H ow worried should you be that getting a Fields medal might destroy your research career? The question seems preposterous, but a recent paper [BD14] by two economists, George Borjas and Kirk Doran, suggests that this is a question that we, the mathematical and scientific community, should consider. Happily, readers over the age of forty do not need to worry, but perhaps young researchers should take this problem seriously. Of course there are so few Fields Medals that the likelihood of being hit by one seems to be virtually zero. Nevertheless, they do not strike randomly. With one exception, only people with a PhD in mathematics have received Fields Medals. Young readers of the Notices of the AMS have a roughly 1:8000 chance of getting one, much higher than being in an airplane crash (about 1:11,000,000),1 a danger many people worry about, but much lower than being considered a nerd (nearly 1:1.1 for mathematicians). Surprisingly, even in the very comprehensive and otherwise excellent encyclopedic volume [Gow08], in Section VIII.6 titled “Advice to a young mathematician,” Atiyah, Connes, and Gowers give not even a hint on what to do should you get a Fields Medal. The paper by Borjas and Doran, while not offering any practical advice, is the first to call attention to this issue. All joking aside, [BD14] is a serious paper about a serious question. The need to understand the right choice of rewards and incentives appears everywhere, from the mundane (should you pay your teenager for taking out the trash?) to some of the basic questions society is wrestling with (should bankers be paid billions?). Labor economists have long tried to understand the optimal level of reward for work done. For a company or organization, but also for society as a whole, it is important to know which rewards encourage better work and which ones do not. There has also been an interest— especially among the intellectual 1 percent—in understanding whether exceptional rewards for exceptional work are the best way to encourage achievement, a question studied by Tournament Theory. The Fields Medals occupy a unique place among the prizes offered for exceptional achievement. Nobel Prizes—perhaps contrary to the original intent—are frequently awarded near the end of a career, at an average age of fifty-nine. Thus, in practice, a Nobel Prizes rewards a lifetime of work. In the economic analysis, its main value is that people who aspire to it work hard before getting it, thereby adding to our store of knowledge. There is no requirement of further scientific work, though many recipients continue to perform exceptionally, occasionally leading to a second Nobel Prize (Bardeen, Curie, Pauling, and Sanger). Janos Kollar is professor of mathematics at Princeton University, and he was a member of the 2014 Fields Medal Committee. His email address is kollar@math. princeton.edu. www.pbs.org/wgbh/nova/space/how-risky-isflying.html.
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