> everyone can, and should, try to improve their mathematical thinking — not necessarily to solve math problems, but as a general self-help technique

Agreed with the above. Almost everyone can probably expand their mathematical thinking abilities with deliberate practice.

> But I do not think this is innate, even though it often manifests in early childhood. Genius is not an essence. It’s a state. It’s a state that you build by doing a certain job.

Though his opinion on mathematical geniuses above, I somewhat disagree with. IMO everyone has a ceiling when it comes to math.