"I prefer math contests where any kid who can reach the library has a downtown tty good opportunity."

It's funny that you mentioned math, because I thought about it while reading the rest of your message.

In my university I know many (over a dozen) people who had their math degree (or most of it) done in high school/are in high school and are currently pursuing it. Virtually all of them (all but one) have a parent who's professionally into mathematics (most have parents who are PhDs or professors of math, another parent has a PhD in electrical engineering, etc.).