Short version: the productivity for mathematicians seems to peak around late 20s or early 30s, with the productivity after the peak falling to less than one-quarter the maximum. However, the average quality of a contribution does not seem to vary with age, and exceptional researchers (in any field) tend to remain unusually profilic, as compared to an average researcher of the same age, even after passing their peaks.
Long version:
In the first place, the location of the
peak, as well as the magnitude of the postpeak decline, tends to
vary depending on the domain of creative achievement. At one
extreme, some fields are characterized by relatively early peaks,
usually around the early 30s or even late 20s in chronological
units, with somewhat steep descents thereafter, so that the output
rate becomes less than one-quarter the maximum. This agewise
pattern apparently holds for such endeavors as lyric poetry,
pure mathematics, and theoretical physics, for example (Adams,
1946; Dennis, 1966; Lehman, 1953a; Moulin, 1955; Roe,
1972b; Simonton, 1975a; Van Heeringen & Dijkwel, 1987). At
the contrary extreme, the typical trends in other endeavors may
display a leisurely rise to a comparatively late peak, in the late
40s or even 50s chronologically, with a minimal if not largely
absent drop-off afterward. This more elongated curve holds for
such domains as novel writing, history, philosophy, medicine,
and general scholarship, for instance (Adams, 1946; Richard A.
Davis, 1987; Dennis, 1966; Lehman, 1953a; Simonton, 1975a).
Of course, many disciplines exhibit age curves somewhat between
these two outer limits, with a maximum output rate
around chronological age 40 and a notable yet moderate decline
thereafter (see, e.g., Fulton & Trow, 1974; Hermann, 1988; Mc-
Dowell, 1982; Zhao & Jiang, 1986). Output in the last years
appears at about half the rate observed in the peak years. Productive
contributions in psychology, as an example, tend to
adopt this temporal pattern (Homer et al., 1986; Lehman,
1953b; Over, 1982a, 1982b; Zusne, 1976).
It must be stressed that these interdisciplinary contrasts do
not appear to be arbitrary but instead have been shown to be
invariant across different cultures and distinct historical periods
(Lehman, 1962). As a case in point, the gap between the
expected peaks for poets and prose authors has been found in
every major literary tradition throughout the world and for both
living and dead languages (Simonton, 1975a). Indeed, because
an earlier productive optimum means that a writer can die
younger without loss to his or her ultimate reputation, poets
exhibit a life expectancy, across the globe and through history,
about a half dozen years less than prose writers do (Simonton,
1975a). This cross-cultural and transhistorical invariance
strongly suggests that the age curves reflect underlying psychological
universals rather than arbitrary sociocultural determinants.
In other words, the age functions for productivity may
result from intrinsic information-processing requirements
rather than extrinsic pressures due to age stereotypes about
older contributors, a point that we shall return to in the theoretical
section (see also Bayer & Dutton, 1977).
[...]
Generally,
the top 10% of the most prolific elite can be credited with
around 50% of all contributions, whereas the bottom 50% of
the least productive workers can claim only 15% of the total
work, and the most productive contributor is usually about 100
times more prolific than the least (Dennis, 1954b, 1955; also see
Lotka, 1926; Price, 1963, chap. 2). Now from a purely logical
perspective, there are three distinct ways of achieving an impressive
lifetime output that enables a creator to dominate an
artistic or scientific enterprise. First, the individual may exhibit
exceptional precocity, beginning contributions at an uncommonly
early age. Second, the individual may attain a notable
lifetime total by producing until quite late in life, and thereby
display productive longevity. Third, the individual may boast
phenomenal output rates throughout a career, without regard
to the career’s onset and termination. These three components
are mathematically distinct and so may have almost any arbitrary
correlation whatsoever with each other, whether positive,
negative, or zero, without altering their respective contributions
to total productivity. In precise terms, it is clear that O = R(L -
P), where O is lifetime output, R is the mean rate of output
throughout the career, L is the age at which the career ended
(longevity), and P is the age at which the career began (precocity).
The correlations among these three variables may adopt a
wide range of arbitrary values without violating this identity.
For example, the difference L—P, which defines the length of a
career, may be more or less constant, mandating that lifetime
output results largely from the average output rate R, given that
those who begin earlier, end earlier, and those who begin later,
end later. Or output rates may be more or less constant, forcing
the final score to be a function solely of precocity and longevity,
either singly or in conjunction. In short, R, L, and P, or output
rate, longevity, and precocity, comprise largely orthogonal components
of O, the gauge of total contributions.
When we turn to actual empirical data, we can observe two
points. First, as might be expected, precocity, longevity, and
output rate are each strongly associated with final lifetime output,
that is, those who generate the most contributions at the
end of a career also tend to have begun their careers at earlier
ages, ended their careers at later ages, and produced at extraordinary
rates throughout their careers (e.g., Albert, 1975; Blackburn
et al., 1978; Bloom, 1963; Clemente, 1973; S. Cole, 1979;
Richard A. Davis, 1987; Dennis, 1954a, 1954b; Helson &
Crutchfield, 1970; Lehman, 1953a; Over, 1982a, 1982b;
Raskin, 1936; Roe, 1965, 1972a, 1972b; Segal, Busse, & Mansfield,
1980; R. J. Simon, 1974; Simonton, 1977c; Zhao & Jiang,
1986). Second, these three components are conspicuously
linked with each other: Those who are precocious also tend to
display longevity, and both precocity and longevity are positively
associated with high output rates per age unit (Blackburn
et al., 1978; Dennis, 1954a, 1954b, 1956b; Horner et al., 1986;
Lehman, 1953a, 1958; Lyons, 1968; Roe, 1952; Simonton,
1977c; Zuckerman, 1977). [...]
While specifying the associations among the three components
of lifetime output, we have seemingly neglected the expected
peak productive age. Those creators who make the most
contributions tend to start early, end late, and produce at above average
rates, but are the anticipated career peaks unchanged,
earlier, or later in comparison to what is seen for their less prolific colleagues? [...]
...and after posting that comment, I remembered that I had made an earlier post citing studies that said that it’s the middle-aged and not young scientists who are the most productive, which is in conflict with the results I just quoted. I feel silly now. I guess I should re-read the studies that I referenced three years ago to figure out what version is correct.
I guess I should re-read the studies that I referenced three years ago to figure out what version is correct.
Just to make the obvious point, your earlier post seems to draw on citations using mostly post-60s and later data, while that 1988 paper uses many citations from the 60s or earlier.
Simonton (1988) Age and Outstanding Achievement: What Do We Know After a Century of Research? Psychological Bulletin, Vol. 104, No. 2, 251-267.
Short version: the productivity for mathematicians seems to peak around late 20s or early 30s, with the productivity after the peak falling to less than one-quarter the maximum. However, the average quality of a contribution does not seem to vary with age, and exceptional researchers (in any field) tend to remain unusually profilic, as compared to an average researcher of the same age, even after passing their peaks.
Long version:
...and after posting that comment, I remembered that I had made an earlier post citing studies that said that it’s the middle-aged and not young scientists who are the most productive, which is in conflict with the results I just quoted. I feel silly now. I guess I should re-read the studies that I referenced three years ago to figure out what version is correct.
Just to make the obvious point, your earlier post seems to draw on citations using mostly post-60s and later data, while that 1988 paper uses many citations from the 60s or earlier.