There is the long held notion that truly creative achievements, for example a great breakthrough in mathematics, can only be done by young people —- which for brevity let us call the *youth-only view*. The youth-only view is perhaps most famously expressed in Hardy’s *Apology of a Mathematician*, where he wrote, “No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man’s game.” In addition, the play *Proof*, which I enjoy very much, connects mathematics genius not only to the young age, but also to madness, agreeing and strengthening the perception of general public.
Out of curiosity I looked up Google Scholar a little, and there are both studies supporting and opposing the youth-only view. I do not plan to write a survey, nor spend more time settling this matter, but I shall share my guess, though quite without empirical evidence.
For concreteness let us focus on mathematics, but I believe the same can be said of other profession that requires immense creativity. Obviously mathematics requires concentration, memory, association, and they may have something to do with physical health too. Physical health usually declines gradually with age, for obviously reasons, but I do not think that it’s like that once you are past 40 you are doomed, unable to do anything significant ever like before. It is not a step function. Even if some calculation takes a 20 year old 1 hour, but takes a 60 years old 2 hours, the 60 year old can still do it albeit taking more time, once his or her mental faculty is intact. It is far from that elder people can’t do any decent research.
Second, it may be just that middle aged people have more obligations than young people have, and these distract them from doing research. Recall that, until change in social norm (indeed very recently), only men, not women, were allowed to pursue an academic career. Moreover, men were in general responsible for family income. They may be forced, then, to turn to something more profitable. This, too, may be somehow related to the impression that young people are more willing to consider harder problems by taking risks. Furthermore, full time professors may be occupied with administrative tasks and teaching responsibilities, making it more difficult to attack harder problems.
In short, this is my take on the youth-only view. The old age may somehow reduce creative productivity, but only quantitatively rather than qualitatively, and social and family obligations may be a distraction (if not restriction) too. What we should keep in mind, though, is that youthful vigor will not forever be with us, and time is precious and we should spend it wisely.
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