Henrik Karlsson read lots of biographies of geniuses and tried to sum up the things their childhoods had in common here. Some highlights:

At least two-thirds of my sample was home-educated (most commonly until about age 12), tutored by parents or governesses and tutors. The rest of my sample had been educated in schools (most commonly Jesuit schools).

As children, they were integrated with exceptional adults—and were taken seriously by them.

They had time to roam about and relied heavily on self-directed learning

A common theme in the biographies is that the area of study which would eventually give them fame came to them almost like a wild hallucination induced by overdosing on boredom. They would be overcome by an obsession arising from within.

They were heavily tutored 1-on-1

An important factor to acknowledge is that these children did not only receive an exceptional education; they were also exceptionally gifted.

There is lots of discussion of John Stuart Mill and John Von Neumann, who each had major contributions to economics:

When they were done, James Mill took his son’s notes and polished them into the book Elements of Political Economy. It was published the year John Stuart turned fifteen….

There is a moving scene in John Stuart Mill’s biography, when John Stuart is about to set out into the world and his father for the first time lets him know that his education had been . . . a bit particular. He would discover that others his age did not know as much as he did. But, his father said, he mustn’t feel proud about that. He’d just been lucky.

Let’s make more people lucky.

Other nice posts along similar lines are Erik Hoel’s “How Geniuses Used to Be Raised” (linked in Karlsson’s piece), and Scott Alexander’s review of Laszlo Polgar’s book “Raise a Genius” (about raising his 3 daughters to be chess grandmasters). Karlsson’s post, worth reading in full, is here.