Are you sure about that? I know at least some number theory can help with quick mental calculations. For example, I remember that if the digits of a number add to 9 the number itself is divisible by 9. I'm sure there are lots of other relationships like that.
Personally, my first introduction into the more abstract mathematical concepts was a trigonometry class in high-school and later was fortunate enough to take more theoretical classes at university. It would be wonderful to introduce some of the more accessible, elegant concepts to kids at an earlier age.
https://www.quantamagazine.org/a-path-less-taken-to-the-peak...
However he took a course high in mathematical content and it sounds like he must have switched to mathematics for grad school, I.e. after his undergraduate or masters. In other words, he did the preparation. If it is anything like physics courses I have seen they feature a lot of mathematics courses anyway.
Some people have a lot of natural ability in mathematics but this is not enough to do good research. There's no way around hard work.
Also, dropping out of high school in many places significantly reduces your chances of going to university because you do the qualifications you need at the high school equivalent.
Yeah, you don't "happen into" a course on algebraic geometry. He must have dedicated a large amount of undergraduate courses to math, or demonstrated aptitude in another way.
Yes, in the United States, you can take a GED to graduate but that's usually reserved for adult high school students. I've never heard of it being used to skip high school and go straight to college admissions.
The closest parallel that I know of is Early Bird/Junior Admission. Essentially, one must first obtain all the credits required to graduate, and then as a high school junior apply to a college/university (although that only seems to be an available option for a few colleges) but it isn't exactly the same as what you're describing.