| People vary in mental attributes. Let's get this out of the way right now. It -has to be the case-. We should obviously remain agnostic about what these attributes are (for instance, I would be hard pressed to say that "good memory" is even genetic because it is hard to disambiguate "memory software" from "memory hardware" in the brain). 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. --- Anyway, if you want a good example of a non-stereotypical mathematician, I recommend you look at the autobiography of Grothendiek. Good read. |