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Many of us have -- or at some point want to have -- children, and wonder how we can do our best to fulfill the "nurture" component of helping them develop mathematical talent... not because we want them to be mathematical professionals, but we'd like them to have the choice, like we did.

However, this is not a question about how one "should" raise children, because of how fiercely debatable even the meaningfulness of such a question would be. Instead,

What reputable statistics are known about how mathematicians or highly mathematically talented people have been raised, especially during their early, formative years when "potential" is thought to be more of a variable?

(This question is community wiki, so everyone can edit it.)

Edit: I changed the title from "How are mathematicians raised?", since I personally only intended to ask for descriptive, not prescriptive, answers. The "However" paragraph above was inserted to further emphasize this.

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    $\begingroup$ is this a trick question? :P i personally believe we shouldn't "raise" mathematician the way former eastern Germany made super-athletes for the olympics during WWII. Just because we believe it is great doesn't mean our children or anyone else should. $\endgroup$
    – Jose Capco
    Commented Nov 12, 2009 at 9:27
  • $\begingroup$ I was just editing the title when you made that comment; see above. $\endgroup$
    – Andrew Critch
    Commented Nov 12, 2009 at 9:32
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    $\begingroup$ @Jose I think it should be "during the Cold War" instead of "during WWII". $\endgroup$
    – Ady
    Commented Jan 28, 2010 at 1:06
  • $\begingroup$ Step 0. Don't force them to do math. Ever. Step 1. Tell them interesting puzzles at their current level of development. Step 2. Set up somewhere to lie outside, so they can gaze up at the heavens, and wonder. To quote Atiyah: "In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life." Step 4. Don't force them to do math. Ever. $\endgroup$
    – goblin GONE
    Commented Feb 16, 2015 at 22:29

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I was raised by a pack of wild mathematicians. We roamed the great planes proving theorems and conjecturing.

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    $\begingroup$ {{citation needed}} $\endgroup$
    – Andrew Critch
    Commented Nov 12, 2009 at 18:48
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    $\begingroup$ This is too funny to not get my +1. ... but ... isn't there some truth in it, maybe? $\endgroup$
    – Konrad Voelkel
    Commented Nov 12, 2009 at 18:50
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    $\begingroup$ haha, nice. A description of a truly mathematical beast. $\endgroup$
    – user577
    Commented Dec 10, 2009 at 1:29
  • $\begingroup$ Were those great planes anything like the ground we have here in mathoverflow? $\endgroup$
    – Anweshi
    Commented Jan 9, 2010 at 20:17
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Here are interesting reviews of russian math circles. Friends who experienced such math circles (in the USSR and copies in other countries) told that it works great, even if one later decides for not becoming a mathematician.

Gromov expressed in his interview here some very interesting thoughts: "Now there are no more Abels... It means that they have been destroyed. The education destroys these potential geniuses – we do not have them! ... There are some experiments on animals which indicate that the way you teach an animal is not the way you think it happens. The learning mechanism of the brain is very different from how we think it works: like in physics, there are hidden mechanisms. We superimpose our view from everyday experience, which may be completely distorted. Because of that, we can distort the potentially exceptional abilities of some children. ... There are very interesting experiments performed with Chimpanzee and Bonobo apes and under which conditions they learn, or even how you teach a parrot to talk. How do you do that? The major factor is that it should not see the teacher. You put a mirror between you and the parrot and then you speak behind the mirror. The parrot then sees a bird – it talks to a bird. But if it sees you, it will learn very badly. That is not an obvious thing. The very presence of a teacher, an authority, moves students in a particular direction and not at all the direction the teacher wants them to move. With all this accumulated evidence, you cannot make any simple decision."

Edit: Alexandre Borovik links in his blog to this very fascianating essay by Gromov: "We introduce a concept of an ergosystem which functions by building its ”internal structure“ out of the ”raw structures“ in the incoming flows of signals. ... We shall argue in this section that the essential mental processes in humans andhigher animals can be represented by an abstract universal scheme and can bestudied on the basis of few (relatively) simple principles."

