Saturday, June 20, 2020
Our world is dominated by groups in ways that most people aren't even conscious of. In math, they tend to be more obvious in their influence, and I'll get to that in second. I want to begin by writing a few words about groups in society, in general:
Let's say you have a conversation with someone... about something in the news, maybe. The person you are speaking with will give their opinion; but, in the back of their mind, they are thinking in terms of the community -- the *group* -- that you are a part of. They aren't really that interested in telling it to *you*; they're interested in your *tribe*.
For example, suppose you were to interrupt the conversation (in a polite manner), and let it be known that you don't have any community connections whatsoever, no family, no friends, no political affiliations; absolutely nothing, that you are basically an alien life form. The person talking to you will probably say something polite -- but what they will be thinking is that the conversation they are having with you is a waste of time. They were thinking about what your connections bring to the table; they were being a good ambassador for *their* group, and were hoping to share that message with *your* group; and they assumed you were some kind of ambassador, too.
As time goes on, the power of groups -- and the need to identify with a group -- becomes ever stronger. You can see it in political polarization in this country. Are you on the Red Team or the Blue Team? To a lot of people, it's very, very important what team you belong to!
In mathematics, groups are much more overt, and you have to join one to keep from getting pushed aside. Departments even write into their "strategic plans" about what the established groups are, and what they can expect, in terms of hiring and such. Comprehensive exams even reflect the different groups -- there's an exam put toegether by the "Algebra Group" (which really should be called the Algebra-Geometry-Toplogy group); there's one put out by the Analysis Group (which might also include parts of geometry); one put out by the Probability-and-Statistics group (which might also include some machine learning); and so on.
And there are some good reasons why you need groups, mostly having to do with "scarcity" (grant money, available postdoc positions, hiring slots, and so on): you need at least a certain number of people working closely to help run and attend seminars, for example. Math research is deep, and it's hard to make sure ones students are getting the training they need to succeed, from just oneself. And, collaboration improves the quality of the output; which increases the chances of securing grants and winning prizes.
But that's not the whole story. Groups in math often become monstrously large, larger than they need to be. Some have mutli-school seminars that run weekly; sometimes two or three per week, for the same group! Everybody within the group knows each other (or most know most others), shares gossip, communicates about the availability of students and people on the job market, and so on. I would compare it to a religion, and the benefits it provides to its members. Math as a whole is not a unified religion; but different factions within the field *act* like organized religions.
And when it comes time to elect faculty to committees, these mega-groups exert powerful control. If a department is filled with "serious guys" (to use that term again, from previous posts), that keep each other at a distance, then when it comes time to suggest and elect others to committees, who do you think they are going to pick? Are they going to pick someone in their own group, that they know?... Or are they going to take a chance with someone in a distant group? More than likely, the former.
I think the field has swung too far in the direction of strengthening groups. What is more needed, *now*, is some strengthening of the *individual*. As time goes on, if it isn't addressed, the field of math will see the same kind of polarization seen in politics in this and other countries.