How much of mathematical intelligence genetic or environmental? It seems to be at least a fair amount genetic. After all, the brain is a body part like any other. Height is genetic, so why wouldn't physical brain characteristics also be?
It is remarkable the amount of asian and male students in this top echelon. It could be because of societal influence - but that really seems unlikely to me to cover this huge gap.
It may be unsavory, politically taboo, and not the way we want the world to be - but are males and people of asian-ancestry just better at math? And would knowing if that is the case help anything in any way?
With regards to top mathematicians being male, it's understood that the variance in male IQ is much greater than for females, so men end up over-represented in both the top and bottom tiers of intelligence.
But society factors do have an effect. In one study with asian american women asked to do a difficult math test, those primed to remember that they were asian did better than those primed reminded that they were female: http://pss.sagepub.com/content/10/1/80.abstract
I'm sorry about nitpicking, as I think your heart is in the right place, but I believe you're incorrect regarding the variance in male IQ vs female.
It is a conventionally believed thing, but I think it is conventionally misunderstood. The IQ tests don't even have validity well outside 2 s.d. (how could they without much more testing outside the sample?) It's not even a particularly valid statistical idea to be contemplating very high IQs beyond the normed values of the tests (how are they supposed to calibrate the scale?) nor is there good evidence that whatever the measures are that we're given are normally distributed. I have personally known several people with "measured IQs" above 200; that is statistically not supposed to happen. There are a lot of conceptual and practical problems with the idea of IQ.
Regarding mathematical ability, please see this paper by the former USA IMO coach Titu Andreescu.
They make a very good case for cultural specific factors in the development of mathematical skill, at least as far as Olympiad maths goes. The presence of women in the competition varies dramatically depending on the culture (and even the team)
> IQ tests don't even have validity well outside 2 s.d.
An easy way to measure above +2 z-scores is to administer an IQ test at a much earlier age than usual. That's what the famous Study of Mathematically Precocious Youth did. It has proven to be super effective even at the extreme right tail of the curve.
> I believe you're incorrect regarding the variance in male IQ vs female.
Belief doesn't enter into it. Many studies report higher male variance and it is widely known in the psychological community. While people try and attack this as a recruitment pattern problem (see [2]) or try to prove that it is partly cultural (see [3]), only people unfamiliar with the literature would outright deny it.
To be clear, I think that the stated belief that there is higher male variance is possibly true. I think it has a good chance of being false, but that's not the point. Statistically, for example, the male population has a greater chance of genetic disease and indeed lives shorter life; this is supposed to be in part because of the lack of two x-chromosomes, which, as a mosaic, both express themselves in the ordinary female body.
What's emphatically not true is assuming a normal distribution -- specifically out to the tails. It's not even clear that the variance doesn't turn around at some point to have higher female variance at the top end of the curve. It is extremely easy to synthesize violations of a normal distribution of ability for female subjects -- there seems to be a powerful threshold effect that, in addition to cutting out large numbers of young women in certain cultures in mathematical competition, tends to preferentially spare the very top. If things were normally distributed, of those women that compete in mathematics competitions, almost none would make it to the very top of the competition, mathematically. That has been proven empirically false.
Few scholars directly assert that the normal distribution is a perfect model for intelligence, but people seem to take the implications quite seriously.
An easy way to measure above +2 z-scores is to administer an IQ test at a much earlier age than usual.
Your graph shows that this study administered a SAT Math test at a much earlier age, not an IQ test.
The study itself says: "Before age 13, these participants scored within the top 0.01% for their age on either SAT mathematical reasoning ability (SAT-M 700) or SAT verbal reasoning ability."
I'm unconvinced that this shows either way if "IQ tests [don't] even have validity well outside 2 s.d"
Thanks for sharing data, that's a pretty good case for cultural factors making up a large part of the discrepancy, as I suspected.
As for the IQ test variability, do you have any papers or research on that? Citation 19 in this wikipedia article doesn't seem to actually address the issue of variance, only the question of absolute ability: https://en.wikipedia.org/wiki/Sex_differences_in_intelligenc...
If I just suggest a reference without a suggested change in "point of view" you're likely to get very confused.
May I recommend as a starting point:
Be skeptical about the idea of a single number characterizing intelligence. We don't even do that for the weather.
Next, learn about the genesis of the entire IQ concept, and later efforts to academically justify past ideas about intelligence. The first really popular writings were by Galton
Afterwards, Binet and Simon, and Terman (at Stanford, the Stanford in Stanford Binet) get at it.
Back then, IQ was really a "quotient," "mental age" divided by actual age. The concept only really makes sense in a developmental context -- after all, how are we supposed to believe that a "developmentally baseline" 23 year old is actually the pinnacle of intelligence?
