"What I fight against most in some sense, [when talking to the public,] is the kind of message, for example as put out by the film Good Will Hunting, that there is something you're born with and either you have it or you don't. That's really not the experience of mathematicians. We all find it difficult, it's not that we're any different from someone who struggles with maths problems in third grade. It's really the same process. We're just prepared to handle that struggle on a much larger scale and we've built up resistance to those setbacks."

I disagree. I understand the purpose of this statement, i.e. not to discourage people, etc. but clearly there are differences between Terry Tao, Wiles, Feynman, and many others and your typical PhD in these fields. This is like saying anyone can become Phelps with practice (although pinpointing his unique advantages can be complicated: https://www.scientificamerican.com/article/what-makes-michae...). Not everybody can be above average! And of course, there are the rare cases such as Ramanujan.

I think a better explanation is the one that Stephen gives in On Writing:

"I don’t believe writers can be made, either by circumstances or by selfwill (although I did believe those things once). The equipment comes with the original package. Yet it is by no means unusual equipment; I believe large numbers of people have at least some talent as writers and storytellers, and that those talents can be strengthened and sharpened."