The latest NSERC newsletter informs us:
At NSERC’s request, the Canadian mathematics and statistics communities will conduct a collaborative long-range planning (LRP) exercise over the next 15-18 months. The exercise will include broad consultation, identify areas of strength and establish a unified vision of priorities and directions for mathematics and statistics research in Canada. The resulting plan will inform the Mathematics and Statistics Evaluation Group of the priorities for current and emerging areas, thereby allowing for the best use of resources to advance the work of the communities as a whole.
Key partners in this process include the Canadian Mathematical Society, the Canadian Applied and Industrial Mathematics Society and the Statistical Society of Canada, as well as the three Mathematical Institutes (the Pacific Institute for the Mathematical Sciences, the Centre de recherches mathématiques and the Fields Institute for Research in Mathematical Sciences) and the Banff International Research Station.
Currently, the Mathematics and Statistics-NSERC Liaison Committee is working with the communities to establish a steering committee, which will develop Terms of Reference that reflect how the communities at large will be consulted and discuss how their input will be incorporated into the final LRP report.
My opinion is not exactly being solicited at this point, and it may well get filtered five times through the fine cloth of poll aggregators when it is formally solicited, to remove my name and any identifying details that might add weight to my story. I do, however, have enough experience with “priority areas”, and especially with falling through the cracks between them, to want to speak up now.
I also would really like NSERC to hear directly from the individual mathematicians, not just from institute directors and those in positions of power. Institutes are designed to support group-based research and prioritize areas; individual mathematicians need to develop their research programs according to their own best judgement. We do not always see eye to eye. It makes no sense for the institutes to control the prioritization of our individual grants.
Here, then, is my story.
Shortly after I was hired at UBC, the department approved an academic and hiring plan that identified areas of strength and established a vision of priorities. Yes, even the language was essentially the same. Several specific research areas were listed, mostly those that already had large research groups associated with them, and future hiring was to focus on these areas. (Just so it’s clear: I’m not disclosing anything confidential here. The same academic plan was posted on the department’s public website for several years and was referred to in job advertisements.)
Soon thereafter, PIMS introduced Collaborative Research Groups as its main mode of operation. These are large groups, usually consisting of 10 or more faculty (sometimes more than 20) at two or more PIMS member universities. The CRG funding pays for conferences, summer schools, visitors, postdocs, and so on right down to teaching releases for group members. (This is on the webpage I just linked.) The CRG areas have often coincided with the departmental priority areas, if only because of the size requirement. Some areas have already been funded more than once. If on the other hand a researcher or group does not have the “critical mass”, they need not apply.
I certainly did not have it.
The academic plan placed me in the PDE group, but my actual research interests were elsewhere. You may have first heard of additive combinatorics in 2004, in the wake of Green and Tao’s breakthrough theorem on arithmetic progressions in the primes. I got my first taste of it around the end of 1998. It was what I wanted to do: a combination of harmonic analysis, geometry, combinatorics and (as I found out later) ergodic theory, with unexpected ideas coming in from many different angles. I finished up other projects and moved on in that direction. The incredibly bright mathematicians who were attracted to it, the intriguing connections being discovered – everything added up to a sense of promise. I think there was a general feeling that something big was going to happen, we just didn’t know what, who or when.
Neither harmonic analysis nor additive combinatorics were among the designated priority areas at UBC. They couldn’t have been. I was the only active researcher in harmonic analysis and that’s not enough for a group. As for additive combinatorics, It wasn’t even a well-defined area at first, just a loosely demarcated group of problems and an increasing number of people willing to step beyond their own comfort zones to work there. That’s how mathematics evolves. It’s an organic process that starts with a question asked in the hallway, a paper interpreted differently, a formula jotted down on a napkin, then continues in individual offices and coffeehouses long before the ranking officialdom can take notice. Additive combinatorics didn’t even have a proper name until sometime around 2004. In a “priority directions” competition, it would have had no chance against officially established areas such as PDE or algebraic geometry.
