It seems that perfect memory or the ability for absolute recall plays a very large part.I mean in calculus you have to figure out the best way to transform/beat the equations into a desired shape, so someone who has every rule, every trig identity, all the tables of integrals perfectly stored in his head will be miles ahead of anyone else.I mean I frequently have to go back, because I forgot that I can easily replace *something* with *something else* in order to get *easy to solve equation*
How did all of these matehmatician prodigies develop these skills at young age?
Most math "prodigies" are children with a genetic predisposition and opportunity to engage in math at young age. Higher level and order math, which involves both realms of the brain (creative and analytic) are more rare gift. Most of these prodigies grow up to be intelligent adults but rarely do they grow up to what we would call math "genius". Of course there are cases of such, such a Srinivasa Ramanujan.. but someone like that comes about once every century or so.
Given the population growth of the world, there are probably more math "prodigies" then there ever has been in human history, but given that there isn't any appropriate increase in math "genius", probably because they are population independent.
It seems that perfect memory or the ability for absolute recall plays a very large part.I mean in calculus you have to figure out the best way to transform/beat the equations into a desired shape, so someone who has every rule, every trig identity, all the tables of integrals perfectly stored in his head will be miles ahead of anyone else.I mean I frequently have to go back, because I forgot that I can easily replace *something* with *something else* in order to get *easy to solve equation*
Meh. When you have access to reference materials this is a lot less of an edge. Good memory will always be a help compared with poorer memory, but you don't need perfect recall by any stretch of the imagination. I mean, you can memorize all of that stuff whether you have a photographic memory or not. Being able to recall all of the material on a page to get one trig identity you need is way less important than the conceptual ability to recognize that a given transformation would help and is valid and then look up the rule or proof you need.
Perfect memory is dramatic and anyone who has it will have some advantages but I don't think it's a make-or-break factor for genius, mathematical or otherwise.
You can call it utopian dreaming, but I am of the opinion that personal interest is orders of magnitude more important than genetic predisposition. I think that if you can pique a child's interest (and hold it), you can teach them anything. That is why many American teenagers will run every day until dark (and until they vomit) just so they can play sports and perform better than their competitors. It holds their interest more than the 20-minute calculus homework they will skip out on. What if kids' interests were captured to the point where they would invest the same passion into their education, borrowing advanced textbooks to study on their own not because of job opportunities or grades, but simply because learning is utterly fascinating? I think these "child prodigies" are nothing special, they just have an interest in things that are useful, important, and relevant to the real world.
Those were examples. I doubt she would actually care to learn C++, but she would be exposed to it. The main point is that in contrast with parents who specifically prevent exposure, she would be exposed to quite a great deal of things and encouraged to explore anything that interests her.I would expose my kid to many stuff, but I wouldn't force her, that's for sure. So I couldn't say things like "she would learn C++, piano, at least 2 languages, and chess starting from a very young age (starting at birth for languages and no later than 5 for the rest)" because it sounds planned, and that's ridiculous if you force that plan on a kid.
L. Spiro
Those were examples. I doubt she would actually care to learn C++, but she would be exposed to it. The main point is that in contrast with parents who specifically prevent exposure, she would be exposed to quite a great deal of things and encouraged to explore anything that interests her.I would expose my kid to many stuff, but I wouldn't force her, that's for sure. So I couldn't say things like "she would learn C++, piano, at least 2 languages, and chess starting from a very young age (starting at birth for languages and no later than 5 for the rest)" because it sounds planned, and that's ridiculous if you force that plan on a kid.
L. Spiro
I see and I agree.
While we are on the topic...
http://news.harvard.edu/gazette/story/2013/10/harvard-professor-wins-nobel-in-chemistry/
"When Karplus was a boy, he recalled, his older brother got a chemistry set. He had wanted one too but got a microscope instead, because his parents didn’t want both boys perhaps setting off small explosions. (“The feeling was that two chemistry sets in the family would be too much,” he explained.) Disappointed at first, he discovered rotifers and watched their rotor-headed gyrations for hours in the microscope, which opened his eyes to the wonders of science."
"While an undergraduate, Karplus also worked with George Wald, performing calculations for him in the vision experiments that by 1967 led to Wald’s share of the Nobel Prize in Medicine or Physiology."
This shows that for some kids, it really came from within. First, he could have asked for different toys. Second, even having getting something else, he can choose to be bored and do other normal kid stuff. But he still doing the same thing at the age of 83.
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