How "learnable" are mathematics?

[StandingOnTheMoon]

I once made the snarky comment to Layra in the ED Sci & Tech forum in reference to her mathematical ability: "So, are you Asian, South Asian, or Jewish?" (I may be paraphrasing)

Given that there is certainly SOME expectation from SOME people that (East) Asians, South Asians, and Jews will be better at mathematics than other demographic groups, and further given that large populations will approach a perfect bell curve of distribution of aptitudes, doesn't this imply that learning higher order mathematics and the like may not be entirely aptitude but cultural? Does anyone have any hard numbers on this? Certainly it's a little from column A, and a little from column B, but in what proportions?  

[Layra-chan]

Warning: unsupported speculation ahead:

I'm not sure if I can really give a cultural reason, as while Judea, South Asian and East Asia have similar attitudes towards education, Russia is still churning out a lot of good mathematicians, and it's only recently that we've stopped seeing Germany and France as the centers of the mathematical world.
I want to say that the reason Europeans aren't the stereotypical majority amongst mathematicians these days is that Judea, South Asia and East Asia are rising powers, although to say such of Judea is kind of misleading. Antisemitism is going down, since nobody wants to be Hitler anymore, and as such the Jews are able to start rising both socially and academically in ways that wasn't possible before. So, as peoples, Jews, South Asians and East Asians are finding new opportunities open to them.
On its own, this wouldn't be enough, but in all three cultures (or at least in most the cultures contained within the umbrella of those three groups) there is a link between scholasticism and social standing. Rabbis are expected to be intellectuals, East Asian imperial bureaucrats were expected to gain their standing through examinations, and the Vedas are full of mathematical structure. So it's ingrained into the cultures that by educating oneself, one can rise above one's birth (at least in some cases).
So when new educational opportunities arrived, Jews, East Asians and South Asians grabbed them.
While the West relaxes after the Cold War, turning to cultural recovery and expansion, making life better for itself, these three try to make themselves better equipped for life, just as they have tried to even when they didn't have the opportunities. It just so happens that the way to get to the top is well-suited for them, just as the US rose to the top when the way to rise was through industrial strength, which suited the US very well.

Of course, one could point out the long, rich history of Western mathematics. But scholars were not the ones in power in the West, and one did not become powerful via education and will. Rather, scholars were subsidized by those in power, clients of wealthy patrons. They existed to make the wealthy and powerful look good, and to teach the children of the rich and powerful. It was simply one job out of many, and not a particularly easy or well-paying one. So while Western mathematics is very well-developed, it is not the culturally standard method of getting to power, so children do not automatically reach for it and parents do not push for it. Now that the subsidy system is gone, there is no longer a real drive for academic esotery anymore.

I don't really have a good explanation of Russia. It's a rising power, but I don't know enough of its cultural history to say whether it has the education->power tradition.  

[Mecill]

I think that math can be learned by anyone, at any level, if they have a genuine interest and desire to learn it.  

[Layra-chan]

It can be learned, yes, but genuine desire and interest (as well as encouragement from family/teachers/etc) definitely seems to be more prevalent among certain groups. The question is why, since mathematics is in theory learnable by anyone with the inclination.  

[Theoretical Physicist]

There is no connection between Jewish and Chinese people naturally being good at math.

That being said, China and most other Asian countries are communist society's that pressure anybody with enough money to send their kid to school for 12 hours a day; and one of the major things they teach is mathematics. Although I can't give you a direct curriculum, mainly becuase it changes so much, I can tell you that children who are sent to these school begin learning algebra by at least age eight. They also hold a lot of competitions for math wizzes who can do extremely complex functions and math problems in their head. If they can pull off first place at these competitions, usually they are given a lot of money and sent to a good school; most of these being in the United States, or Europe.

Because most of the rich Asian people we run into where we live (assuming you are in the United States and Europe; and are white) were sent here becuase they were extremely good at math, the minority you run into in the United States is going to be good at math and other forms of academics. If you compare the education to all of Asia to that of the United States, it is much, much poorer; but the few rich people, or selected people, who live at school and practice 16 hours a day obviously will become much more academically inclined people than the people who are given more freedoms.

I might also add that Asia is notorious for enslaving their own kind and creating forced labor, with girls sold into bondage, and I might also add that the regular discipline in these schools is to beat the kids who do poorly.

