Conventional wisdom suggests that the hope of winning a major award such as a Nobel Prize or a Fields Medal  helps spur top researchers to do their most outstanding work, thereby advancing progress in many scientific fields. What happens after you win one of these prizes, though? Do you become motivated to achieve even greater things?
Those who establish such prizes appear to hope so. As quoted in a paper  by George Borjas  of Harvard University and Kirk Doran  of the University of Notre Dame, John Charles Fields, who founded the Fields Medal—the highest honor in mathematics—wrote that, "while [the medal] was in recognition of work already done it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others."
But continued high productivity isn’t necessarily what happens to major-prize winners, at least in mathematics, Borjas and Doran discovered in their recent study, Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output. Recipients of the so-called "Nobel Prize of Mathematics," they found, generally have lower productivity after winning the award, as measured by publications.
In the period leading up to the announcement of the Fields Medal, which is awarded every 4 years to a mathematician under the age of 40, both the winners and the "similarly brilliant" mathematicians recognized as contenders show similar levels of productivity, Borjas and Doran found. They used "the set of winners from a broader set of prizes for great mathematical achievement (awards which are themselves good predictors of winning the Fields Medal) to construct a representative group of brilliant mathematicians who can be thought of as 'contenders' for the medal." They then compared the research output for both medalists and contenders.
Perhaps surprisingly, "the increased opportunities provided by the Fields Medal, in fact, discouraged the recipients from continuing to produce the pure mathematics that the medal was awarded for" Borjas and Doran found. But this is not necessarily a bad thing, as winners frequently branch out into areas different from the ones they had pursued before winning the prize. Such "cognitive mobility" is "costly" in time, Borjas and Doran claim, because people must familiarize themselves with unfamiliar material before being able to contribute to a new field. This "increased rate of mobility reduces the medalists' rate of output in the post-medal period" and accounts for about half of their productivity drop, the authors add.
This "unambiguous and adverse relation between productivity" and winning a major prize may not, however, exist in other fields, they suggest. Mathematicians are not typically dependent on "expensive infrastructure"—and therefore on grant funding—to do their work. Borjas and Doran speculate that scientists who depend upon such support may see a significant bump up in funding after winning a prestigious award, and therefore boost their productivity in their accustomed field.
One other point to consider: Measuring productivity by counting the papers a researcher produces may not truly reflect his or her impact on the advancement of knowledge. Letting the best minds loose on new problems and new fields in many cases is what it takes to move science forward.