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Speaking of child prodigies--I've noticed something extremely odd about childhood ability in my own experiences. I got a 5 on the Calculus AB AP exam when I wa

Speaking of child prodigies--I've noticed something extremely odd about childhood ability in my own experiences. I got a 5 on the Calculus AB AP exam when I was ~10 years old and around the same time got a ~1490 (I don't remember exactly) on the SAT. 6 years later, I did no better on the SAT than I did when I was a preteen and I didn't feel as if I was any better at math than I had been 6 years earlier. Despite the fact that I had done so well at math as a child, I was never competitive in the higher-level math competitions like the AMC and AIME, where I consistently scored mediocre (~110 on the AMC, ~0-1 on the AIME). I went to school with plenty of classmates who scored near-perfect on both competitions and yet had not been nearly as much of a supposed "prodigy" as I was. Today, I doubt I am even above average at my college; I am relieved to have simply passed the math courses required for my major with barely-tolerable grades. And yet whenever I read stories of "real" prodigies, I never see anything like this--they always seem to continue their trend and prove to be brilliant mathematicians. Or is this selection bias? I still don't fully understand what happened. Does mathematical ability plateau at an early age? Is there something special about courses beyond basic calculus that are inherently more difficult? Did my skill simply stop developing because I lost interest?

nl 17y ago
" And yet whenever I read stories of "real" prodigies, I never see anything like this--they always seem to continue their trend and prove to be brilliant mathematicians." No, it's very, very rare that child prodigies go on to have significant impact in the field they were brilliant at as a child. See http://en.wikipedia.org/wiki/Study_of_Mathematically_Precocious_Youth http://en.wikipedia.org/wiki/Study_of_Mathematically_Precoci... for some details. (I read a very interesting article about Tao previously which addressed this - trying to find it now)
- nl 17y ago
  Hmm. Reading the papers from that study group seems to prove me 100% wrong. I suspect my selective referencing skills need improving.
  - sireat 17y ago
    Note: I read the abstract for the 35 year study and glanced over the paper. The researchers findings seem to be that these prodigies are for most part well adjusted/succesful, but do not necessarily go/stay into math/science fields. Are those the findings, or is there something more?
    - nl 17y ago
      They split the prodigies into science/math people and humanities people. I skim read the paper, and it showed a correlation between the field they were talented in and achievement in that field.
zackattack 17y ago
Your skill stopped developing because you lost interest. Courses beyond basic calculus are not inherently more difficult. They are only more intimidating, and perhaps require a little bit more study time, and spaced repetition. There are more rules, problem types, and proof techniques to remember. If you can do logic, you can do college-level advanced mathematics. Speaking from personal experience, everyone I went to grade school with who showed exceptional mathematical promise was bested by me in college. Indeed, one of my friends who was put in the "slow" math section is now a math major. Math is doable, and simply becomes something that you have to study for; you no longer get a freebie because you're smart.
- DarkShikari 17y ago
  Math is doable, and simply becomes something that you have to study for; you no longer get a freebie because you're smart. I found it was the exact reverse. Many concepts, in my experience, could not be learned well how hard I studied. And yet people who did significantly less work than I did found them extremely easy. One example is natural deduction proofs; I slogged my way through them with extreme difficulty while some friends of mine did them nearly effortlessly by comparison. Overall, at least my own experience suggests that studying and hard work can never fully replace innate ability.
  - kajecounterhack 17y ago
    I find that some concepts are slippery to some people, and others are slippery to others, but when you approach a slippery subject and an excellent teacher explains in the right way to you (or a bright peer), it becomes easier to understand. That combined with practice is good enough to fill you in and hard work does indeed compare with prodigy. I don't know if I believe in prodigies -- any piano prodigy I've known has played piano from a young age. Same with math. Practice is everything. Exercise your brain muscle and it gets bigger.
    - deleted 17y ago
      [deleted]
    - 17y ago
jacquesm 17y ago
Interesting. I absolutely suck at math, and I blame the computer. Here's why :) : When I was a kid I was good at 'arithmetic' in school (grade school, I really wouldn't call it math). Anything up to say raising stuff to arbitrary powers and doing lots of multiplications, long division up to fairly high numbers without pencil and paper. Then high school came along. In the first year I was probably the best of all the kids at math, it didn't cost me any effort either, trigonometry and so on was a breeze. I liked doing it, the teacher was great. Then in the second year of high school we got a fairly lousy teacher (sorry, it's the truth, especially when compared to the guy from the first year), and I got access to a computer. That changed everything. Computers were so much more fun than math yet somehow related that my interest in mathematics dropped like a stone and my interest in computers went through the roof. After that mathematics never managed to wrest my attention away from coding long enough to make it count. Even today I have an almost untouched calculus course sitting on my bookshelves that I've been planning to work my way through 'one of these days' for the last decade or so. Programming is just too much fun. I know I'd be a better programmer though, with more math under my belt, so maybe, one of these days...
jibiki 17y ago
There is a famous story about this: Wunderkind, by Carson McCullers. (You can find it online if you search around.)

