I like the sentiment, but I have to disagree. I believe there is something genetically different about Grothendieck that makes him possess superior intelligence. I don’t think you can cultivate a bunch of Grothendiecks in mass by teaching a bunch of children advanced mathematics at a younger age.
Off subject but on Wikipedia Grothendieck says Riemann was his only main or most admired mathematician. Do their fields match up for this to make sense?
Grothendieck did a lot of work in areas that were built off of Riemann's work.
So, for example, Riemann came up with Riemann surfaces, which were the inspiration for Riemann manifolds. Finding ways to generalize that was a major starting point for algebraic geometry. Which Grothendieck did a lot of work in.
As an example, Grothendieck's first famous theorem in algebraic geometry was the https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E.... Which finds an appropriate generalization of a result originally due to Riemann in a much more limited context.
Side note. When the name Riemann appears on HN, it almost always is in reference to the Riemann hypothesis. Which is a conjecture in number theory. This might mislead you into thinking that Riemann was a number theorist. He was not. His total contribution to number theory was a single paper where he used his complex analysis techniques to prove the prime number theorem, and made his famous conjecture.
The only other context that most on HN will know the name from was the Riemann integral. Which is the main integral that most who take Calculus will know.
I think it is partially genetic, but also the type of environment that Grothendieck was raised in. He was raised in utmost uncertainty during WW2 (he was half-jewish), and i think he gravitated towards the certainty in mathematics. He was also mostly self taught early on, so he definitely had a different way of looking at things than those who came from regular academic backgrounds like serre. I like to think of natural brain power as hardware (genetics) and the set of beliefs, interests, fundamental ways of thinking about the world as software acquired through experience. Even the best hardware can't run shitty algorithms. In any creative fields, there are an extraordinary amount of brute force paths, it takes a special type of touch to find the correct path, and this seems to be very much a function of the life experiences a person had and this is really what differentiates special creative people like einstein or grothendieck from people who are just as intelligent but haven't done nearly as much.
