[Math] Are there any serious investigations of whether “mathematicians do their best work when they’re young”

Question

There is no shortage of anecdotes and conjectures on both sides of this widespread belief, but good supporting data either way is harder to find. Can anyone provide any references for serious (preferably academic rather than journalistic) research that actually crunched the data and produced interesting conclusions about whether this bit of folklore is reality-based?

I put "mathematicians do their best work when they're young" in quotes because this is clearly not a well-posed question–it is only intended to be shorthand for any of a number of questions on this topic.

Historical studies (Évariste Galois, etc.) are OK, but studies on people born after, say, 1950, would be of greater interest and relevance.

Answer 1

These two studies arrive at what seems to be a more sensible conclusion:

Age and Scientific Performance, Stephen Cole (1976).

The long-standing belief that age is negatively associated with scientific productivity and creativity is shown to be based upon incorrect analysis of data. Analysis of data from a cross-section of academic scientists in six different fields indicates that age has a slight curvilinear relationship with both quality and quantity of scientific output. These results are supported by an analysis of a cohort of mathematicians who received their Ph.D.'s between 1947 and 1950. There was no decline in the quality of work produced by these mathematicians as they progressed through their careers.

Age and Achievement in Mathematics: A Case-Study in the Sociology of Science, Nancy Stern (1978).

The claim that younger mathematicians (whether for physiological or sociological reasons) are more apt to create important work is unsubstantiated... I have found no clear relationship between age and achievement in mathematics.

For anecdotes and "advice to aging mathematicians", I might recommend Mathematical menopause, or, a young man's game?, by Reuben Hersh (The Mathematical Intelligencer, 2001).

Until we find a consensus about which advances are "major," we can't refute Hardy's claim that no major advance has been made by a mathematician over 50. But his slogan, "Mathematics is a young man's game," is misleading, even harmful.