So it's a bit more obvious to see that there is no connection between race and knowledge; just government and knowledge.

Also, Jewish people in particular are not more intelligent; but the Jewish religion in particular is extremely strict and usually the members are extremely devout. Being of Jewish descent does mean that a person is inherently more intelligent; but the Jewish religious people are notorious for being heavily involved in both Academic and religious studies. The strictness of the religion essentially forces people to study, and so if a person were to devote themselves to something in this religion they might become more devoted, and therefore excel better at whatever job their in. Also, more pressure is on in this society to become part of the academic "elite" than in most other society, these people also being pressured by their religion, and so they end up being more devoted, spending more time, and therefore being better at academic pursuits then a less motivated person.

This is generally why these stereotypes are created; although demographically, the race of all scientists seems to be just as varied as the demographics themselves.

I hope this clears things up.  

[Mecill]

Yeah, I agree with what you are saying, Theoretical Physicist. Both you and Layra make really good points...

Even in the US if you compare the midwest to the east coast and west coast, attitudes are different, though not nearly as much since there is all one government. But even on a short timescale, attitude can be influenced by the economic condition of a local area.

You mentioned a lot of negative influences in Asian cultures but I think there are also many positive influences in older traditions of art and literature, and scholasticism. My knowledge on this is limited but I have heard historically early China made some discoveries in science and math prior to western Europe and the middle east. Though there has been so much political turmoil in very recent history due to communism. Russia similarly had that, and I read an article where a professor suggested that studying math was an outlet for free expression under an anti-intellectual communist government.

Also, I have a couple friends who are the children of Asian immigrants and good at math and they went through school here from when they were very young. Their attitudes toward education are probably passed down from their parents.

Anyway, diversity is good since more cultures means different experiences and more ideas.  

[Layra-chan]

Communism doesn't explain Asian-Americans, though. Nor does it explain South Asia, which has never been communist.

Sure, China does some rather shady things when it comes to competitions, academic or otherwise, but even amongst East-Asian children born and raised in America, there seems to be a drive toward academics that isn't there in those descended from (Western) Europeans. It's not even just the children of recent immigrants, either. You can often trace back families as having lived here since before World War II, and the children of those are pushed toward academics. Also, there are a lot of people from Hong Kong and the surrounding area, which was run by the British until very recently.
Furthermore, although there are plenty of people who are sent here from China, there are plenty more who have fled here from China; and the children of these refugees do well in school.
And it's not just the Chinese, either. Children from South Korea, Japan, Taiwan, none of which are communist countries, all seem to rise above other ethnicities.

And what can you say about Indians? India has never been a communist nation; it hasn't been totalitarian enough to force children into education and it's never been rich enough to afford to. And again we have plenty of Indian-Americans, born to and raised by Indian-Americans, excelling at academics, so it can't be because of the Indian government.

Also, Judaism? Strict? You obviously haven't met many Jewish people. Sure, orthodox Judaism has a lot of rules, but there is a very broad spectrum of how closely Jews stay to the laws written in the Torah. I had to stop one of my Jewish friends from eating a ham and cheese sandwich on a Friday night (not because it was against the kosher laws, but because it was my sandwich).
There is indeed a connection between religion and education in Jewish culture, but I don't think it's nearly as sinister as you're making it out to be. The connection is that the rabbis are expected to be educated, and so the idea is that educated people are more likely to have religious authority.
This is mirrored entirely in East Asian cultures, although because of the elaborate bureaucratic system and the mostly secular nature of Confucianism, educated people were sucked into the government instead of becoming religious figures. Note that this was inverted under Mao; Mao hated the idea of education in the classical (and modern) sense and in fact purposefully destroyed the Chinese education system in 1966.

Finally, if people with freedom don't learn, well, I can't exactly say that's a good thing.  

[Morberticus]

I was watching a show on attitudes towards academic achievements (especially regarding mathematics) in various cultures in America and the UK, and Asia definitely stood out as far as encouragement and motivation is concerned. The narrator seemed to think Confucius was to blame.  

[Layra-chan]

Confucius was the main proponent of the idea that self-improvement hinged on study and contemplation, and of governance by the literati. More specifically, he believed in governance by the virtuous, and that virtue was in fact being able to perform one's duty in the governmental hierarchy. It's kind of circular.
Education, in terms of the classical texts and some lax forms of empiricism and introspection, would lead to virtue, in that the classical texts spoke of virtue and virtue was embodied in nature and in the self to varying extents, depending on the exact form of Confucianism being considered.
Virtue, in turn, would lead to good governance because people would tend to obey the virtuous and would actively oppose those without virtue. This loyalty is not based on promises or recompense or threats, but just on the notion that obeying the virtuous man makes one virtuous, and thus leads to happiness and harmony.

