Big breakthroughs? Middle Age is where it most commonly happens.

Here’s the thing:
Counting brain cells isn’t ‘it’.
Nor is axion thickness.
Through a lifetime, you have an accumulation of knowledge and the increasing cross-talk improves lateral thinking as you age, allowing for novel solutions that would be unthinkable to an academically trained mind, or one that constrained by societal norms. In short, you’re busy trying to ‘please the boss’. One day, you see the boss in a different light.

http://www.livescience.com/16911-scientific-breakthroughs…

Average age of scientific breakthrough that leads to Nobel prize in science? Age 48.

Late 30s / early 40s are listed from another source for other types.
http://www.theatlantic.com/…/big-breakthroughs…/283858/

I saw another one for authors and their 40s, but I suspect that has more to do with making people connections.

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