Thought experiment: new mathematical institute

So, Scott’s comment about being dictator of a math department got me thinking (very idly), and I came up with a hypothetical for you guys: imagine you earn a preposterous amount of money one way or another, and for whatever reason you decide that the best use of it is a new institution dedicated to research in mathematics (I don’t actually agree with this premise, but one can always assume that one has a truly preposterous amount of money, and have already spent a bunch of it on family planning NGOs and smart growth advocacy, or whatever other causes you might think are a higher priority than mathematics). What model would you go with?

(Disclaimer: obviously what I’m about to say was heavily informed by my experience at IAs, but shouldn’t be read as too much of a criticism. After all, I’m talking about a hypothetical world where IAS still exists, and I doubt anyone thinks they’re going to have much success out-IASing IAS, so almost by definition, it’s better to do something a bit different, not out of criticism, but rather respect for the niche they already fill).

I’ll just note, we’re not talking about all that huge an amount of money here. IAS, which is by no means a minimal conception of a mathematics institute, has an annual budget of about $50 million (split roughly three ways between mathematics, natural science and social science/humanities), about $100 million in real estate and facilities, and around $500 million in endowment. That’s a lot of money, to be sure, but there are plenty of people in the world who have that kind of money. Now, I just have to find one who really likes math, and really trusts me.

Some things to consider:

where would you put it?: Of course, the optimal location varies depending on what kind of institute you want, but is also a question of preference. Urban or rural? Close to an established mathematical center, or further away? I’m firmly in the urban category (many people like IAS’s location, but I think it’s a net minus in terms of quality of life and net recruitment), and a personal believer in returns to concentration, so am inclined toward Central or Inman Square, Cambridge. There’s simply no other spot which gives access on foot to two of the best universities in the country. Even if you include Group II departments, there’s nowhere with the sort of overlap that MIT, Harvard, BU and Northeastern have (not to mention that a quick bike ride to Porter and 20 minutes on the train put you at Brandeis, another Group I department). The only place that’s even close is between Courant and CUNY Graduate Center in midtown Manhattan, which I think is a poor choice for expense reasons. One can certainly argue for the New York area (including Princeton and New Haven) or Chicago or the Bay Area as good competitors on a regional basis to Boston, but none of them has a core at all comparable to the one roughly centered on Central Square. Berkeley and Standford are 40 miles apart, and Northwestern and Chicago are close to 30, both with not particularly convenient transit links.

I’m lazy, so I really think that things need to be close to each other for them really be able to interact well. When I was in Berkeley, going to Stanford or Davis for a seminar was almost inconceivable to me, even though these are departments are “close by” compared to most good math departments and at least have functional transit links (though the Stanford-Berkeley one seems to be deliberately frustrating at times). But, from MIT or Harvard, I would go to Central Square for a sandwich.

But I am curious if there are less obvious choices people would support. Austin? San Diego? Seattle? Maui?

how long would you want people to stay?: honestly, I would be kind of tempted to just clone AIM somewhere else, having just one week with a somewhat loose, open conference format. This is, in part, because I really like AIM workshops, and I think more people should be exposed to that model of conferring (the important points: planning the talks over the course of the conference rather than before the conference, and the topics being assigned by the organizers with input from the audience, with a view toward bringing the audience up to speed on a particular problem, rather than necessarily covering the speaker’s latest research. Also, the room at AIM is laid out in a way that makes it easy to drop in and out of talks, something I consider a good idea).

What do people think: is there more “pent-up demand” out there in the mathematical world for week-long conferences, or year or semesters away? This isn’t a question I feel like I really know the answer to, but don’t feel like I can really hazard a guess.

would you attempt to focus the topic of the research, either over the long or short term?: for example, MSRI does this pretty tightly on a semester-basis, whereas IAS tends to do so more loosely on a yearly basis, and AIM changes from week to week (but is very tight each week). My personal feeling is that making sure that people have people to profitably work with should be one of the paramount concerns, which militates pretty strongly toward tight focus. That’s personally what I would prefer, but one could make a go at being more eclectic.

