If you're a Tao or Feynman, chances are you have been doing "maths" intuitively since a very young age. All these moments add up and reinforce each other. Is that the same as being a genius? Maybe, but then we are dealing with definitions - in my mind genius is a myth created by society to explain "unexplainable" things. That and an excuse for people's relative incompetence - see Hamming in his article "You and Your Research" .
The science of experts and deliberate practise [1, 2] is actually quite solid, despite its gladwellification. For example there have to my knowledge not been found a single person who defies the "logic of practise" - oft cited examples are Mozart and Woods, which are more of a myth making than based in any known facts (consider how both their fathers pushed them extremely hard with the right type of practise from a very early age).
Of course, there will always be variations (but these could in my opinion just as well be ascribed to right-time-right-place mechanisms). I suspect a large "problem" is - if the next 11 year old Tao has already had thousands of hours of something akin to deliberate practise, how on earth are other people - who don't share this natural inclination - going to catch up?
0: From http://www.cs.virginia.edu/~robins/YouAndYourResearch.html
Now for the matter of drive. You observe that most great scientists have tremendous drive. I worked for ten years with John Tukey at Bell Labs. He had tremendous drive. One day about three or four years after I joined, I discovered that John Tukey was slightly younger than I was. John was a genius and I clearly was not. Well I went storming into Bode's office and said, ``How can anybody my age know as much as John Tukey does?'' He leaned back in his chair, put his hands behind his head, grinned slightly, and said, ``You would be surprised Hamming, how much you would know if you worked as hard as he did that many years.'' I simply slunk out of the office!
What Bode was saying was this: ``Knowledge and productivity are like compound interest.'' Given two people of approximately the same ability and one person who works ten percent more than the other, the latter will more than twice outproduce the former. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity - it is very much like compound interest. I don't want to give you a rate, but it is a very high rate. Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime. I took Bode's remark to heart; I spent a good deal more of my time for some years trying to work a bit harder and I found, in fact, I could get more work done. I don't like to say it in front of my wife, but I did sort of neglect her sometimes; I needed to study. You have to neglect things if you intend to get what you want done. There's no question about this.
On this matter of drive Edison says, ``Genius is 99% perspiration and 1% inspiration.'' He may have been exaggerating, but the idea is that solid work, steadily applied, gets you surprisingly far. The steady application of effort with a little bit more work, intelligently applied is what does it. That's the trouble; drive, misapplied, doesn't get you anywhere. I've often wondered why so many of my good friends at Bell Labs who worked as hard or harder than I did, didn't have so much to show for it. The misapplication of effort is a very serious matter. Just hard work is not enough - it must be applied sensibly.