There is a selection bias - 'child prodigy discovers X' is a little more newsworthy than 'eccentric person discovers X after lifetime of mucking around'.

I expect that the average age is probably older than 30 [1]. But 35 year old scientists making discoveries about science doesn't make a very good story; neither does an entire field making slow steady progress. People like to have one genius to study.

Same as how history tends to remember heads of state, but all the actual work is often done by small, highly effective groups of people who nobody remembers (eg, parliaments - I can name a couple of European monarchs from the olden days, but nobody from the Dutch Republic or the East India Company leadership).

[1] http://www.openaccessweek.org/profiles/blogs/age-amp-science...

Isn't that the stereotype for mathematicians? Not so much about scientists and inventors, I think.

Newton and Einstein did their greatest work when pretty young. I am not sure about others.

What about Feynman or Leonardo Devinci?

Besides science and math build and progress slowly. Sometimes there's a new discovery and suddenly there's a whole explosion of progress. Think calculus or the even the computer. Which we're living in right now. But look at quantum mechanics and computing, that's been progressing for the last the century or so but it's progressing through continued and shared effort built upon previous generations work.

Plenty of mathematicians are older I'm sure. I know Wiles was 40ish when he proved Fermat's Last Theorem.