A new paper challenges the conventional  that math is a young man’s game, and also finds that the U.S. share of the global production of mathematical articles has shrunk. They summarize their findings like this:

  • Contrarily to a widely held belief (among both scientists and lay people) the rate and quality of mathematical production does not decline rapidly with age. For mathematicians who remain scientifically active, productivity typically increases over the first 10 years, then remains almost constant until the end of their career. However there is a substantial attrition rate (i.e. mathematicians who stop publishing) at all ages.
  • There is a substantial variation over time of the geographical repartition of mathematical articles. For example although the U.S. are still by far the largest country in terms of mathematical production, their share has declined from 50% in 1984 to 34% in 2006. Similarly, the share of China is rapidly increasing but it is still surprisingly low (only 3.8% in 2006).
  • International mobility is rather weak, and it is much more symmetric than could be expected, both in terms of numbers of mathematicians and in terms of “quality” measured by the output of the mathematicians who change countries.

The study also looks at individual characteristics of mathematicians to determine what it takes to become a “good” one. They found that:

  • Size does matter: large departments are good for individual productivity. However this effect is largely due to good hirings and becomes very small when authors fixed effects are incorporated.
  • Having a specialized department has a negative impact on productivity when no fixed effect is used, but this impact becomes positive with fixed effects. This tends to indicate that a narrower scope lowers the quality of hiring, but that researchers fare better in a department with colleagues close to their mathematical interests.
  • Looking at US universities, we find several interesting results. First, money does not seem to matter: even if the endowment per student has a strong positive impact when authors fixed effect are not used, it has a non-significant negative impact when these fixed effects are incorporated. This negative effect is actually significant when taking into account the fact that the university is public or private.
  • Again for U.S. universities, the fact that a university is private has a small positive effect with respect to public ones. There is also a sizable positive effect of location on the east coast relative to the mid-west, the west coast standing in between the two.