In my experience, qualitative arguments of the form above rarely change people's minds but a quantitative model will help.
The question asked is the causal network that contributes to mathematical genius and the distribution of contributing causal factors within the population -- P(genius | factors)
Various factors are clearly involved: P(genius | intelligence), P(genius | hard work), P(genius | self-confidence), and so on.
If we accept that those functions are probably not uniformly distributed and that some have a stronger impact than others, we can see that most arguments can be reduced to describing those functions or describing the distributions of those factors among the population.
Where most educated people's intuitions lead them astray is that the experience of segregation in higher education and employment has led them to vastly underestimate the actual variance in factors like intelligence, hard work and self-confidence among people.
Vanishingly few individual actually possess the right combination of factors required for mathematic genius.
The question asked is the causal network that contributes to mathematical genius and the distribution of contributing causal factors within the population -- P(genius | factors)
Various factors are clearly involved: P(genius | intelligence), P(genius | hard work), P(genius | self-confidence), and so on.
If we accept that those functions are probably not uniformly distributed and that some have a stronger impact than others, we can see that most arguments can be reduced to describing those functions or describing the distributions of those factors among the population.
Where most educated people's intuitions lead them astray is that the experience of segregation in higher education and employment has led them to vastly underestimate the actual variance in factors like intelligence, hard work and self-confidence among people.
Vanishingly few individual actually possess the right combination of factors required for mathematic genius.