This analysis falls flat when you look into these people or think about how so many other "vons" were not as brilliant. Von Neumann's brilliance preceded formal education and any tutoring. His advanced math tutor noted that he was smarter than him from their first meeting!

Von Neumann was noted to be eidetic by 3. By 6 he could divide two 8-digit numbers immediately in his head. He picked up multiple languages by 7, long before his similarly-instructed cousins and brothers. By 8, he could do calculus. His precocity *inspired* hiring a tutor.

Absolutely tons of upper-bourgeois families in Budapest supplemented schooling with tutors, governesses, etc. But von Neumann—who had far from the best education among them—outmatched them with ease. Moreover, he had plenty of superhuman abilities!

For example, von Neumann could see specially-crafted coins from the RAND milling shop, at a distance, and tell you how much they weighed and their exact dimensions. No tutor, nor any governess, and certainly not any old high school can explain the facts of his life.

Similarly, Paul Erdős was brilliant before education But he was merely middle-class, lacking the Bernays/Weiss/Hilbert-style tutoring and private salon upbringing that *some* of the other geniuses of his time and place had But by age 3, he knew how many seconds he'd been alive

Erdős was doing nontrivial integer arithmetic and elementary number theory at ages 4-5. He independently discovered that if a | b and b | c then a | c, and he began inventing toy conjectures about prime factorizations *before starting schooling*.

The Budapest Martian milieu contained tons of elite men and a handful of actual geniuses, and their stories are highly dissimilar, and the explanations invoked to explain their brilliance do not hold up to scrutiny. Take László Rátz's tutoring story.

The Martian biographies are filled with stories of self-teaching, and parents recognizing brilliance and thus choosing to foster it. They're also filled with people receiving the same educations and just not becoming geniuses. There were many rich families, and few geniuses!