This post is a series of scattered thoughts in reaction to a comment by Mike Shulman dated May 26:
I don’t really know whether there are more democratic methods of organizing mathematics that would be as or more effective than the current dependence on charismatic leaders; it seems related to the search for alternative models for recognizing and validating research that could replace the current referee and journal publication system.
The comment was itself in reaction to the implicit assumptions of two articles on HOTT/Univalent Foundations that appeared in close succession in online publications:
What bugs me is when people assume that because of Voevodsky’s charisma, that his interests define the field, or that the rest of us are all following his “research programme”. I used to find such assumptions totally baffling; but after reading chapter 2 of your book, I get the impression that there are fields of mathematics in which it really is the case that the “big name” mathematicians set out “research programmes” that everyone else is expected to follow. It’s not at all what my experience in mathematics has been like (including work in algebraic topology, category theory, and now homotopy type theory), but maybe the problem is that people from fields that do work that way assume that all fields work that way.
I didn’t want the thoughts to be so scattered, but I’m in a hurry to get to the next post before the ink dries, so to speak.
I organized Chapter 2, and most of the rest of the book, around the Langlands program and Grothendieck’s conjectures on motives, as well as the related Guiding Problem of the Birch-Swinnerton-Dyer Conjecture, not only because that’s what I know best, but because they offer an exemplary picture of mathematics as a collective activity, and therefore a social activity, and therefore (at least for the foreseeable future) a human activity. Probably I should have insisted more strongly on the exceptional character of these research programs, whose expected outcomes have been predicted in unprecedented detail. There is still plenty of room for surprising proofs, but most mathematical fields seem to leave much more room for surprising results. I don’t know whether even so structured a field as homotopy theory has long-term research programs or even Guiding Problems.
I have sat on enough hiring committees and editorial committees and other sorts of committees to know, however, that homotopy theory has its share of “big name” mathematicians, and I’d guess no branch of mathematics that attracts the attention of hiring committees and the rest is very different in that regard. The argument could be made that the very existence of such committees presupposes some hierarchical standards for making decisions. I wouldn’t want to make such an argument, because it one sense it’s a tautology and in another sense it looks like a defense of hierarchy, which is not at all something I’m inclined to defend. On the contrary, the main irony of chapter 2 is that, despite my not particular auspicious beginnings, I’ve learned more than I ever wanted to know about how hierarchy works in practice.
Universities in France are run very differently than in the US. Salaries are public and are determined by the civil service pay scale. Some university professors reach the top of the scale but the highest salary for a professor (classe exceptionnelle, 2ème échelon) is just slightly over 5200 euros per month, after deductions for national pension and health insurance (but before income tax). Some state and local universities in the US have a similar system, but in France there are no exceptions and the university administration cannot make special deals to attract professors. (At least that’s how it was until a few years ago; it is possible that some university presidents are taking advantage of loopholes in the recent laws increasing their “autonomy,” but I haven’t heard of any such cases.)
Within each category, one rises in the ranks on the basis of seniority; then one applies for a promotion to the next category. The big step is from maître de conférences to professeur — both of these are tenured positions — and this involves a separate hiring procedure. Most of the promotions within these two large groups are decided by an elected national committee, one for each discipline, and it was on this committee that I served for a few years as an elected bureaucrat. The number of promotions available to this committee is decided centrally, by the ministry, and there is naturally a fair amount of political maneuvering. (There are also a few promotions decided locally, in principal for service to the university.) Political lines are drawn between fields (algebraists vs. analysts) and between the platforms represented on the committee — in mathematics there were trade union lists and one now called Qualité de la science française. What I want to emphasize here is that, even though the trade union lists are ostensibly committed to promotion strictly based on seniority, while QSF is supposed to be more elitist, in my experience the same charismatic criteria were applied by both groups. (Maybe it’s different in other fields than mathematics.)
The conflict between democracy and elitism is resolved in France by the paradoxical notion of élitisme républicain. This is what allows France to run what may well be the world’s most elitist centralized public systems of higher education and to turn out an elite that is sincerely and militantly democratic. Practically all my French colleagues who were high school or college students in 1968 were either Maoist or Trotskyist (there are still quite a few of the latter), and those of the previous generation were often members of the French Communist Party. And this is hardly surprising when you consider that Louis Althusser was teaching at the Ecole Normale Supérieure, the innermost sanctum of French elite higher education, where a staggeringly large proportion of my colleagues learned to be mathematicians.
The absence of big salary differences, and of the temptation to move elsewhere in search of a higher salary, makes for a healthy atmosphere, and it’s reassuring to know that most of your colleagues will vote to strike to protest a regressive decision by whatever government is in power. The regressive decisions go forward nevertheless, and the result is a shrinking budget for higher education and a steady drop in the number of available positions (in spite of an increase in the number of students), and one wonders how much longer the healthy atmosphere will last.
I have the impression that I wanted to say something else in response to Mike Shulman’s comment, but I have forgotten what it was.