[J.A.Sucker]

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Ok, that mathematics thing is something I read a while back. Let me ask you something though, since I know nothing about the state of modern mathematics. When I think of genius I don't just picture someone who solved a tough proof or made some kind of advancement that happens every few years. I mean someone who revolutionized some area of mathematics or science. Einstein, Newton, Descartes, Copernicus (helio-centric theory is believed to have been born in his 20s), Tesla, probably the guy who invented the wheel. All these guys had their big eureka moment in their 20s. Then many of them went on to postulate all kinds of wrong theories as they got older.

Are there any examples of people having the genesis of some idea that revolutionized their field while in their late 30s or beyond?

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I would suspect that most (if not all) people who have gotten the Nobel Prize in any experimental science over the past 40 years performed their initial work between the ages of 30-40.

Being intelligent is only one step into solving difficult problems. It's a start, but not necessary, either. What's more important is being able to connect between your varied experiences and what you have read/learned over the years to think about something in a new way. Maybe this is what intelligence is, but I think it's more like being CLEVER. No matter how smart you are, if you don't have experience, you can't draw from them. Also, going through the process of doing ANYTHING improves how you will approach another problem in the future. Great experimentalists have figured out how to plan, build, and flat-out do science - the ones that win the Nobel these days are the ones that figure out how to apply varied experiences to solve/invetigate established problems in a new way. These guys are almost never the pure whiz kids, BTW, contray to what many think.