t understand even slightly, and the sixth of which had me excited about math all over again; two, my grad school had just hired a young professor whose area of expertise was related to the topic of the sixth talk. I started working with him, first unofficially, then officially. It took me a few months to work up the courage to abandon EG, but finally I said to myself, out loud, you will never graduate with him. If you want to avoid hurting his feelings, keep working with him. If you want to graduate, jump ship, NOW.

Under my new supervisor, I saw for the first time what the grad student/advisor relationship could be. My new advisor gave me bite-sized pieces of work to do. Each week I’d read over a small section, work on some problems, and come up with questions. Later on, I’d work on more involved questions, and get stuck; during my meetings with him, he’d give me just the push I needed to get unstuck. I’d give him drafts every few weeks, and he’d make copious notes explaining what I needed to correct or clarify. I submited my thesis six months after I officially started working under him.

A year after I snagged the Master’s, I don’t blame my former advisor. Not every professor can be all things to all people; EG was an expert, suited to working with other experts, and perhaps some postdocs. A handful of Ph.D. students might have thrived under him, but I’m skeptical: when I left the school, his most promising Ph.D. student was frustrated by his lack of progress and was thinking of leaving. (EG’s response was to tell this guy to “think it over” at a conference in Europe that he could attend that summer, at EG’s expense.) I do blame the school, though, for assigning me to work with him, even though I’d never expressed an interest in his particular flavour of Impenetrable Geometry. I wish I’d been given an explicit idea of my responsibiltiies to my advisor, and his to me, as a graduate student doing research , so that I wouldn’t, in the absence of any clear guidelines or expectations, conclude that the reason for my lack of progress was because I was too stupid to do graduate level mathematics. I wish I’d been given explicit deadlines and tractable goals against which I could measure my progress. Instead, I was given one goal and told, “Once you can do this, you’ll have a good thesis.” And I couldn’t meet that goal.

I wish I’d been told that my job as a Master’s student was to build a solid background in my chosen field - not to build a reputation in it. I wish I’d been told that I did not need a big-name mathematician to help build a solid background in a respectable field - and that many a big-name mathematician wouldn’t help me get any closer to that goal.

In retrospect, all of this seems so obvious, but it wasn’t to me at the time. When I was in grad school, each failure of mine, contrasted with each success of a student working under a different advisor, eroded further my ability to look clearly at my situation. It blinded me even to the simple possibility that I could ask my peers about how they did their research; when I did find out some details, I wondered what I would do if I quit working under EG. By the end of my second year I was virtually paralyzed with self-loathing, at least as far as my work was concerned. I couldn’t even contemplate an advisor switch; I wasn’t worthy. I couldn’t see past my own inadequacies in assessing the sorry state of my research. It took me two years in grad school before I realized that I could, and should, demand better than what I was getting. It took year away from grad school before I was able to put everything in focus, before I could articulate a clear answer to “why did you leave before you got a Ph.D.?” that didn’t sound to me like an excuse.

Still, though, I can’t help but think that I could have learned at least some of this before. Would have made for a more helpful orientation than the “let’s meet the faculty and then have some cookies” one I attended, that’s for sure.