nl 17y ago

" And yet whenever I read stories of "real" prodigies, I never see anything like this--they always seem to continue their trend and prove to be brilliant mathematicians." No, it's very, very rare that child prodigies go on to have significant impact in the field they were brilliant at as a child. See http://en.wikipedia.org/wiki/Study_of_Mathematically_Precocious_Youth http://en.wikipedia.org/wiki/Study_of_Mathematically_Precoci... for some details. (I read a very interesting article about Tao previously which addressed this - trying to find it now)

nl 17y ago
Hmm. Reading the papers from that study group seems to prove me 100% wrong. I suspect my selective referencing skills need improving.
- sireat 17y ago
  Note: I read the abstract for the 35 year study and glanced over the paper. The researchers findings seem to be that these prodigies are for most part well adjusted/succesful, but do not necessarily go/stay into math/science fields. Are those the findings, or is there something more?
  - nl 17y ago
    They split the prodigies into science/math people and humanities people. I skim read the paper, and it showed a correlation between the field they were talented in and achievement in that field.

zackattack 17y ago

Your skill stopped developing because you lost interest. Courses beyond basic calculus are not inherently more difficult. They are only more intimidating, and perhaps require a little bit more study time, and spaced repetition. There are more rules, problem types, and proof techniques to remember. If you can do logic, you can do college-level advanced mathematics. Speaking from personal experience, everyone I went to grade school with who showed exceptional mathematical promise was bested by me in college. Indeed, one of my friends who was put in the "slow" math section is now a math major. Math is doable, and simply becomes something that you have to study for; you no longer get a freebie because you're smart.

DarkShikari 17y ago
Math is doable, and simply becomes something that you have to study for; you no longer get a freebie because you're smart. I found it was the exact reverse. Many concepts, in my experience, could not be learned well how hard I studied. And yet people who did significantly less work than I did found them extremely easy. One example is natural deduction proofs; I slogged my way through them with extreme difficulty while some friends of mine did them nearly effortlessly by comparison. Overall, at least my own experience suggests that studying and hard work can never fully replace innate ability.
- kajecounterhack 17y ago
  I find that some concepts are slippery to some people, and others are slippery to others, but when you approach a slippery subject and an excellent teacher explains in the right way to you (or a bright peer), it becomes easier to understand. That combined with practice is good enough to fill you in and hard work does indeed compare with prodigy. I don't know if I believe in prodigies -- any piano prodigy I've known has played piano from a young age. Same with math. Practice is everything. Exercise your brain muscle and it gets bigger.
  - deleted 17y ago
    [deleted]
  - 17y ago

jacquesm 17y ago

Interesting. I absolutely suck at math, and I blame the computer. Here's why :) : When I was a kid I was good at 'arithmetic' in school (grade school, I really wouldn't call it math). Anything up to say raising stuff to arbitrary powers and doing lots of multiplications, long division up to fairly high numbers without pencil and paper. Then high school came along. In the first year I was probably the best of all the kids at math, it didn't cost me any effort either, trigonometry and so on was a breeze. I liked doing it, the teacher was great. Then in the second year of high school we got a fairly lousy teacher (sorry, it's the truth, especially when compared to the guy from the first year), and I got access to a computer. That changed everything. Computers were so much more fun than math yet somehow related that my interest in mathematics dropped like a stone and my interest in computers went through the roof. After that mathematics never managed to wrest my attention away from coding long enough to make it count. Even today I have an almost untouched calculus course sitting on my bookshelves that I've been planning to work my way through 'one of these days' for the last decade or so. Programming is just too much fun. I know I'd be a better programmer though, with more math under my belt, so maybe, one of these days...

jibiki 17y ago

There is a famous story about this: Wunderkind, by Carson McCullers. (You can find it online if you search around.)