A comment at this post from the Secret Blogging Seminar, signed "estraven", said that since the Fields Medal is awarded every four years, and only to people under 40, birthdate modulo 4 is relevant.
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.