>What's changed? For one thing, there's simply much more mathematics to learn than there was 100 years ago.
Also, our early education is excruciatingly slow. It would be interesting to follow the children who are allowed to skip through the system at their own pace and see if their period of mathematical creativity still begins later than before.
Does anyone have an example of a better education system? I remember being kept in line with the curriculum until the point I realised I could learn easier myself - has anyone experienced a "good" school? Where does one find such a place?
I don't know a better education system. However, one of my friends in the graduate Mathematics program at Wake Forest was 18 when I was an undergrad there. I don't think he went to special schools. Certain districts let children skip ahead; most make them sit in class, earn all-A's, and suffer boredom.
My friend is now 22 and close to finishing his PHD. He should start his period of productivity at a young age. I know anecdotes are not data, and maybe he is unusually bright for an unusually bright person. However, it is certainly possible for a Mathematically inclined person to start a career early in the modern era.
I have Hawkin's book "God Created the Integers". It's been awhile since I've read it, but I remember that more than a few of the famous mathematicians he profiled were tackling hard problems at a young age. They certainly weren't still taking Calculus I when they were 18.
That's a shame. I wonder why there is no innovation in the education system like there is in other industries? I mean, montessori is considered innovative and it's like 60 years old? Perhaps a chance for a hacker or two :)
Given how fast I have seen young people excel when given the right tuition, I suspect we haven't even begun to optimise human learning.
My stock answer is that public bureaucracies are bad at innovation. Perhaps there is some sort of supplement to school that a hacker could work on for children interested in topics either outside or more advanced than the curriculum.
Reforming the actual schools, though, is equivalent to reforming city hall.
Early education is slow for a tiny minority of people. You can't change the system to suit the most priviledged. That's a fast track towards creating a two-tier society.
If a child is so clever, he can read books himself and he can skip grades. But if a child is lagging behind, he requires help from others.
"If a child is so clever, he can read books himself and he can skip grades. But if a child is lagging behind, he requires help from others."
Part of the problem is that clever children are not allowed to skip grades at most schools. Reading extra material takes time that is often prioritized for homework(often dull for a bright student). Also how is the student supposed to know what books to read on a subject. It is here that a mentor would be very helpful.
I wasn't allowed to skip grades, so I read in other books in high school classes. Most of what I read was undirected and I studied without any conviction, because I was just passing the time. I developed a terrible work ethic that hinders me to this day because I was never challenged at a young age. Not that I would have become some mathematical prodigy but I'm certain I could have accomplished more by now if I had more encouragement early on.
Here's an illuminating anecdote about the attitude most teachers have towards students: One day I finished my reading assignment early in freshman physical science class. I put away the textbook(most high school science texts are terrible and this was no exception) and started to read something of my own, Einstein's book on Relativity for layperson. The teacher called me out for not doing my assignment. She didn't believe that I had finished, because no one could have read that fast. I don't actually read unusually fast, but I did finish the assignment. She demanded to know what I was reading and after I answered sent me to the principals office for, "reading a book unrelated to physics". The principal wasn't in his office but his secretary thought that the incident was hilarious.
A child who skips grades usually faces worse problems. Skipping a grade retards your social skills badly, and that's worse than not studying enough. It's not a good idea to put a child together with other children a year or a year and a half older than him.
There are millions of accomplished people in the world today. 98% of them went through a standard schooling experience, and then ended up accomplished. If you have a problem with your work ethic, don't blame the school system - it seemed to have worked for all those other succesful people.
There is something I realised - there is no point blaming anything in your past for any of your current problems. Because the moment you realise that there is a current problem, you can fix it, irrelevant of where it came from. If instead of fixing, you go casting blame, that is really your problem then.
There have been many times throughout history where children learned in mixed age groups, or teenagers learned from being in the company of adults. Homogenous age group classrooms are a modern invention.
We already have an n-tiered society, partly because not everybody has the same abilities and habits. Even if we were to redistribute all wealth equitably now, soon the same old inequality would reemerge.
The only real solution would be to hit every smart or talented person on the head with a hammer until they were equal with the dumbest person. Crippling the educational opportunities of smart kids is just a half-measure.
Nobody is attempting to create an equal society. The goal is to create a society where the less talented are not living in ghettos and robbing you when you drive by in your BMW.
Everybody should be helped to reach a certain level, otherwise you create a crime ridden society where some people live behind gated communities.
Wealth should never be distributed equally, and your attempting to say that I support that is a distortion of my words. Everyone has to have an equal opportunity, and a minimum of wealth so that he does not starve to death.
And I don't mean 'technically' an equal opportunity, but a real equal opportunity. You know, if I did not live in a country with a free education system, I'd probably be a mechanic or electrician right now. You can't take away my opportunity to be educated, and then say you are better off because you are smarter or more talented.
And speaking of talented - is beauty a talent? Is singing a talent? Is programming skill a talent? Who gets to decide who deserves to have this talent? Some random fluke of nature?
I'm talented in programming, but that sure as hell does not mean that I deserve a better life than some guy who is talented at nothing, but works and struggles every single day. Talent is the lottery, I got my share of this lottery, and some people just did not. I'm not going to spit on them and concentrate only on myself. I believe that every single person should have the opportunity to get further in life.
Hey, I'm as anarcho-syndicalist as the next hipster, but I read your original comment as saying schools need to focus on the lowest common denominator. I'm still kinda getting that vibe from this comment.
Grades are different from money. Yes, society needs to provide a basic standard of living for everyone--but we need to do that in the way that allows the median standard of living to rise as best as it's sustainably able to. Advances in everyone's standard of living don't come from those of us in the bottom 95%, they come from the very best and brightest when their environment challenges them and allows them maximum room for growth.
The incentive structure for many of the most influential people in today's society--lobbied legislators, option-cashing CEOs, income-cutoff-avoiding welfare recipients--is completely screwed. But you don't buy food and housing with grades, and inflating those by pulling down the smartest does nobody much good.
I don't see how creating a school system flexible enough to accommodate diverse abilities and interests would create an evil bias in society. What is so bad about letting parents choose the educational product that is best for their child? We already do this for college.
Interesting article, but it does not prove the assertion in the title.
Grigori Perelman was already exceptional in his teens.
If one does not get the basics(meaning calculus, linear, discrete math) down pat by 20, IMHO, one doesn't have much of a chance at serious math discoveries by later age.
It is by logic we prove, it is by intuition that we invent. — Henri Poincare
[to the tiny minority of fellow 40+ HWers] Intuition comes from being open to it, which comes from doing new things. I'm sure that as we get older, there is some decrease in mental flexibility and energy - but a big part of it is a choice to be less daring, less open.
By analogy: it seems inevitable that old age means loss of bone density. But a study gave some menopausal women weight training - yielding dramatic (50%) increase in bone density. Use it or lose it.
Also, our early education is excruciatingly slow. It would be interesting to follow the children who are allowed to skip through the system at their own pace and see if their period of mathematical creativity still begins later than before.