The talk ends, and in the hallway someone says it: that’s an Annals paper. Or the variant, delivered with the same nod: it settles a conjecture of Professor X. I’m compositing here, but not by much. I’ve heard those sentences in every department I’ve belonged to, and I’ve said them.
They’re compliments, usually sincere and often accurate. But listen to what they leave out. Neither says what the theorem is, why it’s surprising, or what it lets you do that you couldn’t before. They report where the result will live and whose name it will sit next to. The mathematics has been described entirely by its reward.
Psychology has a name for this kind of drift: the overjustification effect, the idea that rewards can quietly replace the reasons you started. I expected to find it everywhere in mathematics. Mostly I didn’t. What I found instead was its mirror image, which explains the hallway sentence better and costs us more.
The ribbon
The classic demonstration is a 1973 study of preschoolers who already liked drawing with markers. Some were promised a certificate with a gold seal and a ribbon for drawing, some got the same certificate as a surprise, and some got nothing. A week or two later, when the markers were simply left out during free play, the children who had drawn for the award drew about half as much as the others. The surprise award did no harm. What hurt was drawing in order to get the ribbon.
The idea is that a ribbon gives you more justification than you need, so some of the credit for why you did it drifts to the ribbon. The effect is strongest when the reward is expected, tangible, and tied to doing the task. Rewards that simply tell you that you did well tend to help.
Read those conditions against a mathematical career. Grants, jobs, tenure, promotion: expected, tangible, contingent, and tied to whether you get to keep doing mathematics at all. On paper, this profession should be very good at turning love into ribbon-chasing.
Nobody pays you per line
What saves us is where the ribbon is attached. In the preschool, the reward was tied to the act of drawing. In mathematics, almost nothing rewards the act. Nobody pays you per line of a computation or per hour spent stuck. The rewards arrive years later, attached to a paper or a file, and only loosely connected to any particular afternoon. On the evenings I’ve spent at the table after dinner, computing until things sorted themselves out, there was no ribbon anywhere in the room. There almost never is.
My own case is easy to check. When promotion arrived, I kept working on the same problems for the same reasons; as I wrote in Go Celebrate, research is the one treadmill I’ve never wanted to step off. That’s exactly what the effect says will not happen to someone whose love has been converted.
Where it does get in is around the work rather than in it: in which problems seem worth starting, and in the strange question set aside because it doesn’t look like a paper. That never feels like losing the love. It feels like being sensible. And it shows up in the hallway sentence, which is where the mirror image comes in.
The inversion
Run the logic backward. If too much external reason makes you discount your internal ones, then doing something hard for too little external reason leaves you needing an explanation. The handiest one is that you must really love it. Psychologists call this insufficient justification. A cousin, effort justification, says that the more something costs you to get into, the more you value it once you’re there. Both come from 1950s research on cognitive dissonance, and both should be held loosely. But they describe something recognizable.
Mathematics supplies the conditions almost perfectly. Most of us could earn more elsewhere and know it. The rewards are rare and distant, the apprenticeship is long, and the problems take years. A field built this way should explain itself through love, and it does. Ask a mathematician why, and you’ll almost never hear money or prestige. You’ll hear about beauty, curiosity, the problem.
None of this is debunking. A love assembled this way is still love; the mechanism describes how motives get built, not whether they’re real.
But a field that defines itself by love has trouble admitting it also wants things. Wanting a promotion sounds mercenary, so the wanting gets spoken in the language of quality. That’s an Annals paper is the reward, smuggled back in as a judgment about the mathematics. In I Only Looked at This Last Night, I argued that the myth of effortless gift teaches us to hide effort. The myth of pure love teaches us to hide wanting. The hallway sentence is where the two meet.
What it costs
The costs aren’t in the love. They’re in what institutions, and we ourselves, do with it.
Love becomes a discount. A 2020 series of studies found that people judge it more legitimate to ask passionate workers to do extra, unpaid, or demeaning work, partly on the theory that the work is its own reward. A field that describes itself through love has told every institution it deals with what it will accept. Unpaid refereeing, adjunct pay, and the postdoc salary defended with you’re lucky to be doing what you love all run on that discount. When an economics journal paid referees a hundred dollars for on-time reports, the reports came faster with no measurable drop in quality, and the paid referees didn’t slow down once the payments stopped. That last part is the preschool test, run on referees, and the love passed it. Whatever we’re protecting by not paying people, it isn’t the love.
Cost becomes standard. I went through it, and it made me who I am slides easily into defending a hard path because it was hard. I’m not exempt; I’ve told students the hard years were worth it, and I believed it. The people setting today’s bar are often justifying yesterday’s costs.
Leaving gets harder. If part of your commitment is a story you built to explain what you paid, walking away means rewriting the story, not just changing jobs. That makes a bad fit stickier than it should be.
These costs land differently by stage.
For a graduate student, the riskiest moment may be the beginning. Something done freely as an undergraduate becomes required, evaluated, and tied to a stipend, which is the most ribbon-like moment a career contains. If the subject feels flatter in your third year, that isn’t necessarily a verdict on your fit. Ask which part flattened: the mathematics, or the requirement attached to it. A problem you’d still pick up on a Sunday, with nothing riding on it, is a better test than how the qualifying exam felt.
For a postdoc, the rewards are at their most controlling, because every paper is also a job application. The discount is most direct too, because the position is framed as an opportunity rather than a salary. This is the stage where it is most reasonable to want the reward plainly. Calling a project a job-market paper isn’t a betrayal of the subject. It’s an honest description, and it leaves room to keep one question that isn’t.
For faculty, the important role is the other side of the ribbon. You hand out the rewards and, more importantly, the framing. This would make a nice paper and isn’t it strange that this is true? teach a student two different answers to why we do this.
What to do with it
Four things, in increasing cost.
Say the content before the venue. Describe what a result shows before saying where it should go. It’s a small speech habit, and it keeps the reason attached to the mathematics, for you and for whoever’s listening.
Name practical motives plainly. Wanting tenure, a raise, or a job is fine. Saying so out loud keeps the wanting from leaking into judgments of quality, where it does more damage because nobody can see it.
Keep the love and the terms on separate ledgers. Loving the work is real. It isn’t payment, and it doesn’t oblige you to accept a weak offer, a fourth unpaid editorship, or a salary negotiated against your own enthusiasm.
If you have standing, don’t spend other people’s love. Don’t use you’re doing what you love as an argument for less. Count refereeing, mentoring, and expository writing in annual reviews instead of treating them as their own reward. And when you praise a student, tell them what was good about the idea before you tell them what it will get them.
I still say the hallway sentence, and it’s often true. An Annals paper is a real thing, and knowing a result will land there is information. What I’d change is the order. The first thing anyone hears about a theorem should be the theorem.
The love was never really in danger; the field’s costs, oddly, saw to that. What’s in danger is the vocabulary. A profession that can’t say it wants things will say them anyway, in the words it uses to say what’s good.