...there is a negative relationship between productivity and winning the Fields Medal...
The production of knowledge is central to long-term economic growth. Yet little is known about how knowledge is produced, making it difficult to design incentives to elicit effort from knowledge producers. Prizes are a common incentive for knowledge production; hundreds of scientific prizes are awarded throughout the world and across all scientific disciplines. Although these prizes are frequently awarded with the explicit goal of inspiring more and better scientific work, whether they are effective remains an open question.
In Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output (NBER Working Paper No. 19445), authors George Borjas and Kirk Doran examine the impact of winning the Fields Medal on the post-medal productivity and research choices of mathematicians. The Fields Medal is the most prestigious award in mathematics, awarded every four years to a mathematician under the age of 40. Established by the Canadian mathematician John Charles Fields, the medal is often thought of as the "Nobel Prize of Mathematics."
The authors use archival data from the American Mathematical Society and the Mathematics Genealogy Project to estimate the age-productivity profile of these exceptional mathematicians along a number of different dimensions, including the number of papers published, citations received, and students mentored.
The authors find that the age-productivity profiles of the Fields Medal winners and the losing contenders in their cohort are similar until the year in which the medal is awarded. After the award, the rate of output of the Fields medalists, regardless of how it is measured, declines noticeably.
The authors also find that the medalists exhibit far greater cognitive mobility, shifting across sub-fields within mathematics, in the post-medal period. The winners are more likely to pursue topics that are not related to their pre-medal work. Because cognitive mobility is costly and additional time is required to prepare a paper in an unfamiliar field, the increased rate of cognitive 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.
Although there is a negative relationship between productivity and winning the Fields Medal, the authors caution that other types of prizes may have different post-prize productivity effects. The Fields Medal is awarded at a relatively young age and the timing of the prize could have a significant impact on post-prize incentives. Similarly, mathematics is an unusual field in that researchers typically do not need expensive infrastructure to produce theorems. Prizes in the physical sciences, and even in economics, may open up funding opportunities that could significantly increase post-prize productivity for the winners.
The findings suggest that the post-prize productivity impact of winning a prestigious award can be substantial, affecting both the quantity and type of research the winners produce. The authors argue that the increased opportunities provided by the Fields Medal discouraged the recipients from continuing to produce the pure mathematics for which the medal was awarded, and encouraged time-consuming investments in ever more distant locations in the space of ideas.