You are exposed to the right sets of ideas at the right time and your brain through random chance happens to take a particularly fruitful paths to explore the ideas creating an exceptionally useful mental model. You have emotional preconditions that cause you to process this success in a helpful rather than a harmful way. This feeling of success and excitement causes you to spend more time daydreaming about the subject, slowing building a reservoir of powerful and useful mental patterns. Someone can daydream 10-16 hours a day for 14 years, but it is very hard to find someone that can study a subject they don't like for 8 hours a day for 5 years straight. I would argue that studying a subject is less likely to result in new ideas than day dreaming.
Due to having an environment to grow these ideas, not being run over by a car, having the money to pursue schooling, and exploring a field which is undergoing a revolution at the time you could up 'a genius'. Would anyone outside of Academic Physics know Feynman's name, if he entered Physics in 1995 when much of the low hanging fruit had already been harvested?
One could argue that Grothendieck is a counter example to this argument because he grew up in very harsh conditions that for the most part actively suppressed his learning. However I would claim Grothendieck for the luck and timing argument for four reasons:
First the trivial argument, if Grothendieck had starved to death while hiding from the Nazis as a child no one would name him as a genius.
Second, when he started college he was doing very poorly and he almost gave up, but he had mentors and an early success that enabled his later successes. What if he had gotten a cold that stopped him from that early success. It seems likely that given different friendships in college he would have dropped out and never been heard from.
Third, he was very interested in political movements and dedicated much of his life to it. However, he was not particular good at this. If he had an early success in a political tract he wrote, it likely would have led him into an area that he would not have succeeded in as much as Mathematics.
Fourth, French Mathematics at the time was undergoing a revolution because so many of the older Mathematicians had died in WW1 and WW2. This created opportunities for younger Mathematicians to rapidly advance their careers and these younger Mathematicans were critical to Grothendieck not being sidelined.
You are exposed to the right sets of ideas at the right time and your brain through random chance happens to take a particularly fruitful paths to explore the ideas creating an exceptionally useful mental model. You have emotional preconditions that cause you to process this success in a helpful rather than a harmful way. This feeling of success and excitement causes you to spend more time daydreaming about the subject, slowing building a reservoir of powerful and useful mental patterns. Someone can daydream 10-16 hours a day for 14 years, but it is very hard to find someone that can study a subject they don't like for 8 hours a day for 5 years straight. I would argue that studying a subject is less likely to result in new ideas than day dreaming.
Due to having an environment to grow these ideas, not being run over by a car, having the money to pursue schooling, and exploring a field which is undergoing a revolution at the time you could up 'a genius'. Would anyone outside of Academic Physics know Feynman's name, if he entered Physics in 1995 when much of the low hanging fruit had already been harvested?
One could argue that Grothendieck is a counter example to this argument because he grew up in very harsh conditions that for the most part actively suppressed his learning. However I would claim Grothendieck for the luck and timing argument for four reasons:
First the trivial argument, if Grothendieck had starved to death while hiding from the Nazis as a child no one would name him as a genius.
Second, when he started college he was doing very poorly and he almost gave up, but he had mentors and an early success that enabled his later successes. What if he had gotten a cold that stopped him from that early success. It seems likely that given different friendships in college he would have dropped out and never been heard from.
Third, he was very interested in political movements and dedicated much of his life to it. However, he was not particular good at this. If he had an early success in a political tract he wrote, it likely would have led him into an area that he would not have succeeded in as much as Mathematics.
Fourth, French Mathematics at the time was undergoing a revolution because so many of the older Mathematicians had died in WW1 and WW2. This created opportunities for younger Mathematicians to rapidly advance their careers and these younger Mathematicans were critical to Grothendieck not being sidelined.