Only after this did the Weschler Adult Intelligence scale come in. Read (some) of the criticisms Weschler had of the Stanford Binet here.
This was devised as a clinical scale. This is still one of the only widely administered and normed tests. The norming takes place only over a few thousand individuals. The types of abilities typical in an international IMO context are simply unlikely to show up in these cases, much less register statistically in the test!
and the mathematics behind what suggested it, "Factor Analysis," which has many capabilities but is worthy of many criticisms, including particularly that there is no obvious weigh to norm or weight any of the tests, so ultimately you end up with a judgement call for which tests to include, and how much to gather from their results.
A far more enlightening study of genius, I have found in the book "Human Accomplishment", by Charles Murray. When you're sample is all of those humans who have left a mark on history, and your measure is impact, and our remembrance of it, you learn far more about the heights of human capability, I believe, than by scoring how well people match patterns to a preconceived idea of the "right answer" on a test.
> Intelligence exists and is accurately measurable across racial, language, and national boundaries.
> Intelligence is one of, if not the most, important factors correlated to economic, social, and overall success in the United States, and its importance is increasing.
> Intelligence is largely (40% to 80%) heritable.
> No one has so far been able to manipulate IQ to a significant degree through changes in environmental factors—except for child adoption—and in the light of these failures, future successful manipulations are unlikely.
> The United States has been in denial of these facts. A better public understanding of the nature of intelligence and its social correlates is necessary to guide future policy decisions.
And who then went on to argue in Human Accomplishment that the most important humans were European males based on a biased application of Pagerank on modern encyclopedias written in English?
This is the response to the reply above; I'm unable to directly respond to a comment that deep.
I thought similar things about Charles Murray, and I don't think that the Human Accomplishment book is without flaws -- it has many. Nonetheless, the whole book is worth reading. Honestly, I think it faces some serious facts on the distribution of impact on civilization.
The fact that some cultures, like classical Athens and Elizabethan and Enlightenment England, have had an outsized impact on modern science and civilization, that we have a massive debt to particular thinkers from Europe of the past few centuries, is a fact I think a serious study of great scientists needs to come to terms with. That being said, past contribution is not a good indicator of genetic, racial superiority! We should do well to ask what made those contributions possible, from nurturance, to growth, to self belief, and belief in the idea of progress.
Just FYI the lack of comment button is based on time, and is meant to prevent deep threads that become flamewars, or devolve into arguing over semantics.
> nurturance, to growth, to self belief, and belief in the idea of progress.
I'd also guess: encouraging risk taking; valuing radical ideas, or at least individualism; and a safe environment, or at least a sufficient military.
I'll take a shot at this (your bait). For context have an undergrad in Math, my parents are mathematicians and theoretical computer scientist. Read quite a few biographies on famous mathematicians, and one salient inescapable conclusion is that the most prominent mathematicians tend to be European or American, and very rarely Asian (chinese, Korea or Japan). There are of course exceptions, but few. The top mathematicians are not Asian, just a fact. And yet, the majority of IMO gold winners are, not sure how to explain the discrepancy, but the most likely conclusion is that solving Olympiad math questions has very little correlation with with doing creative mathematics.
> The top mathematicians are not Asian, just a fact
Alright I'll bite as well. Though I don't think the OP's conclusion is correct, I also don't think the lack of prominent asian mathematicians is entirely indicative of ability or creativity, but rather largely caused by the availability bias of English speakers and our current vantage point in history.
First: availability bias. We're reading English books and working within an education system born out of Europe. Asian history has been full of interesting wars, rulers, artists, politics, etc for thousands of years, but few in America will ever learn anything except for where it relates to America / Europe. Much of the information about Asian history will be in another language as well.
Second: Recent history. Knowledge-creators in other countries are playing a game they are disadvantaged in, having to first learn English, then travel abroad for the best universities, etc. (Imagine if you had to learn Japanese and travel to Japan to go to get a decent higher education!)
The reason of course is that 1500s and onwards (post-renaissance), most of the knowledge generation was happening in Europe. But that wasn't always the case: if we look a thousand years prior, or 2 thousand years prior, knowledge was being generated by Greek, Arab, or Chinese mathematicians. For instance, the concept of 0 arrived to Europe pretty late: http://www.livescience.com/27853-who-invented-zero.html
So circling back to the original question of the importance of genetics vs environment:
That the world's patches of knowledge has shifted across different cultures, peoples, and places over the last maybe 8 thousand years to me doesn't imply such a large importance on inherent genetic ability, and that time frame is too short for any evolutionary changes.
Culture seems to be a much larger factor (and this is where I will concede that asian culture can stifle creativity). Culture is the main difference between the heads down religious conviction of the 9th century in Europe and the renaissance, not genetics.
