There's an easy explanation, if true -- assuming that people get something done in their late thirties, a 39-year-old is more likely to have done Fields-worthy work than a 36-year-old. It's our version of the effect that Malcolm Gladwell talked about in Outliers: The Story of Success
. There, he points out that the cutoff for most junior hockey leagues in Canada is January 1, and as a result players born earlier in the year are more likely to be selected for teams since they're older than their competition; thus they get better instruction and more practice, and as a result a surprisingly large proportion of players in the highest-level leagues are born early in the year. Something like two-thirds of players in the highest Canadian junior hockey leagues are born between January and April. (You wouldn't see this in the NHL, I suspect, because not all their players are from Canada.)But I don't feel like doing the research to determine if birthdate modulo 4 actually has an effect on Fields Medal winning. If you feel like it, I'd like to know the results.
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I think Fields Medals are awarded for work done before age 40, so it is possible to get one at age 43.
complexzeta: here's the page at the International Mathematical Union that describes the Fields Medal. I quote: "A candidate's 40th birthday must not occur before January 1st of the year of the Congress at which the Fields Medals are awarded."
There have been 48 Fields medalists. Nine were born in May.
The youngest (on January 1 of the award year) was Jean-Pierre Serre at 27.3; the oldest was Jean Bourgain at 39.84.
Twenty of the medalists were over 36, and so could not have gotten the medal next time. Their ages were: 36.44, 36.56, 36.59, 36.7, 37.01, 37.22, 37.28, 37.39, 37.53, 37.77, 38.09, 38.32, 38.35, 38.5, 38.73, 38.8, 38.85, 39.55, 39.7, 39.84. You be the judge, but that looks uniform enough to me (the average is 37.96).
Here are the other 18 ages, if you want to do any analysis: 27.3, 28.37, 28.7, 28.71, 30.37, 30.46, 30.86, 30.94, 31.43, 31.75, 31.79, 31.85, 32.18, 32.55, 32.75, 33.25, 33.27, 33.36, 34.12, 34.33, 34.7, 34.75, 34.83, 35.15, 35.17, 35.47, 35.58, 35.91.
The overall average is 34.77. The mod-4 average is 2.19. Twenty-nine (60%) were of age 2 to 4 mod 4. (The distribution mod 4 is 0:10, 1:9, 2:16, 3:13.) So maybe there's a small effect.
Michael, you work with a lot of distributions. What distribution would you expect for the ages, ignoring any of these mod-4 effects?
I don't see how the Fields Medal can be considered the top prize in mathematics when it imposes an age requirement.
Jack: do you know of any *more* prestigious awards in math?
I would consider the Abel price more prestigious. It gives more money and it is usually given to old people based on their full trajectory.
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