These people went through the process I described above. I'm not saying you need a degree to do scientific work. I'm saying you need to do scientific work to achieve scientifically relevant results.

These aren't coming out of nowhere however. They are obviously being exposed to new material through their education and then extrapolating into some new tangent. These aren't epiphanies that just happen later in life unless you are working to understand these concepts. Not saying it can't be done, it just hasn't been done yet, and every generation builds upon the foundation of what came before it.

And this would be larger with better education.

Because it's not always about the "potential of the student" if there's no support or validation.

Finland didn't have a gifted program, you're not supposed to be better at anything than others. Except in sports, where it's the whole thing.

There were special programs for slow kids. But none for fast ones.

First grade teacher put me in an empty classroom to read by myself when everyone else was just learning what sounds different letters make.