Didn't know school starts so early where you live. In my country it starts at 5, or preferably 6.

I probably overreacted, too. It's hard to take care of a kid. My kid is only 3, but I know some "genius" kids started at age 4 (like Mozart, or Tiger Woods or the Polgar sisters). Nobody wants to talk about it, but my impression is that it is possible to train for special talent. I don't want to spoil my kid's childhood, though, so I only want to encourage such things if he enjoys them (and also I am not really qualified for teaching many things).

Also, I'd say that school is overrated...

By the time kids are three or four, they learn a large part of their native language. It's actually pretty complex - at least on par with algebra - but they learn it, because other people around it do that. Imagine the world richer in math, where young kids are immersed in it from young age...

The best I can say is ... apprently parents have quite a small influence on the kids adult success - genetics, peer groups, and I suspect luck have a bigger role than us.

I am not fully convinced. Parents try to influence peer groups (by choosing schools and neighborhoods), and no matter what role genetics play, you still want the best outcome the genes allow. Luck is of course a big factor.

I am not advocating "genius training" because I am not sure what it does to the kids. But if they enjoy it, why not.