In general, I guess one should have the time frame of brain development in mind: One 'developmental window' is ca. from birth to age 4, the other around puberty. In both, many new nerves/nerve-connections build up, but untrained ones are then deleted. Reports of recent studies suggest that pre-birth risks fro the brain like stress, lead exposure, malnutrition are important too and widely underestimated.

Comes the dawn of 'Algernon mathematicians' ?

Edit: Here is the link to an article about a project to identify "good teaching": "The most stunning finding to come out of education research in the past decade: more than any other variable in education—more than schools or curriculum—teachers matter. But we have never identified excellent teachers in any reliable, objective way."

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    $\begingroup$ Very interesting. $\endgroup$
    – user577
    Commented Dec 10, 2009 at 1:31
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There are two factors I'd like to share, both based on observations of many people from the former Soviet Union.

  1. In the fSU, quite a few later-to-become-famous mathematicians chose maths because it was a creative field of study which was relatively ideology-free, - thus huge popularity of maths back then, and amazingly high numbers of famous mathematicians.

  2. (an addition to the answer by Jose Capco) Russian specialized mathematical high school served as some sort of reservation for talented students who failed to "fit in" among their classmates from regular schools; entering those mathematical school, they escaped all bullying they would have faced otherwise, and were able to explore their creativity in maths without the peer pressure (which was rarely approving of "maths geeks").

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Buy the kid Duplo and Lego - the generic blocks, not the fancy kits.

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As far as I know there are no such measured stats.

Speaking only for myself, my parents pretty much let me do whatever I wanted to do. And that was never mathematics. At least, not until university. Before university I largely viewed mathematics as a dreadfully boring and useless subject where the high point was the quadratic equation. Continual exposure to engineering (through my father) slowly weakened my resolve. I was quite reluctant to respect mathematics. Eventually I came to a grudging respect for mathematics but the pile of non-trivial applications got pretty deep beforehand. Then, as a 1st year undergraduate student I learned about the Smale-Hirsch theorem. That turned my head around, there was something to mathematics after all.

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This is not something i would advocate, but since you asked for only descriptive answers.. apparently a reputable statistics for very talented mathematician has been their inability (or that they did not have the chance) to socialize in their early years. I'm sure there are many out there who are exceptions. But the biographies of most of the very gifted ones that I have read show this pattern of life.

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  • $\begingroup$ Do you know of a source for such statistics? $\endgroup$
    – Andrew Critch
    Commented Nov 12, 2009 at 10:08
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    $\begingroup$ That sounds like total bunk to me. Plus, how would you quantitatively measure how much one has been socialized? $\endgroup$
    – Kevin H. Lin
    Commented Dec 27, 2009 at 21:21
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    $\begingroup$ I believe there have been some serious studies correlating mathematical abilities to Asperger's syndrome, which is on the mild end of the autistic spectrum. However, it is also the case that many people wish ill upon those who show discomforting strengths, and thus, stereotypes like this are spread gleefully far more than they are supported by facts. $\endgroup$
    – Douglas Zare
    Commented Jan 18, 2010 at 21:39
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    $\begingroup$ I think that Douglas is hinting to the research by Baron-Cohen and al, for instance <a href="ncbi.nlm.nih.gov/pubmed/11439754">this article</a> and many others as well as popular science news version. $\endgroup$
    – ogerard
    Commented May 11, 2010 at 12:33
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    $\begingroup$ ogerard (and Douglas Zare), thanks --- that is very interesting! BTW, clicking on the link didn't work for me, although I could easily see what it was meant to be. Perhaps it is the fault of my browser. $\endgroup$
    – Ravi Vakil
    Commented Jun 16, 2010 at 21:42
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Wouldn't we need some kind of randomized comparative design for such a study?

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