How Winning the Fields Medal Affects Scientific Output

That is the subtitle of a new paper (pdf) by and George J. Borjas and Kirk B. Doran, the abstract is this:

Knowledge generation is key to economic growth, and scientific prizes are designed to encourage it. But how does winning a prestigious prize affect future output? We compare the productivity of Fields medalists (winners of the top mathematics prize) to that of similarly brilliant contenders. The two groups have similar publication rates until the award year, after which the winners’ productivity declines. The medalists begin to “play the field,” studying unfamiliar topics at the expense of writing papers. It appears that tournaments can have large post-prize effects on the effort allocation of knowledge producers.

For the pointer I thank Sarah Brodsky.



Another example of the left hand (TC) not knowing what the right hand (man, AT) is writing about. Or a senior moment. Or the criticism that TC makes yesterday's news seem like today's all over again. LOL I do recall this discussion.

Also it's sad but true that in economics past effort is not rewarded, only future effort is, but I would say this is short-sighted. 19th century inventor E. Drake got nothing for inventing a drill to prospect for oil (aka the oil derrick) but the Pennsylvania state legislature thought highly enough of him to give him a pension when he went broke for failing to patent his invention. You could say this Penn. award rewards lack of foresight and encourages laziness to patent un-savvy inventors, or, you could say it encourages people to take risks knowing in the end they will get a reward.

This is arguably a feature and not a bug. The prestige of the prize is meant to free the most brilliant scholars from the confines of the publish/perish rat race and pursue potentially transformative scientific horizons.

True for the "tenure" prize. But let's all agree that serious contenders to the Fields Medal are unlikely to perish no matter how little they publish going forward.

The post-prize effects on the effort allocation of one prize-winner is less important that the pre-prize effect on the effort allocation of a thousand wannabe prize winners.

"It appears that tournaments can have large post-prize effects on the effort allocation of knowledge producers."

Given that the winners were productive before winning and the non-winners continue to be productive when they continue to be in the non-winning or pre-winning state, perhaps it is more accurate to say that the *lack* of prizes left to be won is what reduces effort allocation. Fields Medals don't reduce productivity; the absence of something higher than the Fields Medal does.

Suppose Fields Medals winners believe that they are very unlikely to win a second Fields Medal or, even if they do, they put much less value on winning a second medal than the first. Then, this scenario is equivalent to having a 100% or near 100% confiscatory, progressive "tax" on Fields Medals, one that kicks in after the first medal. This study finds that such a tax may have severe disincentive effects. In most other professions, people are compensated with dollars instead of Fields Medals. The implication is that high tax rates on those professionals' dollar-based incomes is...

if there was an an award higher than the Fields, would the Fields have any substantive incentive effect? The Fields only very slightly edges out the Abel and Wolf awards in terms of fame, but Fields winners are much more well-known. The linked paper itself uses Abel and Wolf winners as a control group for what the mathematician's career path would be like without winning the Fields.

This seems unlikely. The Fields Medal has an age limit of 40 and is only awarded every 4 years so a large fraction of contenders who don't get it in a given year will never be eligible again.

david and Max, both good points. My question would be does winning the Fields somehow diminish (significantly) the incremental value of other awards/recognition that could come afterwards, such as the Abel and Wolf awards, i.e., would a Fields winner place significantly less value on an Abel than if he hadn't won a Fields? If so, then it would seem that my point would still stand: the incentive effects facing a Fields winner are similar to someone facing a confiscatory tax on future income or wealth, "wealth" in the Fields case being measured by prestige rather than dollars.

One side note: using Abel/Wolf winners in the control group of contenders would seem to introduce some sort of selection bias, assuming that the Abel/Wolf prizes were won after the age of 40. I know that the authors try to filter out contenders that "produced their best work after their eligibility for the Fields Medal ended". However, it seems like they are not selecting people into the control group that, at age 40, might have been considered contenders for Abel/Wolf prizes, but due to lack of subsequent productivity, did not end up winning the prize. Including ex-post Abel/Wolf winners but excluding a priori Abel/Wolf contenders would seem to risk biasing the post-40 productivity of the control group upwards.

