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I hate to sound like an old fogie here (I am almost 40) but one thing that occurs to me is that as we age our thinking changes and all the things you mention often develop over time. When you are 20 you are pretty much at the height of your mathematical abilities. This is fine for certain kinds of programming, but it is not really ideal for others. It ensures that algorithms primary and the domains in a real sense be…
> When you are 20 you are pretty much at the height of your mathematical abilities. Is that really true? There are many examples of people who came to mathematics late in life and did good things: http://mathoverflow.net/questions/3591/mathematicians-who-we... I think you only get better with time if you keep yourself sharp. What has changed for me is that I can't sit still and pound back Redbulls for six-hour coding…
It's almost certainly not true, at least among those that would be called mathematicians. This follows if for no other reason than the fact that it takes years to get up to speed with the forefront of any particular branch of mathematics, which is the prerequisite for testing out one's mathematical abilities (in the context of research). While you occasionally have a few teenage prodigies, most mathematicians won't get started on their career until much later.