The Fields Medal is the thing you want if you're a mathematician with ambition: It's on the prestige level of the Nobel Prize, it's only given out every four years, and you can only win it if you're under 40.
As researchers George J. Borjas and Kirk B. Doran find in a new paper, if you should climb the top of the mathematics mountain and win the award, your productivity will drop by one paper a year, which is significant when you're either publishing or perishing.
"Remarkably," the authors conclude, "the rate of output of the Fields medalists—regardless of how it is measured—declines noticeably in the post-medal period."
Why do we stop working so hard after we win?
If you'll permit a rare fit of journalistic humility, we don't know. (By the way, is there an award for not knowing?) Humans and their motivations—and how those things intersect in small worlds like high-level math and corporations—remain mostly inscrutable, though we're beginning to scrutinize pieces of the ambitious puzzle.
As Tabarrok notes, the drop off in production of math papers isn't solely due to folks resting on their laurels. The shift from mathematics is a little more calculated than that, with medal-winning scholars working in biology, jumping into vision and pattern theory, and developing things like catastrophe theory—which doesn't sound all bad.
However, as Borjas and Dura note, this branching out has its productivity costs:
The medalists exhibit a far greater rate of cognitive mobility in the post-medal period, pursuing topics that are far less likely to be related to their pre-medal work. Because cognitive mobility is costly (e.g.,
additional time is required to prepare a paper in an unfamiliar field), the increased rate of mobility reduces the medalists’ rate of output in the post-medal period. The data suggest that about half of the decreased productivity in the post-medal period can be attributed to the increased propensity for experimentation.
The emphasis above is added, for it reminds us of the tensions companies feel regarding innovation—since innovation requires doing new things, and that doing new things is called experimentation, and experimentation requires doing something you're not as good at, and that not-being-as-good takes time and vulnerablity. And that a beginner's time decreases productivity.
So what are mathematicians to do? The thing they do best: figure it out.
Hat tip: Marginal Revolution
[Image: Flickr user George Alexander Ishida Newman]