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This is something I’ve always wondered about. It seems individual differences in innate capacity explains a lot when it comes to math ability, but don’t young m

This is something I’ve always wondered about. It seems individual differences in innate capacity explains a lot when it comes to math ability, but don’t young math prodigies also need to do the brute force time consuming stuff too? Does it take them as many practice problems to learn to differentiate polynomials or are they able to skip over much of the drudgery somehow? If so, how? There are many concepts which require exposure and practice in order to master, so how can one speed up that part as some children seem able to do. In music I’ve heard the answer is that no, you can’t speed it up, you have to do the practice. But then how to explain the Mozarts of the world who somehow seem to have, innately, the knowledge that for others requires training and time?

Jensson 4y ago
> Does it take them as many practice problems to learn to differentiate polynomials or are they able to skip over much of the drudgery somehow? If so, how? Why would it take everyone the same amount? It isn't like there is a natural law that you need to drill the same problem 20 times to understand it, why wouldn't someone's brain be able to process it and understand it after doing it the first time or even just looking at someone else doing it?
zozbot234 4y ago
> But then how to explain the Mozarts of the world who somehow seem to have, innately, the knowledge that for others requires training and time? Those kids didn't really start out with "innate" knowledge, or anything like that. They get intensive training starting at a very early age, that's how they do better than others. Also, practice is not necessarily boring. When you're actively learning/mastering a skill at close to optimum effectiveness, practice is quite enjoyable and it's easy to rack up a lot of it.
- 2devnull 4y ago
  I suspect that’s true, it sort of has to be, but then it seems to contradict various anecdotes. There’s a notion of the prodigy as a different type of person, a qualitative difference in kind rather than a difference in degree (of effort, iq, focus etc).

Jensson 4y ago

> Does it take them as many practice problems to learn to differentiate polynomials or are they able to skip over much of the drudgery somehow? If so, how? Why would it take everyone the same amount? It isn't like there is a natural law that you need to drill the same problem 20 times to understand it, why wouldn't someone's brain be able to process it and understand it after doing it the first time or even just looking at someone else doing it?

zozbot234 4y ago

> But then how to explain the Mozarts of the world who somehow seem to have, innately, the knowledge that for others requires training and time? Those kids didn't really start out with "innate" knowledge, or anything like that. They get intensive training starting at a very early age, that's how they do better than others. Also, practice is not necessarily boring. When you're actively learning/mastering a skill at close to optimum effectiveness, practice is quite enjoyable and it's easy to rack up a lot of it.

2devnull 4y ago
I suspect that’s true, it sort of has to be, but then it seems to contradict various anecdotes. There’s a notion of the prodigy as a different type of person, a qualitative difference in kind rather than a difference in degree (of effort, iq, focus etc).