Could you elaborate on the level for programs like these? I am familiar with a kid who was writing proofs regarding tensors (this is how it was described to me, my own math skills are extremely minimal in comparison) in the 5th grade. His father is worried about his social life going forward while wanting to nurture his talent. The kid was sent to the Johns Hopkins Center for Talented Youth for a summer which he apparently found really boring. I think he is actually being tutored by a professor at a local university now, but I wonder if he'd find peers of his own age group and ability level at these programs?
It sounds like his math skills might be slightly more advanced than the kids in these programs, but I would say that these programs are probably still worth a look for two reasons: (1) the kid may not similarly advanced in other subjects (it's not uncommon for kids to come in advanced in math but at the same level or lower for, say, English), and (2) even though the other kids are not as good at math, the kid you're familiar with may nevertheless get along with them better than they would with kids at a normal school.