what balance of seniority would you opt for?: existing mathematics institutes seem to try to spread this pretty evenly, with something of a tilt toward people early in their careers. While this seems like a pretty reasonable strategy, I would certainly like to see some other models tried. One interesting possibility would be a aggressively recruit a big group of postdocs (or perhaps, say, people within 5 years of their Ph.D.) for one or two year stays and then parachute in more senior people on a shorter term basis (say a week or two). When I say big, I mean like 30 or 40. If you were willing to pay a bit more in salary, and put it in an appealing place (this is where choosing a location like Cambridge would come in handy), I think you could recruit very successfully (though in 2007, about 160 new Ph.D.’s were employed at Group I schools, so 40 would be a huge chunk). Of course, my position as a postdoc colors my view of this a bit, but I think greater concentrations of postdocs could have some really positive effects in terms of collaboration and spreading ideas. Other industries know that there are big benefits to people all being in the same place to physically exchange ideas (this is why MIT is developing a crust of pharmaceutical companies around its campus). On some level, it would be ideal if we could stick all the mathematicians in the world in the same city, but for various reasons, that’s not so possible for more senior people, but it might be more possible amongst people at a mobile stage in their career.

Also, this might sound trivial, but it also would be fun, which I think is easy to downplay the
importance of. Postdocs tend to have fewer peers in the same place compared to graduate students or even ladder faculty, which I think can be problematic.

Anyways, what do you guys think? What questions did I entirely forget to address?

22 thoughts on “Thought experiment: new mathematical institute

  1. Where? Hapuku Valley in rural Kaikoura, three hours north of Christchurch. Visit lengths? From two weeks to three months. Research focused? Yes and no. Category Theory and applications in a wide range of disciplines. Seniority? Mostly young people.

  2. Speaking from the perspective of a theoretical physicist, and a postdoc at the Perimeter Institute, (which is exactly a large, recently built, well-funded institute), I think you’re understating the importance of graduate students. When I first arrived to start my postdoc at the end of 2007, I found that postdocs all seem to have their own research agendas and it can be difficult to encourage collaboration amongst them. If a project doesn’t look like it could be completed within a few months, then it’s just not going to happen; it is too much investment and there are lower hanging fruits around. Grad students, on the other hand, have a much more open attitude to tackling problems. They don’t mind spending a lot of time on a project. Admittedly, though, progress is slower. Plus, I think that grad students are invaluable because they ask seemingly naive questions that turn out to have real insight once you try to answer them. I feel as if grad students aren’t afraid to contribute “breadth”, while postdocs can unfortunately become all-to-comfortable contributing only more “depth”.

    So I think that it is vital for an institute to have a large pool of graduate students. This of course means that there must be senior people around to advise them. One could either draw graduate students from a nearby degree-granting university, or allow permanent faculty funding to hire their own students and become a degree-granting institute. I haven’t thought about the proper mixture of these two, and perhaps there are other options as well.

  3. Putting it in Boston would result in too much concentration of people. I like the idea of having it in (or near) a big city, but let it be some other city with a top math dept, rather than one with two top math depts.

  4. JK-

    The concentration is the point. If you were going to design mathematics research as an industry from the bottom-up, you would make it vastly more concentrated than it already is. There’s a reason that all the car companies ended up in one city, and all the country musicians in another, and all the financial firms in a third. There are good reasons that this doesn’t happen in mathematics, since college teaching is not a very easily transported good, but from the perspective of doing research, it really would be optimal for most of us to be in the same place.

  5. Having spent 10 years in Boston, people from MIT/Harvard never go to Brandeis for seminars or colloquia, and only rarely go to BU or Northeastern (not to speak of BC, Tufts, UMass Boston, Wellesley, … ) So the huge concentration you are talking about actually comes down to drawing people into the MIT/Harvard neighborhood.

    In New York, I think the Joint CUNY/Columbia/NYU Number Theory Seminar probably draws as many participants as the Joint Harvard/MIT Algebraic Geometry Seminar used to draw (at least the ones I have seen at Columbia). So even if Boston is unique in having 2 top-tier universities so close, there are other locales that optimize their concentration of institutes about as well.

  6. So the huge concentration you are talking about actually comes down to drawing people into the MIT/Harvard neighborhood.

    Yeah, that’s why I argued for that as a location, rather than Fenway.

    What you seem to be saying is that the ability of departments to interact as they get further away from each other falls off fast, which I absolutely agree with.

    On the other hand, if I ever get too lazy to go to seminars at BU, I will be thoroughly ashamed of myself. I mean, it’s one stop on the CT2 from the main building at MIT.

    So even if Boston is unique in having 2 top-tier universities so close, there are other locales that optimize their concentration of institutes about as well.

    Do you have any examples other than Manhattan? My reading of the situation was that in terms of world-class departments with convenient transit links between them there’s Cambridge/Boston ahead of New York by a nose and then….. well, basically nothing. NY to Princeton or Yale, Davis/Berkeley/Stanford, UCLA/USC and Chicago/Northwestern aren’t bad, but aren’t what I would call convenient. Some others are not too bad with a car (though then you have to park that car. Princeton to NY isn’t bad in a car, but then you have to park a car in Manhattan), but that’s hard for a lot of people.