I also don't believe there is a genetic difference, however I think there is a clear cultural difference which favors westerners. Asian culture with its emphasis on harmony and respect for the elders does not IMHO foster radical innovation. A key problem for China is that it is united. This stifles competition in ideas of how to organize society. Europe has benefited tremendously from being divided. That has prevented Europe from stagnating the way China did for hundreds of years. One stupid ruler can bring down all of China. One stupid European leader can't bring down the whole of Europe.
It is also false to consider Europe being a laggard in earlier times just because it was behind in maths and higher learning. One tends to think the Roman empire was so superior due to its progress in the arts and sciences. However medieval Europe saw far more progress in e.g. machinery and labour saving devices. Windmills, waterwheels, better plows etc was developed in this period.
In the short term the unit of China reaped a lot of benefits in the form of having much more peace. Europe suffered many setbacks due to the frequency of wars. But in the long run this proved a benefit. The fierce competitive nature of westerners could not be countered by harmony focused asian cultures.
Yes, competition tends to be bad for most individuals (who lose) but good for society.
China of course started taking off recently too after capitalist reforms in the 80s. The US, arguably one of the most "pull-yourself-up-from-your-bootstraps" of nations has done pretty well, despite lack of social programs. And back to Europe, I do think it was held back due to the forced conformity to the Church (IMO Christianity held back European science for hundreds of years).
So yes, culture is a very big current as far as steering people!
There is strong genetic factor for intelligence but it's not divided between races. Most human genetic variation happens between individuals.
There are large regional differences between intelligence, but they are explained with environmental factors:
1. parasite load and infectious diseases are strongly negatively corrected with intelligence. This applies between different countries and between states in United States.
2. Nutrition, prenatal nutrition is very important. Intelligence correlates with height. Most likely common cause for this correlation is nutrition.
3. Then comes other things like culture etc. Natural abilities can be enhanced with hard work and cultural incentives. In some cultures mathematically gifted may become lawyers. Edward Witten got degree in history and became a journalist. He published articles in The New Republic and The Nation and worked in George McGovern's presidential campaign. His physics and math carer came later.
Funny you should pick height, since it is a classic case for the influence of the environment. Large differences in height between countries today is primarily due to the environment. The dutch are the tallest today, but used to be the shortest in Europe. White Americans used to be far taller than Europeans but today Americans are relatively short in comparison to most European nations. Japanese used to among the shortest in the world but the young generation has almost caught up to the American average.
As for math, why have Russia and the Soviet Union won so much if Asians have such advantage? They have much smaller population than China? Why does Hungary have so many wins? How many asian immigrants do you think they have? Considering the small population of Hungary they are completely outperforming China.
There is a fixation that many things are genetic.
Here is what Po-Shen Loh says in the article:
"P-S.L.: I don’t want to say it’s genetic. A lot of people say you must be born with something very special. Maybe once in a while, you may see something like that. But people are basically the same."
> How much of mathematical intelligence genetic or environmental? It seems to be at least a fair amount genetic.
That would be my guess too. For instance, in France, some of the most prestigious "schools" base their selections on maths. It's interesting to see some students that got all the possible help from their rich family (very best schools, tutors...) being totally outcompeted by kids that grew up in much less favored environment. With maths, it seems either you have it or you don't.
Tutors and riches can't make up for lack of interest. If you look at top sports athletes many of those who reached the top did so because they had a motivation to train harder and longer than the rest. I remember a story about our best skier. She said her sister had more natural talent than her and was better. However her sister did not have the zeal for getting better and training hard, that is why she never became a top athlete.
I think there is a lot of truth to this. I drew better than my peers and I tended to do better in math. But if I reflect on it, I'd say it was mostly about interest. I drew a lot of drawings as a kid and I obsessed a lot about problems which are mathematical in nature. I wanted to understand how things worked. It wasn't enough to just get the right answer. I had to know why it was right.
The people I talk to who aren't very good at math typically strikes me as simply having no curiosity for why things work the way they do. They just want the answer and move on.
My brother e.g. has no curiosity like that, but he was born with better math skills than me. He could always do mental arithmetic better than me e.g. But as soon as math started getting abstract he fell behind me. Ability simply can't carry you if you have no motivation, curiosity or desire.
I believe "genes for math" is simply genes for having a personality that is curios and patient.
Asian parents usually regards their children's academic achievement as family prestige. As the result, the children spent a lot more time studying compared to other children from other families since young age. At the extreme end, getting scolded for getting a B is not unheard of.
It is remarkable the amount of asian and male students in this top echelon. It could be because of societal influence - but that really seems unlikely to me to cover this huge gap.
It may be unsavory, politically taboo, and not the way we want the world to be - but are males and people of asian-ancestry just better at math? And would knowing if that is the case help anything in any way?