To what extent is maths talent innate? My dad always talks vaguely about how 'only 20% (or some other small figure) of the population has the kind of brain equipped with the machinery to process [insert high-level mathematical process, e.g. sophisticated engineering technique or something of the like].' This also applies to people's struggles with probability (e.g. neglecting base rates), et cetera. I was wondering how much of math's talent is just there or not there from birth, vs capable to be learned. Thanks. 

In particular, is the majority of the population actually unequipped with the mental machinery (like, say, a frog) to process high-level (say, advanced high school and beyond) maths? Prediction: no.
Intelignece is a combination of nature and nurture, like most human attributes. The exact percentage is not possible to measure, at least with todays knowledge.

Extract from the article by Neill, J.T. (2004). "Nature vs Nurture in Intelligence" :


  In the overfocus on nature vs. nurture issues, the attempts to
  estimate the relative contribution rests on the somewhat naive notion
  that there is a constant, true value. In reality, "gene expression is
  environment dependent" and it impossible to obtain pure estimates of
  genetic vs. environmental contribution - one could not exist without
  the other.