11–20 of 89 posts
25 percent of fields medal winners vs. 0.227 percent of world population. >100x difference. [discussion of statistical signfigance omitted.] Nature vs. Nurture is a stupid discussion, as "nurture" is costly and transient and a ripe subject for government boondoggles. People are different. No way around it.
On the other hand, a basic command of mathematics can be widely shared, and learned at most ages.
http://www.jinfo.org/Fields_Mathematics.html 25 percent of fields medal winners vs. 0.227 percent of world population. >100x difference. [discussion of statistical signfigance omitted.] Nature vs. Nurture is a stupid discussion, as "nurture" is costly and transient and a ripe subject for government boondoggles. People are different. No way around it. On the other hand, a basic command of mathematics can be widely sha…
Probably not.
In other words, is precocity a prerequisite to doing good work in Math?
Maybe, depending on whether you by "precocity" you mean "demonstrated precocity".
Intelligence is something you either have or don't have -- and while there's still debate about how much of intelligence is genetic (25%? 50%? 75%?) it's clear that the nurture which is most important is that which takes place before age 5, when the brain is still at its most plastic. Consequently, I would say that anyone who is not gifted when they're 5 years old is unlikely to have a significant mathematical impact.
However, not everybody with intellectual gifts demonstrates them early. Mathematics is a field known for child prodigies, not because it's particularly suited to prodigies, but rather because mathematics prodigies tend to get noticed. Some fields, like mathematics or chess, have little knowledge required before intellect can be applied; others, such as chemistry or biology, require years of prerequisite study. Moreover, just like chess prodigies, the abilities of a mathematics prodigy are obvious and unarguable, while a remarkable writer is still likely to be rejected by his first 19 publishers -- and what 9 year old writer is going to send his manuscript to 20 publishers?
In short: You have to be smart to do make a significant contribution to mathematics, and I don't believe that people can "become smart" past a very early age. However, it's possible for someone to be smart despite not having been recognized as such, depending on which fields his intellect is applied against. Finally, it's definitely possible for someone who is smart but has never done well in mathematics to make a contribution to mathematics -- if he can develop the interest which is necessary for him to apply his intellect appropriately.
Is this a useful answer? I have some other ideas about intelligence and IQ and the Putnam and flashes of insight floating around, but I'm not entirely certain how to explain them -- and given that news.yc stories don't stay on the front page for long, I thought I should post what I could promptly rather than waiting for everything else to crystallize.
Cultures screen for genetic attributes at a young age. This is not necessarily a good thing, but it just happens to be the case. Attractive children are treated differently. "Bright" children are treated differently. "Slow/inattentive" children are treated differently.
The sum of genetic attribute and cultural reaction to that attribute produces higher-order attributes which are consumed by new cultures, etc.
There is an academic culture of Mathematics. To participate, you need to have had the right experiences (enabled by the right genetics, pre-conditions, and cultural/socio-economic starting-point). People like MIT's Daniel Kane or Reid Barton were made-and-born.
So no, you can't become part of the culture of mathematics if you're not. Sorry, they're very picky. They also have a lot of resources (people to talk to, seminars to attend, journals which are expensive) which you can't have if you're not in the club.
Another unfortunate thing is that new math research really has to be presented in terms that "old math" can understand. E.g. constructivist mathematics struggles to get widespread approval. Adoption of ZFC axioms seems arbitrary in some senses (the C part).
So what does it mean to do "good" research? You need to create a result and argue it. Creation requires resources, argument requires facility with standards and ears to listen. Without acceptance into the community, you have neither.
That's one definition, anyway.
Do you just want to develop truth for yourself? Do you want to understand math deeply?
The fact is that there are many people who are extremely gifted in terms of genetic skills, who can do good math, but who don't quite "fit the mold" (trivial example: people with tremendous visuo-spatial reasoning abilities vs. people with tremendous pure-abstraction symbolic-manipulation abilities). These people can still do good math. They just have to do it largely on their own and they may have trouble communicating it with others.
In short, it's insanely complicated and has to do with the marriage of genetics and -culture-, not nurture, per se. If you want deeper insights into this question, I recommend you look at the history of mathematics and mathematicians.
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Anyway, if you want a good example of a non-stereotypical mathematician, I recommend you look at the autobiography of Grothendiek. Good read.
Very great mathematicians are born. You're either born as Ramanujan or Erdos or you're never going to be Ramanujan or Erdos. No way around it. But, merely pretty damn good mathematicians can work really good and be a thousandth as useful as an Erdos or Ramanujan.
Can people who are not inherently 'gifted', start with an immense interest in math at a mid-point in their life, and still go on to make meaningful and significant contributions to the field? Probably not. In other words, is precocity a prerequisite to doing good work in Math? Maybe, depending on whether you by "precocity" you mean "demonstrated precocity". Intelligence is something you either have or don't have -- a…
I am highly turned off by the idea that we can't "become smart" after an early age. I feel like I "got smart" after I started playing go, I feel like I "got smart" after I learned category theory. I feel like every year I get smarter - and not smarter in the sense of "having more knowledge" but smarter in the sense of being able to solve larger classes of problems, and more complicated problems.
and c.
http://www.jinfo.org/Fields_Mathematics.html 25 percent of fields medal winners vs. 0.227 percent of world population. >100x difference. [discussion of statistical signfigance omitted.] Nature vs. Nurture is a stupid discussion, as "nurture" is costly and transient and a ripe subject for government boondoggles. People are different. No way around it. On the other hand, a basic command of mathematics can be widely sha…
That may well be true, but I think the problem of disentangling the incredibly powerful Jewish cultural influence (or any other cultural, influence, really, as a half-asian I can tell you my heritage helped push me) from whatever biological differences there might be is an incredibly tricky one. So I think that asserting such conclusions here is either chauvinist or premature.
Also talking about a certain community doesn't necesarily mean something related to race. There could be some kind of selection for people that become jew marrying or people that quits.
I am surprised so many people here seem to lean towards "nature". I am pretty sure you can pick up mathematics at any age. Sometimes I also wonder: humans manage so many really complicated tasks in their daily lives, can it really be a much farther stretch to reach into mathematics?
Of course experience and knowledge and training help in mathematics, but as in other fields, maybe sometimes an outsider can bring a fresh view into it. It might also depend on the field of maths you choose, some might be more approachable than others.
That said, I agree with the other post that genius mathematicians are probably somehow born or made very early on.
Math education is so bad right now that any genetic differences are drowned out almost entirely. Of all the mathematicians I've met (including IMO gold medalists, Fields medalists, etc.), there seems to be little correlation with siblings, at least beyond what you would expect from having parents who emphasize learning math. To answer your question, if you want to contribute significantly, you will need to study hard…
I'd bet for a set of negative factors. For you to be 100%, you need to have full 15% of genes (maybe there are a lot involved, so it could be very improbable to have more than 10% of that 15%), 30% of early nurture and 40% of favorable social conditions (good environment, or just not being poor that lets out a big part of humanity) and the rest of luck, effort and good teachers.
The lack of any of these conditions could explain why the siblings are not so bright. The lack of genetic conditions and the early nurture could also ruin more easily the posibilities.
"Genetic" is also broad. It could be quicker thinking, focus, even a illness that forces a child to stay home reading instead of playing outdoors.