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Mathematical genius: extrapolate from your own experience?

The BBC biography series Great Lives covered in its most recent episode Srinivasa Ramanujan. In the closing minutes of the programme, host Matthew Paris said this, which I found quite interesting (or at least, interestingly expressed):

I’m so far from understanding the mind of a mathematical genius that it’s simply inconceivable that you could tell a person an apparently random number and he could intuit or deduce the kind of fact that he deduced about that taxi license number. I mean, I can’t run a four-minute mile, but I once ran a five-minute mile, and I can extrapolate from my own experience, in a way understand how someone might just be a lot better than me at something that, in an inferior way, I can also do. But Ramanujan isn’t like that. It’s as though this man were a different species, not just a superior example of the same species. Can you learn to do this kind of thing? Could I, if I had applied myself? Or is it that goddess again, is it really just genius?

Answers on a postcard!