The competing incentives of academic research in mathematics

Alexander Coward is a lecturer of mathematics at UC Berkeley. The other day he posted a long article on his website denouncing the UC Berkeley mathematics department for their (alleged) misguided reasons in firing him.

There are a lot of moving parts in this particular story, but Dr. Coward’s central claim is that he’s being fired for teaching too well and making the rest of the department look bad. He has some evidence to back up his claims. But even despite the fact that the university is free to fire and hire whomever they want for whatever reason they like — in particular, it has always been and will always be a fireable offense to piss of your boss (if you don’t have tenure) — this story highlights the strange role that academic mathematics research has grown into over the past half century.

Whether Dr. Coward likes it or not, research mathematicians at research universities have no incentive to teach undergraduates well. Every aspect of their career incentivizes them to neglect teaching:

1. Their status as a researcher is solely based on the quality of their work and the degree to which they convince other researchers to study it.
2. Their job advancement (from graduate student to postdoc to assistant professor to tenured professor) is based solely on the quality and quantity of their academic research.
3. Mathematicians who put too much emphasis on teaching (or took time off from research to teach) are often not offered jobs for fear they will focus on teaching instead of research.
4. Because grants are judged by the same community of peers that decides whether to hire you, grant money is also purely dependent on research quality.
5. Decisions about tenure are unrelated to teaching.
6. If you spend less time preparing lectures and meeting with students, you have more time for research.

On the surface there are checks to counteract this, but they are all superficial. Job applicants are expected to provide a “teaching statement,” but nobody reads it. If someone does read it, it has no bearing on the final decision. Likewise, grants expect a discussion of “wider impact” and inclusivity of broader groups, but the game there is to find a way to “launch” a program for helping minority students which coincides with your regular advising of graduate students. Because, and you seen this coming, graduate students have the potential to do good research with you and doing research is what matters. In other words, it’s not hard to game the system because the people who matter in the system also only care about research.

University administrators (desperately looking for reasons to justify their own jobs) often require faculty to submit teaching evaluations of themselves or their peers, but as far as anyone knows they go into a wastebasket after some cursory statistics are gathered for use in a report that nobody will ever read. And for what it’s worth a research university administrator’s job is also not related to providing good teaching. Their job is to maximize revenue from tuition, donors, and arbitrary student fees. And that works by building nice gyms, sports centers, cafeterias, and comfortable student housing. That’s what attracts students and allows them to hide the myriad of fees and tuition spikes inside a litany of boring legalese. Administrators don’t care about the actual education their students are getting because to them the university is a business and teaching quality is unrelated to their bottom line . That is, in the short to medium to not-so-long term; if in fifty years people finally start to realize they can get a better education outside research universities (if the “bubble bursts” so to speak) then the folks at Berkeley will start to rethink their greedy optimizations.

So the university administrators don’t care, and the researchers are incentivized not to care. But to the public everyone is saying they do care and that education is their top priority.

I’m not trying to make a value judgement about universities or researchers or administrators. I personally enjoy teaching in general, and think it can be really exciting when the environment is set up to allow efficient use of the professor’s and students’ time. All I’m doing is observing incentives that partially explain the current state of the world. The real question that needs answering is what the role of a research university should be. And it seems there are two competing answers.

The first is that a research university should primarily be a place where top-notch research gets done that impacts the world. In this case the current state of the world is as good as it can be: we have lots of great people doing great work, universities only hire those with research talent who won’t waste their energy teaching students. Administrators and PR departments have convinced (a.k.a. tricked) the world into thinking that the average student who attends University X can get a great education by absorbing the radiation emanating from geniuses (and the hope that some small fraction of them can become great geniuses, too). So there is enough cash flow coming in to support researcher salaries when grant money is scarce. What the students actually do during their time at the university is irrelevant so long as researchers keep outputting great research, and if the students want an education it’s their responsibility to read the textbooks.

This is a rather cynical view of education, and I think most people’s first knee-jerk reaction to this is that it’s evil. But the more I think about it the more this stance seems like an onion, and the more layers you peel the less outrageous it seems.

The first fact is that university attendance is skyrocketing. Every year millions more students go to college, and every middle class US teenager has the “college track” ingrained in their psyche. And it’s only getting worse, just the other day I overheard a woman say she was putting her child in a lottery for kindergarten. Parents are preparing their students for college before they can even read!

The obvious foundational question is whether every student should go to college. And I think the answer is obviously no. A close friend of mine who I’ll call Navid hated school growing up. He absolutely hated it. By junior year Navid was skipping class so often that I thought he had switched schools or dropped out. In fact, he did drop out, and then later got his GED and found out he liked working with machines. So Navid went to a cheap two-year mechanic training program, started working as a mechanic for luxury cars, realized that when you learn to fix fancy cars you can basically fix anything, and then he got a job traveling the country repairing turbines. He has a comfortable life, no debt, a nice car, and he was doing this before I could even finish undergrad.

Then you have the thousands of students with degrees in art history and philosophy and anthropology and drama who end up waiters and baristas and flight attendants and sales clerks, and they’re unhappy because nobody seems to want to pay them to philosophize or critique art. And for what it’s worth they’ve never tried fixing a machine in their life, so they wouldn’t have any chance to tell whether they enjoy it. They even brag about how little they understand about their computer (which turns out to be the only tool they use to do any work). But they like how structured school is and if you just follow the directions and draw within the right lines you’ll get an A and … profit, right?

