[mbeex]

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]

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

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

[mbeex]

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]

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_E...

Not all Groupies die young, 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]

> 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]

> 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.