Is it safe to say that anyone with a doctorate in math was probably a math prodigy when he/she was growing up?

My second grade teacher was convinced that I had a learning disability. Now I am in my third year at Yale, working on a PhD degree in mathematics (I’m into analytic number theory, if you are curious).

“Prodigy” describes neither me nor anyone that I know. I think that it is a word that is far too overused, abused, and misused. My experience tells me that (with possibly a few, singular exceptions that we don’t yet understand well enough to properly gauge) people don’t become experts in something by being innately good at it, but by putting in the 10,000 hours necessary to make the subject an inherent part of their make-up.

I have told this to students before—there is no shame in not studying higher math because you think your time would be better used elsewhere. But for the love of God, don’t quit just because you feel like you aren’t good enough.