This is a tangent, but since you mention the "good founders started [programming] at 13" meme, it's a little bit relevant ...

There is a rule of thumb that achieving exceptional mastery in any specific field requires 10,000 hours of practice. This seems to be true across fields, in classical musicians, chess players, sports players, scholars/academics etc... It's a lot easier to meet that standard if you start from childhood. Note that people who make this claim in the computing field are talking about hackers, not professional programmers in a general sense. It's very possible to become a productive programmer at any age.