There's a joke online about amateur mathematicians.
It basically tells the story of someone posting online, claiming that they spent decades creating an important mathematical theory, and then publishing their proof process on the internet.
As it turns out, a real mathematician took a look at it and told him on the forum that this theorem was actually proven by a mathematician over eighty years ago. Anyone who's studied mathematics in graduate school would know this theorem and just use the conclusion directly.
Whether this joke is true or not, it at least shows that these days, learning mathematics first requires a solid foundation.
This is why after discussions with Xue Song, Tian Yanzhen set a series of systematic courses for Qiao Yu to make his knowledge more structured. But when Tian Yanzhen discovered that after just one night of reading Peter Schultz's paper, Qiao Yu had his own ideas and insights, he abandoned this decision.
The reason is actually quite simple.