Earlier quoted context omitted.
Off topic I know, but what time is you talking about with "genius per capita"? I wonder how this have been measured.
So here are a couple of references. This one makes the assertion, but doesn't describe how it was derived. http://www.winwenger.com/socmeth3.htm However, this one does describe how probably such an estimate has been derived and used. http://scientific-child-prodigy.blogspot.com/2007/09/mysteri... And as an additional FYI. Some more modern related research. http://www.wired.com/2013/10/free-thinkers/
So it is absolutely not the case that everyone in golden age Athens was educated through the Socratic method. It seems to have been more of a fringe school. After all, Socrates was controversial enough to be executed for corrupting the young! If the satire in Aristophanes "The Clouds" represents the mainstream view, Socrates was considered kind of a nutcase.
In any case, the Socratic method might be useful for teaching critical thinking and philosophy, but it has pretty limited use for the natural science, since it doesn't help you to discover new facts about the world, only to think logically about the facts you already know.
The Socratic method will not help you decide if the earth is round or flat, and neither will it help you decide if evolution or creationism is the most correct theory. You need observations and experiments in addition to logic to discern that.