In addition to everyone else's very useful comments: Finishing college at 13, representing your country in Math Olympiad are not typical feats of gifted children. They are typical feats of profoundly gifted children, usually with great interest in the thing they've succeeded at, and great support.

Very few schools genuinely cater to these kids. Most gifted schools or programs cater to much more frequently occurring gifted children. Your 1:50 or 1:100 kids, maybe your 1:1000 kids. Not your 1:10-50,000 kids. Those kids need super personalized pathways (and often don't get them, often to their detriment).

I have a friend who went to school with Terrance Tao, as he made his very unique path through education. She felt her child was not that gifted: "no Terrance Tao." To which a group of us would say : "Your yardstick is broken".

Your child does not need to be on track to graduate college at 13 in order to be better off in a gifted program at school, or a specialist gifted school. Whether that school fits your child, only you can know (and possibly not until they've been there a while).