The idea of intelligence has always made me leery. I have a little brother who placed second in a state competition (musical instrument) for kids who almost doubled him in age before his tenth birthday. People like to say he's a genius, but only my family knows the truth: two hours of piano a day, four on weekends, since before he was even in kindergarten. I don't really believe in intelligence.
"Polgár and her two older sisters, Grandmaster Susan and International Master Sofia, were part of an educational experiment carried out by their father László Polgár, in an attempt to prove that children could make exceptional achievements if trained in a specialist subject from a very early age.[11] "Geniuses are made, not born," was László's thesis. He and his wife Klára educated their three daughters at home, with chess as the specialist subject."
Which begs the question, when people are willing to commit their children to this kind of super-intensive training regimen at such an early age, why on Earth are they doing it for games or music and not something (if you will excuse a crass way of saying it) useful?
Imagine a physicist or mathematician or engineer tutored in their discipline from age five! And imagine if those were as common as the little kids one sees dutifully going to piano practice every afternoon. The world would look very different.
Quite a lot of physics and mathematics is less useful than playing the piano, since it is equally lacking in practical application and doesn't even give other people pleasure.
If only your family knows the truth, how do you know that the people twice his age that he beat didn't practice for four hours a day since they were in kindergarten?
Is a very good tennis player a genius? Some things simply can be trained and while extremely impressive, they have nothing to do with intelligence.
So far it does not appear to be possible to increase intelligence via training. You can increase some proxies for intelligence that way, for example memorization, or puzzle solving.
True intelligence is very hard to define, but I define it as the capacity to reason in a non-linear way. i.e. to reach a conclusion without any obvious steps that took you from a to b.
