In September 2018, Michael Atiyah, renowned mathematician and Fields Medal winner, claimed that he had simple proof of the Riemann Hypothesis. Atiyah said, in an interview with New Scientist, “Nobody believes any proof of the Riemann Hypothesis, let alone a proof by someone who’s 90. People say ‘we know mathematicians do all their best work before they’re 40’. I’m trying to show them that they’re wrong. That I can do something when I’m 90.”
I searched about him, and it was said on Math Overflow that he had published some crackpot papers, like a shortened proof of Feit-Thompson theorem and nonexistence of complex 6-sphere. (Although, to be honest, the first time I heard of Atiyah was the reference to the Atiyah-Singer index theorem in «Not Even Wrong» by Peter Woit.)
I saw the whole video, and I wasn’t prepared for this. This wasn’t only crackpot, but it verged on insanity. Atiyah talked for about an hour, but there was only one slide which was relatively substantial, and most of it didn’t make sense. The audience was silent when Atiyah finished talking and asked them whether they had questions.
Atiyah died in January 2019, 4 months after the speech, and he probably died thinking he had resolved a problem even greater than the index theorem.
There is the long held notion that truly substantial creation in mathematics can only be done by young people. This, for brevity, let us call the “juvenile thesis”. The view is most famously expressed in «Apology of a Mathematician» by Hardy, 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» (and its film adaptation), which I value highly, connects mathematics genius not only to the young age, but also to madness, strengthening the perception of the general public.
Out of curiosity I attempted to look up relevant studies supporting and opposing the “juvenile thesis”. It appears there are few decisive quantitative researches, and the question does look too broad to settle. I am not able to write a survey, but I can share my guess on possible underlying reasons.
Obviously mathematics requires concentration, memory, association, and more, and hence they definitely have something to do with physical health, which declines gradually with age. But the “juvenile thesis” seems to have mistaken quantity with quality. That is to say, people put it the way that once you are past 40 you are doomed, and you are never going to do any decent research ever. This is absurd: the journey of life isn’t a step function. If some calculation takes a 20-year-old 5 minutes, it might take a 60-year-old 15 minutes, but the 60-year-old can still do it, once his or her mental faculties are intact. The same, I believe, can be said of other creative professions.
Or it may just be that middle aged people have more obligations than young people have, and these distract them from their research. Until the recent change in social norm, only men, not women, were allowed to pursue an academic career. Without saying, female mathematicians like Sofya Kovalevskaya and Emmy Noether obviously underwent lots of pressure. (The reader may want to read ‹Too Much Happiness› by Alice Munro for Kovalevskaya’s story.) Moreover, men were thought to be responsible for family income. Male mathematicians who didn’t make progress in their research for some time, may be forced to turn to something more profitable. Therefore, both women and men in their middle age had been under immense social pressure that discouraged them from undertaking creative work without much compensation, like mathematics. This further agrees with the impression (as Hardy would have said) that young people are more willing to take risks by considering difficult fields of research. Furthermore, full time professors are sometimes occupied with administrative tasks and teaching, making it more daunting to attack tough problems.
So this is my take on the “juvenile thesis”. Old age may somehow reduce creativity, but only quantitatively rather than qualitatively. Social and family obligations too may be a distraction, if not a restriction. We should keep in mind, though, that youthful vigor won’t forever be with us, and every day should be spent wisely.
❧ March 14, 2019; rewritten July 9, 2021
References
❉ S Cole, ‹Age and Scientific Performance›. In «American Journal of Sociology», 1979
❉ R Crowell, ‹On Michael Atiyah and the Riemann Hypothesis›. In AMS blogs, 2008
❉ R Hersh, ‹Mathematical Menopause, or, a Young Man’s Game?›. In «The Mathematical Intelligencer», 2001
❉ N Stern, ‹Age and Achievement in Mathematics: A Case-Study in the Sociology of Science›. In «Social Studies of Science», 1978