Sounds interesting, tell me more.

Personally, I would say that a truly talented programmer is simply someone who is very capable in mathematics and can produce a working and extendable program in a reasonable amount of time, that does something new and useful.

I would also say a criterion is that he really understands abstraction and how to get more from less. Ie think of how John Carmack creates abstraction which is just right for the problem (and in C at that). Or think about the metalinguistic paradigm in programming (or OOP used right, for that matter). Or how JQuery (and these days Coffeescript) makes client-side web code clean and accessible to everyone, without the previous Javascript hacks and DOM-spaghetti. An average programmer just plods along and hacks out a solution in a linear manner, a great programmer will traverse levels of abstraction to not only solve the problem but also shine a light at it from a superior perspective.