  7. I would put it in San Francisco. It’s less than an hour by car to either Stanford or Berkeley, and not much over an hour if taking Bart or Caltrain. It also wouldn’t take much arm-twisting to get people to come for short-term (or even long-term) visits. It doesn’t hurt that it’s my favorite place to be…

  8. Ben,

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    I considered two points of view

    1. The Cambridge area already has so much, why not spread the wealth, e.g., to the midwest, with Chicago being a natural spot. After all, isn’t it ultimately beneficial to build many centers in the US? Wouldn’t building an institute in Cambridge provide only diminishing returns?

    2. With a concentration of strength in the Cambridge area, no amount of money is too much to spend to further develop math opportunities there.

    I felt 2 was the strongest point towards Cambridge, but your quote seems to suggest you don’t believe that. True, the Bay Area has MSRI and AIM, but Cambridge has Clay and all the other schools to form a virtual massive institute already.

  9. (I was trying to quote

    “it’s true, though “Bay Area mathematics institute” is a niche which is already relatively full….”)

  10. Alex-

    As they say, “A foolish consistency is the hobgoblin of little minds.”

    More seriously, I would say this: SF is pretty good choice as choices go. But even if you put it in SOMA, close to Caltrain and BART, it’s not that easy to get to Berkeley or Stanford (about as easy and quick as getting from Cambridge to Brandeis, which we’ve already agreed no one does). This sounds silly, since people will gladly commute that distance, but people will commute much further than they are usually willing to go for a seminar.

    Also, while I’m all in favor of concentration, there is something to be said for the value of diversity of institutional forms. If I were going to make another AIM (as I suggested I might), I’m not sure I would want it right next to the old AIM. Though, who knows, maybe I would. It is true that being right in SF would be pretty sweet.

  11. Hi Ben,

    I also used to go to BU and Northeastern, and even out to Brandeis a couple of times. In fact I went to BC quite often (but not actually for math — I lived next to BC). Most mathematicians at Harvard and MIT (at least the ones I knew) would go to seminars outside Cambridge only rarely.

    Outside Boston and Manhattan, I have attended a large joint seminar in Paris attended both by people from Paris and from Orsay. Talking with other mathematicians, I gather there are also large joint seminars in Tokyo.

  12. Hi again Ben,

    To park a car in Manhattan, I have been instructed to take a car to a shop and leave it for an oil change. The shop will let you pick it up later in the day. And the cost of the oil change is a lot less than for a garage.

  13. Jason-

    That’s a good trick, though I feel like it would obviously collapse very quickly if too many people did it. By which I mean, you probably shouldn’t spread that around too much.

  14. I would be more of an “empire builder”, and place the institute somewhere in which there is demand but not supply. Maybe Vietnam, since there seem to be so many good Vietnamese students (and it’s quite centrally placed in Asia), or maybe even Rejkjavik which has a strong intellectual culture but no real math scene as far as I know. Or Hungary… to plug a brain drain.
    Also, I would focus on things which were not necessarily the latest fashion… deep rather than fashionable topics… and have enough interesting activity to attract interesting visitors from abroad for short to medium stays. My model in this respect would be RIMS in Kyoto I suppose…

  15. I think there is a law of diminishing returns with the number n of nearby universities to an institute; n=2 may not be twice as good as n=1, and it is not even clear that n=1 is better than n=0 (see for instance Banff or Oberwolfach for some excellent examples of n=0 institutes). Firstly there is the issue of redundancy: if one wants to interact with the top mathematical minds in Harvard and MIT, one does not need to go to a special-purpose institute for this – one simply visits Harvard or visits MIT, and takes two stops of the T rather than one. Also, working at a math department that is less than fifty meters from a fantastic maths institute (IPAM, in this case), I can tell you that one’s attendance at an institute can actually decrease with the proximity to that institute – there’s too much going on, it’s always there, one still has classes to teach, and so forth.

    I think network effects are less pronounced in mathematics than in, say, finance, because we have more of a closed ecosystem. In finance, one has interactions between many different groups (e.g. brokers, investment bankers, accountants, lawyers, etc.) and so one can take full advantage of Metcalfe’s law. But maths departments interact largely with themselves, and with other units within the same university; the networking we need is already largely met by conferences and the internet, with physical proximity being only a modest benefit.

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