Ask cperciva: Are great mathematicians born or made?

Okay, I have been reading quite a bit about this whole nature vs nurture debate. But I want to hear it straight from the horse's mouth. Can people who are not inherently 'gifted', start with an immense interest in math at a mid-point in their life, and still go on to make meaningful and significant contributions to the field? In other words, is precocity a prerequisite to doing good work in Math? I'd be interested to hear from a Putnam fellow like you. Also, what are the rest of YC readers' thoughts on this?