You have psychological problems

Something on CM last week made me think of my PhD adviser.  I haven’t talked to him in years, but I’ve promised myself I won’t miss his next birthday conference (or retirement bash, when that happens.)  In my experience mathematicians—especially the good ones--among themselves are direct to the point of bluntness, a quality I find refreshing, but which unfortunately we have to repress in most professional situations.  Being a great man, he never had this problem:

This theorem is too good for you.

This after I had been working on a problem for five months. It was something very topical at the time, and I had the idea of approaching it using techniques from a former mathematical life, which he knew zip about. So I stopped him in the hallway one day (you had to do that) and showed him my idea for a solution; I just had to check some estimates. After hearing me out for five minutes, out came the encouraging words.  In a way, he was right; I never found a way to get enough uniformity with that method.  And neither has anyone else, in the roughly thirty years since; the problem was eventually solved (in a sense) years later, with techniques from a different area of mathematics. I say “in a sense” since some of those techniques are a little hocus pocus for my taste. But the whole area is no longer “topical”, so it doesn’t matter.

You only want to work on famous problems.

Isn’t that what ambitious graduate students are supposed to do? This was the early 1980s, a lot of exciting things were happening in the area.  I kept reading these preprints on really interesting new mathematics, with clearly a lot of room for growth, and naturally tried to find a doable problem along those lines. He wouldn’t hear of it, insisting instead I work in a class of problems that, by comparison, seemed almost “technical”. Eventually I got frustrated at seeing other students in the same group work on the flashy stuff with other advisers, and tried to switch to someone else (one of his friends).  This led to:

You have psychological problems.

And well, maybe in a way he was right! But in precisely what sense would only come to light years later (and it is a good kind of “problem”, once it is solved.)  The other students, by the way, have not fared that much better (with one exception) in terms of difficult theorems, but are certainly in “flashier” places. So I kept working on the same topic, and that led to a thesis, and later even to a surprising result. But it is not surprising that at one point I heard:

You are not very enthusiastic.

(Again, I have come to understand that was a very perceptive remark--I am wholly unable to feign enthusiasm for something when I don't feel it, and I feel it rarely--but that's a topic for another post.)

At around the same time, he became very upset with the department chair. One day at a party with colleagues and graduate students in his research group he uttered the unforgettable:

Yesterday he little shit. Today he chairman. Tomorrow, he will be little shit again!

(Comforting words to recall when I'm feeling harassed by my department head.)

Not even cuddly animals were spared. At another party years later, a generally beloved threatened species with very particular dietary habits came up. Not an issue for him:

Picky eaters deserve to die!

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In anyone else, it might be taken as arrogance, or insensitivity; and maybe it is. But knowing him, I think comes from a place of utter honesty; a certain purity, even.  Even when he's being a little too aggressive in the pursuit of his goals, it is done openly, without subterfuge. I have a lot of respect for that.

Tirfurcation

For a brief moment, three futures are possible.  I stare into the fog of the next few months, and wonder which one it will be.

I could go on being an academic—research, teaching, same-old, same-old; just somewhere else. Somewhere where colleagues are a little more sociable, a little less academically conservative. Hopefully in a more reasonable town, not this place, which is pleasant enough except for the people. This future probably involves international relocation; exciting in a way, but a big transition to make.

Or I could do administration; set teaching and most research aside, maybe temporarily.  I can do that, I don’t think it’s hard. I have ideas, integrity, fairness, compassion; I’d be an awesome department chair. Dealing with deans, other chairs, disgruntled faculty…what’s that like? I’d probably have to control an occasional wish to punch a hole on the wall, or say something highly inappropriate. Dress nicely, be social. It would be different, but that’s good.

Then there’s the government option. That's kind of bureaucratic: write glowing reports, go to staff meetings, be political. I can do that, too. The challenge would be doing a little research on the side, not letting the brain congeal before its time.  It’s decent money (for an academic),  you live somewhere reasonable and never, ever have to deal with students. Lots to be said for this option.

All three are possible right now. I have no control, I’ve done what was needed and all I can do is sit and wait for the call. It’s driving me crazy.

And maybe no call will come. The fog will lift, and instead of three paths I’ll see an impenetrable thicket, to be hacked into with a lot of effort, networking and maybe some pleading. I’ll be stuck in this place for another year, at least.

It’s hard to do anything that deserves being called research with this level of uncertainty, with the question `what for?' so clearly in the background. For the moment all I can do is think about easy expository things, teach my classes, and wait. 

Post-Tenure Review and Me

The envelope from the provost's office has an ominous confidential stamp, so I just set it down on my desk and go about my business, avoiding the distraction of dealing with its contents. When I do open it, it's the expected: the provost concurs with the head that my performance `needs improvement', so I'm facing `post-tenure review'. And by the way, your sabbatical is canceled until you're again a faculty member in good standing.

