The Stroke of Genius Strikes Later in Modern Life
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In fact, fundamental theoretical physics has been more-or-less stagnant since the late 60's when the Standard Model was finished. But they have to keep handing out Nobel prizes. So the outcome is predictable: you see prizes being awarded to people who are fleshing out ideas which have been known for a half century; the low-hanging fruit has already been picked, so you have to work for years in the nitty-gritty to push the bounds. Hence, the prize winners are old.
But this doesn't tell us anything about physicists and when they are capable of genius (and how could it? does anyone really think that human nature has changed?), it tells us about the stagnation of the field.
The really interesting question is this: is the stagnation of physics more attributable to (a) some combination of fundamental technological/intellectual limitations or (b) institutional/social pathologies in Academia. Most people say '(a)', but I (as a young physicist) worry that '(b)' plays a substantial role.
Kuhn would say that science consists of long periods of "normal science", in which people flesh out basic theories that have been known for decades, and short periods of "paradigm shifts", where previously ignored evidence is suddenly incorporated into brand-new, world-shifting theories that completely upend the old order. Just because you happen to be in one of those long doldrums of normal science doesn't mean that something is wrong with science, or that the field has stagnated. It just means you're not in a revolutionary paradigm-shifting phase.
Again, mere time is a bad metric for baseline progress.
Another way to put it is that big science is replacing science, and i think it is. (Feyerabend's perspectives, albeit very different from that, seem to point out many of the problems...)
For instance, the thing that corresponds to general relativity today is quantum gravity. Other paths exist, but the two that are most traveled are string theory and loop quantum gravity. The math involved in either one is considerably heavier than Einstein's relatively theory, and neither one is in a place where you can calculate real observable things.
There's plenty of (b) to go around, but it's hard to believe we'd know what dark matter is, discover supersymmetry, or have an established "theory of everything" if we cleared away the cobwebs.
In other words, the barrier to entry has been raised in science. Nobody is going to place a 25 year old Phd in charge of a major chemistry research laboratory these days.
On the other hand, in software development, the arts, and other creative fields with low barriers to entry, younger people continue to demonstrate genius regularly.
Point is we may not be able to solve the aging problem, however as we progress we our children will be smarter to grasp complex subjects in shorter time. How much short time? That will depend on the intellect of the child. When I was in 8th standard my father told me that if I can I should finish all the math books upto 12th standard in a year. It may not be a full proof knowledge but it will give me some vision about what the math world looks like. I tried and succeeded partially (No claims here just what happend in my life). It was wonderful to know the world of maths. So we need to expose our young minds to so called advance topics in the subject of their choice. We do not know who is a genius. Moreover, a genius will eventually find a way to solve a problem that he/she wants to solve. Why? My guess - because he/she is a genius(also we do not know how a human brain works now and how it will work in the future).
You need to accumulate more knowledge and do more work before the breakthrough. Meaning you have to start very early on your highly specialized journey.
Are there any recent (past 50 years or so) examples of someone doing great work in some field, but who started late (say age 25 or 30)?
Feynman formulated the path integral at age 30
"It may be that young scientists did better, in part, because they never learned the older ways of thinking and could think in new ways."
Replace 'scientists' with e.g. 'musicians', 'designers', 'developers', or your profession of choice.
I've recently turned 30 but realize there is no race to make it. Not for me anyway. Maybe I'm turning Zen about it but who really cares when you "succeed"? "The people that mind don't matter, and the people that matter don't mind."
By the way, Colonel Sanders (http://en.wikipedia.org/wiki/Colonel_Sanders) began franchising KFC at age...65