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G. H. Hardy wrote: "Mathematics is a young man's game." Of course, you can continue to be a mathematician later, but for top performance, especially in terms of

by mbeex 2y ago

G. H. Hardy wrote: "Mathematics is a young man's game." Of course, you can continue to be a mathematician later, but for top performance, especially in terms of novelty, you have to start early.

defrost 2y ago
Euler started strong early and peaked later During his Berlin years (1741–1766, aged 34-59), Euler was at the peak of his productivity. He wrote 380 works, 275 of which were published. ~ https://en.wikipedia.org/wiki/Leonhard_Euler https://en.wikipedia.org/wiki/Leonhard_Euler Admittedly some of that was playing a Swiss Charles Dodgson to 15 and 10 year old girls. ~ https://en.wikipedia.org/wiki/Letters_to_a_German_Princess https://en.wikipedia.org/wiki/Letters_to_a_German_Princess
- mbeex 2y ago
  Individual examples do not contradict the general statement. Galois was dead at an age when I wasn't even at university. Abel a bit later (so avoid groups if you want to have a long life), same with Ramanujan (which incidentally may be a factor in Hardy's comment). And so on, just as singular at the first glance. As a mathematician, however, I continue to argue Hardy's point, both for the present and for the past as a general and observable phenomenon. And the number of books as a measure of quality, really? I think that view is skewed by today's “publish and perish” environment (nothing against Euler).
  - defrost 2y ago
    There's no suggestion that Euler is anything but an individual example however it is explicitly stated that number of works was a measure of productivity not quality. If you want to split the difference on the age of mathenaticians I happened by chance to be in Adelaide in 1985 when this was snapped: https://en.wikipedia.org/wiki/Terence_Tao#/media/File:Paul_Erdos_with_Terence_Tao.jpg https://en.wikipedia.org/wiki/Terence_Tao#/media/File:Paul_E... Not all Groupies die young, https://mathematical-research-institute.sydney.edu.au/news/professor-john-cannon-fellow-australian-academy-science/ https://mathematical-research-institute.sydney.edu.au/news/p... is still grinding along having created and steadily expanded on a system from 1980 through to today that is still actively used to beat quantum cryptographic cipher candidates.
    - mbeex 2y ago
      > it is explicitly stated that number of works was a measure of productivity not quality. I have noticed that. But my entire posting, to which you replied, had the subtext of excellence - in this case, the comparison of professional basketball and mathematics. And in the latter at least, quality and originality plays first fiddle. In this respect, I would be reluctant to shift the discussion to other qualities such as “productivity”. For me, this is not the relevant measure in this context and, as I said, I also view it critically as a criterion for whatever. As for Tao, I knew the picture and the story. Yes, an old and a young one. So what? It's not countering my or Hardy's point. These are statements from experience about a whole profession.
      - defrost 2y ago
        > But my entire posting, to which you replied Do you assume that I accepted terms of discussion that you set? How odd. > had the subtext of excellence Is this a peak value or an integral? > In this respect, I would be reluctant to shift the discussion Goodo, you do you. Catch you later. Maybe.

by mbeex 2y ago

G. H. Hardy wrote: "Mathematics is a young man's game." Of course, you can continue to be a mathematician later, but for top performance, especially in terms of novelty, you have to start early.

defrost 2y ago

Euler started strong early and peaked later During his Berlin years (1741–1766, aged 34-59), Euler was at the peak of his productivity. He wrote 380 works, 275 of which were published. ~ https://en.wikipedia.org/wiki/Leonhard_Euler https://en.wikipedia.org/wiki/Leonhard_Euler Admittedly some of that was playing a Swiss Charles Dodgson to 15 and 10 year old girls. ~ https://en.wikipedia.org/wiki/Letters_to_a_German_Princess https://en.wikipedia.org/wiki/Letters_to_a_German_Princess

mbeex 2y ago
Individual examples do not contradict the general statement. Galois was dead at an age when I wasn't even at university. Abel a bit later (so avoid groups if you want to have a long life), same with Ramanujan (which incidentally may be a factor in Hardy's comment). And so on, just as singular at the first glance. As a mathematician, however, I continue to argue Hardy's point, both for the present and for the past as a general and observable phenomenon. And the number of books as a measure of quality, really? I think that view is skewed by today's “publish and perish” environment (nothing against Euler).
- defrost 2y ago
  There's no suggestion that Euler is anything but an individual example however it is explicitly stated that number of works was a measure of productivity not quality. If you want to split the difference on the age of mathenaticians I happened by chance to be in Adelaide in 1985 when this was snapped: https://en.wikipedia.org/wiki/Terence_Tao#/media/File:Paul_Erdos_with_Terence_Tao.jpg https://en.wikipedia.org/wiki/Terence_Tao#/media/File:Paul_E... Not all Groupies die young, https://mathematical-research-institute.sydney.edu.au/news/professor-john-cannon-fellow-australian-academy-science/ https://mathematical-research-institute.sydney.edu.au/news/p... is still grinding along having created and steadily expanded on a system from 1980 through to today that is still actively used to beat quantum cryptographic cipher candidates.
  - mbeex 2y ago
    > it is explicitly stated that number of works was a measure of productivity not quality. I have noticed that. But my entire posting, to which you replied, had the subtext of excellence - in this case, the comparison of professional basketball and mathematics. And in the latter at least, quality and originality plays first fiddle. In this respect, I would be reluctant to shift the discussion to other qualities such as “productivity”. For me, this is not the relevant measure in this context and, as I said, I also view it critically as a criterion for whatever. As for Tao, I knew the picture and the story. Yes, an old and a young one. So what? It's not countering my or Hardy's point. These are statements from experience about a whole profession.
    - defrost 2y ago
      > But my entire posting, to which you replied Do you assume that I accepted terms of discussion that you set? How odd. > had the subtext of excellence Is this a peak value or an integral? > In this respect, I would be reluctant to shift the discussion Goodo, you do you. Catch you later. Maybe.