So from the university’s perspective they’re just reacting to natural market forces. If there’s a businessperson who realizes city X doesn’t have any good gyms and builds the best gym, we don’t criticize them just because gym-goers are bad at maintaining their commitments to their health. It’s their fault: all the workout machines are there, there are plenty of colleagues to go to the gym with, most people are just lazy and don’t want to expend effort. It’s not evil to make a profit off of that fact, is it? The same logic holds for people who aren’t committed enough to their education. If you’re opposed to universities who expect their students to work hard, you must also be opposed to gym owners.

Now you might say, “Thank goodness that wasn’t me! I was very dedicated to my education.” Really? When you took calculus, did you read the textbook as the class progressed? If not, then the university was taking advantage of your laziness. Regardless of your self-esteem, your mindset was that you would go to lecture and that it was the professor’s job to teach you what you need to know. That is how the university takes advantage of your laziness.

One important counter is that universities are cramming people into larger and larger classes, which makes it very difficult to interact with the professor even if you’re the best student. Shouldn’t the classroom be a place where, if you have done the reading, you can go to ask questions on the parts that were difficult and have a genius explain them to you with dazzling clarity?

That would be ideal, but once this thing is a business the question is what product are you paying for? In this case it’s the lecture (since the assumption is now that most students don’t read the book) and the diploma. Just like the gym analogy, if you want interaction you need to find friends who can help you, or hire a personal trainer. So the University might reasonably argue by putting more people in the classroom they’re giving you a larger community of students you can work with. And they also pay for personal trainers (graduate students) to run discussions and hold office hours and run tutoring centers.

All the while your tuition and future debt pays for researchers to do great research. So where’s the problem? Lazy people will have bad job opportunities and be in debt because it’s their own fault, motivated people will learn and find summer internships and do projects outside of class and start businesses with their classmates. The only problem is that someone (who?) convinced the average student that they belong in college when they simply don’t.

The second answer to “What should a university be?” is that it should be a place to train students who then go out into the world and do great things. The glaring problem with this view is that it’s mutually exclusive with research. For every faculty member a university hires whose sole job is to teach, they lose a faculty member who can do research (and all the graduate students and grant money and prestige that comes with that).

But fine, let’s take this train of thought to the extreme and suppose that there was no more research at universities. At least in pure mathematics, this would likely destroy all research efforts period. As far as I’m aware there are no research jobs for pure mathematics outside of academia. There are lots of applied math research jobs, but they are almost entirely in government labs on mathematical modeling. There is some small amount of weather modeling, but mostly weapons design, counter-terrorism computational science, and NSA efforts to circumvent the cryptography ensuring your communications are private. Data science and statistics jobs in practice are generally not research.

Mathematicians estimate there are around 30k research mathematicians currently working in the United States. And at a conservative salary of $60k per year (this is really more like a high postdoctorate salary) their salaries are 1.8 billion USD in total. On the other hand, the National Science Foundation, Department of Defense, and Department of Energy, the main government funders of pure math research, spend no more than 500 million a year on all math research grants (pure and applied). Meaning without universities to fund mathematicians, we’d be able to fund at most 8,500 mathematicians in the US. That’s just over a quarter of what we have now. Are we really willing to sacrifice the sort of foundational advancements in science that mathematicians tend to usher in for the sake of getting better teachers to train lazy students?

And this is just math, what about biology, physics, chemistry, engineering, and all of the other (much larger and more expensive!) fields that also have limited funding from the government. Maybe industry would step in and hire them to do long-term foundational research, but industry labs these days are known to be fickle. More likely, their skills will end up going to endeavors that are practical, but not earth-shattering. Like making slightly more efficient file systems, or the next mobile chat app, or designing better medical devices for diagnosing illnesses in pets. I hear pet care is a lucrative market.

This second view about the role of a university is one I can’t morally support until there is viable large-scale funding for research outside of academia. I’m convinced there is a business model that can sustain research better than academia can. I just don’t know what it is yet. But if a student wants a top notch education and they can’t afford to go to a private liberal arts college where they actually care about teaching, the best option is to find the cheapest state polytechnic school where, even if you’re lazy, you’re forced to get your hands dirty and learn a skill. Because Dr. Coward’s ranting and whistleblowing isn’t going to change the incentives of the Berkeley math department. The foundation of Berkeley’s business is too sturdy for anyone to care. Oh, and they’re not incentivized to care, because there’s that research that needs doing.

So is there some sort of middle ground that universities can have between all research and no research? Some universities have been trying, but then you get friction between teaching and research faculty over where to devote resources, students stop signing up for the classes taught by the research professors, people start wondering why we keep the researchers around anyway, and the Alexander Cowards of the world come along and try to ignite the gunpowder.

It seems like when researchers are in charge the only stable state is “all research,” and when educators are in charge the only steady state is “no research.” There doesn’t seem to be a middle ground. However, industry does seem to be poking their heads back through the research door in a good way. YCombinator (one of the country’s biggest tech investment firms) is launching a new research lab and investing a lot of money in it. Hell, I’ll even apply for a job there if they announce a group that aligns with my research interests. I’ll be very interested to see how they make it profitable, or whether the lab will become the rich venture capitalist’s plaything until they get tired of funding it and close it down.