Post-tenure review arose in academia in the 1990s; in the USA first, where tenured faculty have no class consciousness, and you can change any rule of engagement as long as it only affects new people. It is part a result of `business values' worship in American culture, part resentment at the only profession with essentially guaranteed long-term employment, in a country where most employees are treated as serfs with no job security. It was harder to do in Europe, but gradually introduced there too, through the back door of `America worship' by euro-academic bureaucrats.

PTR was sold as a way to get rid of tenured `dead wood', or of people who spend all their time on outside consulting. So it still carries an imputation of `serious misdeed', incompetence even. Sorry, that's not me, not by a long stretch. My research `exceeds expectations', my lectures are clear, my class interaction with students completely normal, graduate students ask me to guide their work.  And yet, it can be done. The mechanism is there, and all it takes is a committed department head.

For these reviews have become something entirely different: a mechanism for the expression of power, one of the few in unhierarchical tenure-track academia. You might think it means your colleagues don't like you, but really all it takes is a couple of determined people with a grudge, and access to the head's ear. Or a head with an agenda, who feels a sense of mission in `doing something about people who can't adapt to where they are'. Or a naive head, an insecure newbie struggling with the job, believing this kind of action will make his faculty take him seriously. Then it moves to the dean, and the provost. To them it's all about sending a message  to the faculty: `yes, as a matter of fact we can use this mechanism to enforce our current policy priorities, even if you're doing your job just fine'.

So this spring term, in addition to my regular teaching and advising and (hopefully) research, I'll have to deal with this nonsense. The head tries to pass the process as `advisory', when in reality it's adversarial and very personal, a wasteful game involving a few men in their early fifties who should have more useful things to do with their time: the head, the dean, the provost and myself. At some point a mea culpa, an act of contrition will be expected from me. If at all possible, I want to deny them that pleasure, to leave in the written record, as clearly as possible, the many reasons why they're wrong. (Or to make sure they know it's given grudgingly; just what it takes to keep the job and no more). This will take some willingness from colleagues who don't know me to stick their necks out and support my position, which at the moment seems like a tall order; why should they?

Bill (1946-2012)

I still remember the aura of mystery that surrounded Bill Thurston’s work when I first encountered it as a graduate student in a past life: a late afternoon seminar on the Travaux de Thurston sur les surfaces, a reading course on the notes The Geometry and Topology of Three-manifolds. Laminations with transverse invariant measure? A hyperbolic structure on the figure-eight knot complement? How many hours spent poring over those diagrams and drawing new ones, until I convinced myself (rightly or wrongly) that I could see what he was talking about. It was unlike anything I had ever seen in mathematics.

Later, sometime in the early 1980s, for a while I attended his group’s research seminar at Princeton (called “graduate course” there). The topic was compactifying the moduli space of postcritically finite rational maps, and he was developing it during the course, using the audience as a sounding board.  Laminations of the disk were involved, and at some point I joined his students and postdocs in computing examples.  My notes on this have been lost; I just checked Bill’s Mathscinet list, and did not find a publication corresponding to this. Since, like myself, the other participants had other main interests, it could be that some beautiful mathematics has vanished.

 That’s the risk with doing things in “Thurston mode”: for it to become a permanent part of mathematics, somebody else has to understand it well enough to be able to record it for people who operate at a “normal level”, and that didn’t always happen. Implementing parts of a "Thurston program" has been a nontrivial creative activity in itself, inspiring the careers of many.

Bill was aware of this problem; he appears to have given a lot of thought to the gulf between understanding a mathematical situation intuitively/geometrically and the need to communicate  (and record) it in a necessarily downgraded symbolic version:

Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual --> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replace the conceptual forms of understanding. (Mathoverflow)

Here is Bill’s comment on the real reason mathematics is important:

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example, any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

Elsewhere he said “the goal of mathematics is to develop ways for humans to see and think about the world”.  But, in that case, it is not enough for one human (or a handful) to reach such “increased understanding”; the work is not finished—not really useful as a new way to “think about the world”—until it reaches a form in which (at least) scientifically educated non-mathematicians can make sense of it; but by that time it is no longer research, and mathematicians have moved on.

(Think, for instance, of the recent proof of Thurston’s Geometrization Conjecture in the style of Hamilton and Perelman. How long until the “understanding” implicit in this approach can be put into a form that would make sense to a student--or an expert-- in Geometric Topology, or to a physicist? Who is going to do the work?)

Bill was a unique mathematician, and his passing at a point when he was still contributing so much saddens geometers everywhere. The memorial page set up by the Cornell mathematics department has links to sources including some of his views on mathematics, like this one:

Mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others.

Exactly.  You can do it (up to a point) while separated from your `tribe’, but it’s no fun. And while all mathematicians know this is true, I hadn't seen it stated so precisely and eloquently until now. We'll miss him.