As a former (3-time) MathPath student, I have the feeling I've seen you before. I must admit that it's only a feeling.

I was there in 2004, 2005 and 2006.

As far as Grothendieck goes, I think he is simply channeling Buddhism's concept of beginner's mind.

I think that there's some overlap, but that's not all of it. The quotation is taken from a much larger document that he wrote. Maybe it's not realistic to expect people to be able to guess with so little context. Anyway, more will be forthcoming.

The main problem I have with your post is that none of it is math-specific; take out the "math" repetition, the few mentions of calculus etc., and it's simply a generic description of ability.

I've said very little about what mathematical ability is in this post, it's the first of a sequence and I'll write more about things specific to mathematical in my upcoming posts. However, I'm also not sure what you mean. A large fraction of the post is about the math SAT and cognitive abilities that are more relevant to math than they are to most other activities.