Prizes may well be a useful idea for people at that stage in life when there will be more prizes available next year - at school or university, say - so that nature's pot-hunters won't rest on their oars. After that, I suspect they're a dubious idea. But there are so few that carry any weight that I don't suppose it matters much - the Fields and Abel prizes, and the three serious Nobels, say. What you'd need to know to make any useful judgement is whether "The medalists begin to “play the field,” studying unfamiliar topics" results in any major, unexpected advances. Or does that habit tend to yield thin gruel, much as Einstein's later life did?

"The medalists begin to “play the field,” studying unfamiliar topics at the expense of writing papers"

So, freed from the publish-or-perish treadmill, medalists choose more interdisciplinary lines of research?

Also in the article:
"It is important to emphasize that the decline in productivity resulting from the wealth effect that increases leisure is conceptually different from the decline induced by the increased experimentation. Although the cognitive mover publishes fewer papers, those papers may provide a social benefit. The medalist is applying his talents to unfamiliar questions, and may generate important insights in areas that were previously under-served by exceptional mathematical talent. In fact, among the great architects of late twentieth century mathematics in our sample, there are three well-known examples in which a Fields medalist who made extraordinary contributions to a specific area of pure mathematics went on to mathematize a distant applied subject later in their career."

At a humbler level, I once knew a young pure mathematician who got a big promotion at an early age. His response was give up pure maths and start working with medical and biological researchers on the mathematical problems they faced.

In economics, the prestigious John Bates Clark medal is both a highly desired prize and a non-terminal honor, since the Nobel (yeah, yeah, quasi-Nobel) is still a higher prize. Does the Clark prize reduce future productivity, or is it the terminal nature of the prize? The second question is whether the top mathematicians would collectively produce fewer papers if the Fields Medal didn't exist. Many top producers might slow down if it wasn't for the allure of gaining the Fields. So even if the winner slows down post award, the discipline itself may have a net gain.

Doran ad Borjas probably would be studying this question about the effect of the John Bates Clark award if they have the data. They may have it (I'm not sure), but I know that the math citation dataset they do have was a non-trivial data collection enterprise to acquire, and I suspect if they aren't studying the economists, it's got to do with something like that.

Regression to true (super-high) talent is a thing.

Interestingly, this contradicts Richard Hamming's claim in You And Your Research that winning a Nobel kills future productivity by making them feel like they have to play the role of the Great Work guy in their field and prevents them from playing around with unfamiliar ideas.

"When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go...

Some things you could do are the following. Somewhere around every seven years make a significant, if not complete, shift in your field. Thus, I shifted from numerical analysis, to hardware, to software, and so on, periodically, because you tend to use up your ideas. When you go to a new field, you have to start over as a baby. You are no longer the big mukity muk and you can start back there and you can start planting those acorns which will become the giant oaks."

"studying unfamiliar topics at the expense of writing papers."

It makes it sound like a crime. "Playing video games all day instead of studying......"

But is it the effect if the fields medal or a sense of mission accomplished? Once you reach your lifetime goal, why not indeed explore and dabble?

I bet winning a race also has strong post-victory effects on the velocity of runners, as well.

Who cares about the effects on the very few winners -- in comparison to the effect of motivating many many researchers to work hard in oder to maybe win at some point?

Doesn't this discovery prove more that it is just luck in who wins the Fields Medal? In other words the winners were lucky in that the problems they set out to solve proved tractable to their approach, so they looked good to the award committee. It is extremely hard to evaluate the difficulty of someone else's problem solving. There could be more brilliant people that just were unlucky in the problems they chose in the early stages of their career. It is the old fund manager problem, how do you know if the fund manager is smart or just lucky?

Maybe we need a Medal for people within a field

Making significant contributions

Outside their Field.

