Ask HN: Is programming a “young person's game”?

I've heard this being said about mathematics and we know that both programming and math are logic based and pretty much require the same thinking techniques and programming is derived from math. So, wouldn't it be true that it's a young man's game for programming too?

You only see top programmers who started as kids and probably won some Olympiads and programming competitions, and this continued in their 20s and maybe kept their skill up till 30s but that's about it. What do they do after that?

I'm 30 and missed my chance to be a kid prodigy in programming or math and clearly not happening now. Is there an area where you can be good at as you get older and what is the old man's game options as a programmer?