Broken or not, fix it anyway?

The latest issue of the AMS Notices starts with an op-ed by J.-P. Bourguignon:

Lately, in many countries, the financing of research has been following a very common trend, according to which, to be financially viable, a project should have a pre-defined critical size as well as cluster a number of activities. There are undoubtedly disciplines for which this is all well and good, but except under very special circumstances this is not what fits mathematicians’ needs. […]

Obvious questions include: what forms should infrastructures have in order to help mathematicians develop their research in the best possible conditions?

To spell it out more clearly: the “common trend” refers to investing more research money in flashy big programs and enterprises, while at the same time neglecting our daily bread and butter programs, especially individual grants. Bourguignon talks about Europe and in particular the EU, but Canadian science is not immune to this, either.

This is not at all surprising from the political point of view. Administrative units such as institutes, brandishing significant political clout and a capacity to lobby and advocate for themselves at all levels of government, deal mostly in collaborative modules that support a large group of scientists for a limited period of time. It’s obviously in their interest to promote this model of funding. Individuals, regardless of their preferences, aren’t able to exert the same type of influence. Meanwhile, it looks good on a politician’s résumé to have reorganized a funding mechanism, proposed new strategies, developed innovative solutions. Maintaining a long-established program does not carry the same bragging rights.

But from the scientists’ point of view, there’s no funding mechanism that’s more vital to us than our individual research grants. No amount of funding for institutes and other large initiatives can replace that.

Because, for the most part, our research is a sustained long-term individual effort. We don’t just flare up for the duration of a thematic program and go into hibernation afterwards. Our projects grow and mature over long periods of time, through the many afternoons that we spend holed up in an office, the evenings when we work at home. We sometimes think about a problem for years before we have anything to show for it.

This is not to say that conferences and thematic programs aren’t important, because, quite obviously, they are. That’s where we get up to speed on current developments, make contacts, seek new ideas. The best part is that, sometimes, two or more people meet and find out that each of them holds a different piece of the solution to the same problem. Add up the pieces, and voilà! That’s the sort of thing that conference centers and institutes are particularly fond of: a breakthrough that takes place right there, during the conference, with a paper or two to follow shortly.  It looks just perfect, too, on the institute’s application to have its operating grant increased.  What’s often ignored is that such breakthrough moments don’t come from nowhere.    They happen because everybody has already spent some time, possibly months or years, working on the problem.  That’s why they had something to contribute.   If we’re not supported on an ongoing basis throughout those thematic-programless years, we’ll have much less to bring with us when we do get together. 

A major difference between mathematics and most other physical sciences is that our research is much more unpredictable.  It’s not just that we work on a much longer time scale, as I’ve already mentioned.  It’s also that we never really know in advance which project will work out and which one won’t. We might work on something for months, only to come up short or to get scooped. Think of it as a long-term, high-risk investment of our time and energy.  Since we are nonetheless expected to produce at a reasonable rate, we take the same precautions as stock market investors: diversify, hedge, have a long-term strategy. We work on several things simultaneously. We make sure that they’re connected, so that if something does not pan out, at least we’ll have other uses for the expertise gained in the process.  We watch out for blind alleys and try to get ahead of the curve from time to time. 

If this sounds difficult, that’s because it is.  But one thing that helps us manage the risk is flexibility.  We want to be able to move in a new direction immediately when there’s an opportunity, to start a new collaboration, to suspend or abandon an idea that’s not working out.  There’s a quote I’ve seen somewhere to the effect that it’s hard to run into something when you’re sitting down.   That’s so very true.

I would add that there’s a certain personal quality to our research. We all have different tastes in mathematics: we might be attracted to the high fallutin’ abstract, or to the concrete and down to earth, or to the continuous as opposed to discrete, or whatever. I believe that it’s very important for us to follow such preferences. When you embark on a hard problem, you should expect that you’ll spend at least several months on it and that it will likely be two steps forward, one step back, interrupted by long periods of being stuck on something or other.  You’ll be thinking about the problem at nights and on weekends.  And, as I’ve said already, there’s no guarantee that you’ll get anywhere.  It’s pretty much impossible to do all this if you’re not really interested in the problem.  I don’t mean “interested” in the “I get paid for it” kind of way.  You have to be attracted enough to the problem to keep probing it even when things are moving slowly, you’ve just had a setback, and moreover you’re frustrated with your calculus class and your roof is leaking at home.

Individual grants give us the flexibility to move around and pursue our interests according to our best judgement. That’s how we make the most of the limited supply of our time and energy. Group funding, on the other hand, tends to have strings attached to it, in terms of the scope of the supported research, the selection of participants, the time frame, the administration of the grant, and so on. This can work very well, or not well at all, depending on how the program is set up; but that’s a subject for another post. The point that I want to make here is that increased funding for institutes and similar programs does not compensate for the shrinking sizes of individual grants. It just serves a different purpose.

Unfortunately, individual grants in mathematics have not increased in ages, not even enough to keep up with the inflation. Two years ago the NSERC individual grants budget was not adjusted for the size and quality of the pool of applicants, resulting in cuts to our individual funding, even though the three Canadian mathematics institutes had their NSERC funding increased substantially in the same competition year. I wrote about it here in more detail. I hope that we can, somehow, campaign to make sure that funding agencies start paying more attention to individual grants again.

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