My local high school's track team each year runs a devil-take-the-hindmost invitational race. Starting with the second lap, the trailing three runners are pulled from the race; the coach doing that is wearing devil horns and pokes them with his pitchfork. As the field dwindles down, two are pulled per lap, and then one at a time. The race ends when one runner is left. Anyone lapped by the leader is also pulled out, so it is undetermined how far the race will end up being. The winning girl managed to lap everyone last year and ended up running a 4-1/2 mile race. The winning boy couldn't build up a full lap lead over his competitors, so that race continued out to 6-1/2 miles.

Of course there is the infamous Grigori Perelman. Having turned down the Fields Medal in 2006 he went on to be awarded the million dollar Millenium Prize in 2010 for proving the Poincare conjecture. Of course, he also declined that award and the prize money. He subsequently decline the award of the European Mathematical Society.

I know nothing about math, but I always assumed the purpose of prizes like these (and others like the Nobel) was to reward past behavior (and therefore encourage more people to do the good work that turns them into prize contenders), not influence future behavior of the winners. The Nobel Peace Prize appears to have recently changed into an award that attempts to influence future behavior, and I think its clear that this has failed.

"But let me say why age seems to have the effect it does. In the first place if you do some good work you will find yourself on all kinds of committees and unable to do any more work. You may find yourself as I saw Brattain when he got a Nobel Prize. The day the prize was announced we all assembled in Arnold Auditorium; all three winners got up and made speeches. The third one, Brattain, practically with tears in his eyes, said, ``I know about this Nobel-Prize effect and I am not going to let it affect me; I am going to remain good old Walter Brattain.'' Well I said to myself, ``That is nice.'' But in a few weeks I saw it was affecting him. Now he could only work on great problems.

"When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go. So that is another reason why you find that when you get early recognition it seems to sterilize you. In fact I will give you my favorite quotation of many years. The Institute for Advanced Study in Princeton, in my opinion, has ruined more good scientists than any institution has created, judged by what they did before they came and judged by what they did after. Not that they weren't good afterwards, but they were superb before they got there and were only good afterwards.

"This brings up the subject, out of order perhaps, of working conditions. What most people think are the best working conditions, are not. Very clearly they are not because people are often most productive when working conditions are bad. One of the better times of the Cambridge Physical Laboratories was when they had practically shacks - they did some of the best physics ever."

No good deed goes unpunished with increasing committee work and administrative duties.

The title assumes that more published papers means more productive research. Is this really justifable?

Even if the productivity of the winners is reduced, perhaps the chance to win the prize causes everyone else to be a bit more productive.

I assume that a big prize is not to encourage the winners but also (and even more so) to encourage "the others".

Not to nitpick, but the Fields Medal is awards for achievement in Mathematics, not "Science"--the two are most certainly not coterminous.

Receiving it may indeed slow "output" in mathematical work for the recipient, but it is doubtful that it would slow the winner's "scientific output" whatsoever.

I wonder what percentage of these under-40 prize winners get married within a few years of winning? I suspect a Fields Medal could change a man from "geeky" to "strangely attractive" overnight.

"The medalists begin to “play the field,” studying unfamiliar topics at the expense of writing papers."

Perhaps "play the field" is meant literally? Maybe they begin "studying unfamiliar topics" such as the opposite sex?

Seems people don't know 1. Its a 15,000 CAD prize (hardly life changing), it must be awarded before recipient turns 40, and the paper evaluated 3 different criteria of 'productivity': number of papers, number of citations, and number of students (one wonders if they shouldn't have looked at number of citations of students' papers', also). They conclude that in all 3 measures, productivity was harmed by the Fields. I was too lazy to make sure they controlled for age, tenure, and salary. (My guess is they did not). They did take into account reversion to the mean. FWIW, the solution is obvious: Instead of announcing the winners, announce only the finalists - then give them 10 more years to compete.

15,000 CAD sounds a huge amount to me. The only prize in my career that I set out to win amounted to 280GBP. Mind you, in those days …..

Makes me wonder how many criteria they cycled through before they settled on these 3 criteria.

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