But as for the actual research potential? That, I think, has been answered. The field underwent a period of explosive growth, becoming one of the most dynamic and active areas of mathematics. Green and Tao have been collecting all possible prizes, including Tao’s Fields Medal in 2006; but I shouldn’t leave out Gowers, or Bourgain, or Konyagin, or the Steele Prize recently awarded to Endre Szemeredi. Or many, many
others. And the younger generation: I hesitate to list names here, lest it be read as some sort of ranking, but I feel that the future of additive combinatorics is more than assured. We’ve had ICM talks in additive combinatorics, AMS and CMS plenary talks, Current Events Bulletin talks, grants, awards and prizes – any way you look at it, we’re doing well. But I’m getting ahead of myself.
Let’s go back to the years 2000-06 when I was isolated and de-prioritized. There were a few bright spots. In Spring 2003 I co-organized what was likely the first ever institute program in additive combinatorics, at the Erwin Schrodinger Institute in Vienna. I’m proud to say that Ben Green was a PIMS postdoctoral fellow at UBC when he and Tao wrote their first paper. But how did PIMS and UBC follow up on that? Very simply, they didn’t. There was no mechanism to create opportunities outside the priority areas. No priority group, at UBC or elsewhere, will ever be eager to relinquish their hold on resources, and I learned soon enough that there was no point in trying to join groups that did not share my research interests.
It was hard enough for me just to continue to function. I could and did supervise graduate students, but there were only 2 graduate courses in harmonic analysis from 2000 to 2006, plus a third one on the combinatorial side of additive combinatorics. (For comparison, each priority group offered 2-4 advanced courses per year, not including summer schools.) A harmonic analysis seminar was me talking to my students in my office. And what if I’d taken leave from campus for family or medical reasons? It’s probably good that I didn’t have to.
What made a huge difference, though, was the support I had beyond the department. I was able to organize and chair a thematic program at the Fields Institute, including one of the largest conferences in additive combinatorics in recent years. This was an opportunity that I would not have had at PIMS or UBC and for which I will always be grateful. I was supported by Discovery Grants. I was awarded a Discovery Accelerator Supplement grant – one of the best new programs from NSERC. I’m not saying this just because I got funded – I’m saying this because there’s too much emphasis already on funding research groups and not enough on funding individual researchers, and the DAS program helps rectify the imbalance.
Eventually the department hired more harmonic analysts, in 2006 and again in 2008. I’ll omit the details. We now have graduate courses on a regular basis. We still can’t apply for a PIMS CRG (that would require participating faculty from other PIMS institutions), but there is a long-term visitor working with me who was funded through one of PIMS’s international agreements.
But what if NSERC and all institutes, including Fields, had adopted the same priority lists as UBC and PIMS and locked me out? Most likely, I would have left Canada already. It’s not exactly like there haven’t been opportunities. At this point, additive combinatorics in Canada is doing well enough now and I don’t expect that we will be going down anytime soon. What we don’t know is where the next big breakthrough is going to come from. Although there might be individual mathematicians close to the ground who can see it coming already, as I did 7-8 years ago.
It would be beautiful if the new priorities and directions for mathematics were decided solely on the basis of academic merit, by a high-profile committee that has a broad view of current mathematical research all around the world and no self-interest whatsoever in the resulting funding decisions. Further, the priority rankings would be revised on a regular basis to include emerging and reinvigorated areas. Efforts would be made to identify research topics where a major breakthrough hasn’t happened yet but the experts can see it coming any day now. Also, everyone would get a pony.
In reality, I expect the ranking to be a combative political process where having control over the procedure can influence the results. The third quoted paragraph above admits as much, indirectly. And in a system where the winners take all, diversity cannot flourish and new directions cannot emerge. Scientific merit is less important than adherence to the calcified power structure. I thought that NSERC understood this. The recent changes to the Discovery Grant program, as I understand them, were designed to make room for emerging research that does not fit well in the traditional framework. I’d like to ask NSERC to apply the same philosophy here.