I disagree with everything you say on multiple points.
Firstly, Mathematicians don't peak at an early age this is just one of the many nonsense Hardy spouted. And I say this as a non mathematician < 25 who just enjoys the history of science - I have no horses in that race.
There are many examples of people who not only contributed work at a late age > 30 (some near or over 40) but did so while being outside of the academic community - George Green, Faraday (physics) and Grassman. Then there are those such as Weirstrass who started late or those who produced an amazing work later, some in addition to earlier success e.g. Poisson, Bayes, Fourier or Hamilton whose quaternions came quite late. And then there were the Eulers who were just none stop greatness.
Nextly, although maths is a subject where some topics require very little background knowledge the vast majority of these low hanging fruit (knowledge wise) are gone. It was much easier to sketch out the core of an algebra while still in jail and have it be new and profound 200 years ago than it is today. As the amount of knowledge increases I expect the mean age of precocious contributions to increase. Knowledge and even experience will increasingly become a hard minimum.
Finally, you imply that only young people want to build things and have enthusiasm. I think an eagerness to learn and build great works is something you never lose. At least I hope so, otherwise growing old sounds like a very miserable prospect to me. And while the examples of old fellows not keeping up abound, I think this is simply a philosophical state that can be consciously guarded against.
Firstly, Mathematicians don't peak at an early age this is just one of the many nonsense Hardy spouted. And I say this as a non mathematician < 25 who just enjoys the history of science - I have no horses in that race.
There are many examples of people who not only contributed work at a late age > 30 (some near or over 40) but did so while being outside of the academic community - George Green, Faraday (physics) and Grassman. Then there are those such as Weirstrass who started late or those who produced an amazing work later, some in addition to earlier success e.g. Poisson, Bayes, Fourier or Hamilton whose quaternions came quite late. And then there were the Eulers who were just none stop greatness.
Nextly, although maths is a subject where some topics require very little background knowledge the vast majority of these low hanging fruit (knowledge wise) are gone. It was much easier to sketch out the core of an algebra while still in jail and have it be new and profound 200 years ago than it is today. As the amount of knowledge increases I expect the mean age of precocious contributions to increase. Knowledge and even experience will increasingly become a hard minimum.
Finally, you imply that only young people want to build things and have enthusiasm. I think an eagerness to learn and build great works is something you never lose. At least I hope so, otherwise growing old sounds like a very miserable prospect to me. And while the examples of old fellows not keeping up abound, I think this is simply a philosophical state that can be consciously guarded against.