Once upon a time I was good at math -- like, win state-wide competitions, get a scholarship good. It's sad that I can easily follow the path laid out here, but I am nowhere close to being able to lay out this course on my own.
Nobody can do this on their own. You don't get to do this by having a great aptitude for high school maths and then being exposed to one or two more concepts that just intuitively click - which is enough to be competitive at the level you describe, though not enough to make the US Olympiad team. You get the level of understanding necessary to create this blog post by already having worked through several textbooks an…
As an aside, I once worked with an IMO bronze medalist and a gold medalist. They were scary smart. And then there's the fact that I once got to talk with Erdős. I wish I had known to take that opportunity more seriously.