I don’t usually like to sound like a doomsayer but today I’m going to make an exception. I’m going to describe an effect that I believe will be present, even if it’s not as strong as I am suggesting it might be. There are three points to my post today.

1) Math research is a byproduct of calculus teaching

I’ve said it before, calculus (and pre-calculus, and linear algebra) might be a thorn in many math teachers’ side, and boring to teach over and over again, but it’s the bread and butter of math departments. I’ve heard statistics that 85% of students who take any class in math at a given college take only calculus.

Math research is essentially funded through these teaching jobs. This is less true for the super elite institutions which might have their own army of calculus adjuncts and have separate sources of funding both from NSF-like entities and private entities, but if you take the group of people I just saw at JMM you have a bunch of people who essentially depend on their take-home salary to do research, and their take-home salary depends on lots of students at their school taking service courses.

I wish I had a graph comparing the number of student enrolled in calculus each year versus the number of papers published in math journals each year. That would be a great graphic to have, and I think it would make my point.

2) Calculus MOOCs and other web tools are going to start replacing calculus teaching very soon and at a large scale

It’s already happening at Penn through Coursera. Word on the street is it is about to happen at MIT through EdX.

If this isn’t feasible right now it will be soon. Right now the average calculus class might be better than the best MOOC, especially if you consider asking questions and getting a human response. But as the calculus version of math overflow springs into existence with a record of every question and every answer provided, it will become less and less important to have a Ph.D. mathematician present.

Which isn’t to say we won’t need a person at all – we might well need someone. But chances are they won’t be tenured, and chances are they could be overseas in a call center.

This is not really a bad thing in theory, at least for the students, as long as they actually learn the stuff (as compared to now). Once the appropriate tools have been written and deployed and populated, the students may be better off and happier. They will very likely be more adept at finding correct answers for their calculus questions online, which may be a way of evaluating success (although not mine).

It’s called progress, and machines have been doing it for more than a hundred years, replacing skilled craftspeople. It hurts at first but then the world adjusts. And after all, lots of people complain now about teaching boring classes, and they will get relief. But then again many of them will have to find other jobs.

Colleges might take a hit from parents about how expensive they are and how they’re just getting the kids to learn via computer. And maybe they will actually lower tuition, but my guess is they’ll come up with something else they are offering that makes up for it which will have nothing to do with the math department.

3) Math researchers will be severely reduced if nothing is done

Let’s put those two things together, and what we see is that math research, which we’ve basically been getting for free all this time, as a byproduct of calculus, will be severely curtailed. Not at the small elite institutions that don’t mind paying for it, but at the rest of the country. That’s a lot of research. In terms of scale, my guess is that the average faculty will be reduced by more than 50%, and some faculties will be closed altogether.

Why isn’t anything being done? Why do mathematicians seem so asleep at this wheel? Why aren’t they making the case that math research is vital to a long-term functioning society?

My theory is that mathematicians haven’t been promoting their work for the simple reason that they haven’t had to, because they had this cash cow called calculus which many of them aren’t even aware of as a great thing (because close up it’s often a pain).

It’s possible that mathematicians don’t even know how to promote math to the general public, at least right now. But I’m thinking that’s going to change. We’re going to think about it pretty hard and learn how to promote math research very soon, or else we’re going back to 1850 levels of math research, where everyone knew each other and stuff was done by letter.

How worried am I about this?

For my friends with tenure, not so worried, except if their entire department is at risk. But for my younger friends who are interested in going to grad school now, I’m not writing them letters of recommendation before having this talk, because they’ll be looking around for tenured positions in about 10 years, and that’s the time scale at which I think math departments will be shrinking instead of expanding.

In terms of math PR, I’m also pretty worried, but not hopeless. I think one can really make the case that basic math research should be supported and expanded, but it’s going to take a lot of things going right and a lot of people willing to put time and organizing skills into the effort for it to work. And hopefully it will be a community effort and not controlled by a few billionaires.