The September issue of the CMS Notices has a front page article on the long-range strategic planning exercise. We learn that the NSERC Major Resources Support program is being shut down; the mathematics institutes, which have been supported through MRS in recent years, will have to find some other funding mechanism.
Our community is thus being asked to develop a long range plan for mathematics and statistics in Canada. The plan should examine our discipline, identify scientific trends, and propose the right structure of resources to develop the mathematics and the statistics. It should not, however, deal with individual allocations. [...] It has worked well for the astronomers and the physicists, so why not for us?
Because we’re neither astronomers nor physicists, perhaps?
There are of course many issues. First some scientific ones: where is our discipline going? Getting some sense of this is important for explaining what we then want to do, not in the sense of only deciding to fund, say, number theory or geometry (mathematics in its own organic way has been doing very well on its own), but in giving the right structures. For example, a question of proportion: the mainstream (80% or so) individual funding of research is complemented by collective vehicles (the Institutes, BIRS), which have had a transformative effect (think of the increase in the number of post-doctoral fellows) and which have a remarkable record of leveraging additional resources from provinces, universities, and private sources, as well as foreign granting agencies.
There are worse ways to start that discussion than pointing out that the two most important “structural” new ideas in mathematics in recent years had nothing to do with leveraging funds from provincial governments, international cooperation agreements, or with institutes for that matter. Math Overflow, which has just celebrated its first birthday and earned an article in the Atlantic, was created by a few people who thought that mathematicians could use a site similar to Stack Overflow in computer programming. With over 7500 registered users and an unknown number of lurkers, it might have already replaced the department coffee lounge for many of us. The other major innovation, Polymath, was the brainchild of a single person with a blog. Tim Gowers imagined the possibility, set out the rules and started the first project; other participating blogs and wikis were added in short order.
That’s where mathematics is really being transformed. The number of actual Polymath participants may still be relatively small, but its effect on the way mathematicians think of collaboration has been enormous. Of course, the internet had started changing the way we work much earlier. As soon as we had TeX to typeset papers and e-mail to send files instantly to our long-distance collaborators, the rate of collaboration started increasing exponentially. In some ways, though, we were still stuck in our old habits at first, using e-mail to send the same formal or semi-formal letters that we would have otherwise sent by snail mail. The new generation of mathematicians has grown up with instant chat, quick email exchanges and rapid multithreaded discussions in blog comment sections. In terms of polymath-type collaborations, it’s quite possible that we haven’t really seen anything yet.
Now imagine that a polymath project would not be allowed to proceed unless at least 8 of the participating scientists were from western Canada. Or that at least two junior French scientists would have to be involved every time. Or that it would have to be a mix of Canadian and Mexican scientists, about half and half. Or that the project would have to be assigned to one of several prescribed areas and coordinated by senior faculty in that area, instead of the people whose research interests defy simple classification but who actually understand the problem at hand.
Sounds… weird? And yet this is the model that’s being forced on us over and over again: PIMS collaborative research groups, funding opportunities created by international agreements, priority research areas. And if I’m reading that CMS article correctly, we’ll only see more of it.
This is where we are different from physicists and astronomers. They require expensive infrastructure, complicated funding arrangements and a research team in a fixed location. We need a connection of minds, on a level that can be hard to find when the pool of people to choose from is small. For us, the lack of formal structure is an advantage. The internet, polymath projects, Math Overflow – we embrace them because they allow us to transcend geographical and institutional constraints. They help us find potential collaborators and communicate with them in real time, wherever in the world they might be. That, you might recall, was also the reason why the first of the new generation mathematics institutes, MSRI, came into existence: it offered new collaboration opportunities by breaking down geographical barriers. That’s what the institutes still do very well when their mode of operation allows it.
But the institutes, at least in Canada, have also evolved into centers of political power. As they seek new sources of funding by brokering political agreements, more and more of that money comes with strings attached. Forgetting that the original idea was to free us from geographical, institutional and political constraints, institutes such as PIMS now place us under similar constraints of their own creation.
The fact is that a successful career in mathematics does require strategic thinking and a long-term perspective. The key consideration, though, is that our strategy must be tailored to our particular expertise and based on our best scientific judgement, not on the shifting details of the political landscape. If the institutes support that – as Fields does, in my experience – good on them, and I will support them back.
But if the funding is contingent on the geographical location or institutional affiliation of my collaborators…
… there’s always the internet.