So we have dual incentives for education: virtue, and power. Of the Asian-Americans that I know, it's mostly about power, but the notion of virtue and self-improvement is still intertwined.  

[Mecill]

Layra-chan

Confucius was the main proponent of the idea that self-improvement hinged on study and contemplation, and of governance by the literati. More specifically, he believed in governance by the virtuous, and that virtue was in fact being able to perform one's duty in the governmental hierarchy. It's kind of circular.
Education, in terms of the classical texts and some lax forms of empiricism and introspection, would lead to virtue, in that the classical texts spoke of virtue and virtue was embodied in nature and in the self to varying extents, depending on the exact form of Confucianism being considered.
Virtue, in turn, would lead to good governance because people would tend to obey the virtuous and would actively oppose those without virtue. This loyalty is not based on promises or recompense or threats, but just on the notion that obeying the virtuous man makes one virtuous, and thus leads to happiness and harmony.

So we have dual incentives for education: virtue, and power. Of the Asian-Americans that I know, it's mostly about power, but the notion of virtue and self-improvement is still intertwined.

That certainly makes a good case for the ideology of Confucianism, and it doesn't mesh completely with modern American culture where the power holders in the government and business worlds aren't always the most educated. Education and ingenuity are still seen positively. It's just that most don't see a need to learn higher mathematics. Also, from a Christian background, virtue is not linked to education directly though it can be linked through a concept of responsibility.

I would say my main motivation to continue learning is my curiosity to understand how things work, along with my understanding of effective techniques of problem solving. I'm not sure where that fits in, culturally.  

[Jerba2]

The answer you're looking for is that Asian people simply compensate for their lack of understanding in liberal arts with lots of focus on math and science, because those subjects are universal. Language and history are tough for people who grew up with a completely different language and culture.  

[StandingOnTheMoon]

Perhaps over a certain threshold of mathematical ability, one can learn mathematics to the highest level. However, the speed at which you learn and understand will vary from individual to individual (I can't imagine I shall ever be at Layra/Vorpal's level, no matter how hard I try nor the skill of my teacher).

And Layra: DON'T EAT PORK!!! Pigs are very intelligent creatures!!!!  

[Layra-chan]

But bacon is delicious. How could I possibly give up bacon?

Also, one of my mathy friends a while ago speculated on the existence of a personal "abstraction limit", wherein a person finds a kind of mathematics too far removed from reality to be comprehensible. I'm pretty sure that logic/model theory is beyond my abstraction limit, and for certain subjects I'm just going through the motions without any real understanding of why what I'm doing works.

But this is a personal thing, without any apparent ties to ethnicity or culture.  

[Mecill]

StandingOnTheMoon

Perhaps over a certain threshold of mathematical ability, one can learn mathematics to the highest level. However, the speed at which you learn and understand will vary from individual to individual (I can't imagine I shall ever be at Layra/Vorpal's level, no matter how hard I try nor the skill of my teacher).

And Layra: DON'T EAT PORK!!! Pigs are very intelligent creatures!!!!

It is really my personal belief that a "threshold" of mathematical ability does not exist. It is true some people may learn faster than others (and they are really great to have around!) but people learn in different ways so it is possible for anyone to learn math if they want to, they just have to find the right way to learn it for them.  

[StandingOnTheMoon]

Layra-chan

But bacon is delicious. How could I possibly give up bacon?

Also, one of my mathy friends a while ago speculated on the existence of a personal "abstraction limit", wherein a person finds a kind of mathematics too far removed from reality to be comprehensible. I'm pretty sure that logic/model theory is beyond my abstraction limit, and for certain subjects I'm just going through the motions without any real understanding of why what I'm doing works.

But this is a personal thing, without any apparent ties to ethnicity or culture.

Hmmm...well, I can tell you my brain works in some VERY strange ways. Also, I may have some brain trauma which may interfere w/abstraction. Of course, this is a personal thing.

Also:



EDIT: hmmm...why is my image not appearing? And why is this thread acting like the Midgard Serpent?