Short answer: nurture, very early on, because children have a fantastic curiosity and ego-less stubborn determination.
Long answer: From my personal experience, a lot of what some claim to be 'nature' is actually very early-age 'nurture'. So it's not that children of academics are genetically smarter, it's that they are raised by people with whom dinner or a walk in the park ends up being as educational as a university lecture. On top of that, if you consider that knowledge is like money under compound interest, I think it's possible to explain people that seem smart beyond comprehension as just having gotten a good head start on learning.
Math is also a special case for two (related) reasons: (1) emotions, especially ego, has a lot to do with learning math, and (2) math is filled with "aha" moments, where one thing which seemed incomprehensible one moment is obvious the next. Little kids have an advantage related to both of these - they (hopefully) don't yet have an ego to build or protect when it comes to knowing things, and they take a lot more pleasure from the "aha" moments.
So to answer your question - I would say it's nurture, but the kind which is (most of the time) limited to very young ages. On the other hand, given the determination and stubbornness of a 5 year old facing a challenge, it's nothing you can't do at 40. But I worry that I don't quite have that determination at 22, and will only have less of it as I am starting to worrying about becoming financially secure, starting a family, etc.
I whole-heartedly agree with everything you wrote.
I competed in Math competitions while in high school but never made it to the IMO. My friends who went to the IMO were doubtlessly very smart, but they had something else: they had many years of training under their belts. I failed because I was an amateur, they succeeded because they trained like professional athletes.
To do Math, intelligence is required, but not sufficient. Tenacity, patience, stubborness, an obsession to figure things out, and the willingness to work very hard are also required. Prof. Terence Tao knows much more than I do on the subject and he explained things clearly:
When one is young, one does not mind feeling stupid. Understanding something in Mathematics takes a lot of time and effort. After a certain age, one does not want to feel that stupid anymore. That's why many great mathematicians did their best work before they were 30. It's more psychological than intellectual, I'd say.
When one is young, one does not mind feeling stupid. Understanding something in Mathematics takes a lot of time and effort. After a certain age, one does not want to feel that stupid anymore. That's why many great mathematicians did their best work before they were 30. It's more psychological than intellectual, I'd say.
That's right on the spot, and a much better way of saying it than I did when I talked about ego.
Long answer: From my personal experience, a lot of what some claim to be 'nature' is actually very early-age 'nurture'. So it's not that children of academics are genetically smarter, it's that they are raised by people with whom dinner or a walk in the park ends up being as educational as a university lecture. On top of that, if you consider that knowledge is like money under compound interest, I think it's possible to explain people that seem smart beyond comprehension as just having gotten a good head start on learning.
Math is also a special case for two (related) reasons: (1) emotions, especially ego, has a lot to do with learning math, and (2) math is filled with "aha" moments, where one thing which seemed incomprehensible one moment is obvious the next. Little kids have an advantage related to both of these - they (hopefully) don't yet have an ego to build or protect when it comes to knowing things, and they take a lot more pleasure from the "aha" moments.
So to answer your question - I would say it's nurture, but the kind which is (most of the time) limited to very young ages. On the other hand, given the determination and stubbornness of a 5 year old facing a challenge, it's nothing you can't do at 40. But I worry that I don't quite have that determination at 22, and will only have less of it as I am starting to worrying about becoming financially secure, starting a family, etc.