I’ve been in the collegiate environment for a while now and spent a lot of time around various people in academics, but I have consistently noticed a striking difference in people gifted in mathematics. I find that people with serious mathematical talent have an extremely propensity for thinking about mathematics. It’s the most striking example of the sort of thing you’re mentioning that I have ever come across. It’s frequently given me the impression that mathematical talent is the academic talent that is most like athletics or sportsmanship in terms of just weird, unusually demonstrable performance characteristics.
It’s difficult to be more specific than that, but when I started noticing this, it made me extremely interested in the sort of topic you’re discussing. One of the ways this became apparent to me was when I realized that it wasn’t just the difference between someone being stupid and smart, or something generic like that. I think at first I was disconcerted by this level of mathematical aptitude in some people, but then eventually after getting to know a lot of people like this I realized I could still hold my own with them, the aptitude wasn’t some kind of signal for all around mental supremacy. I’m sure many people in my profession and people in various other areas of academia (biology, chemistry, all the engineering areas, philosophy, etc.) are just as “generically smart” as pure mathematicians, but when it comes to high level mathematics, it’s astonishing what kind of massive gap you can observe between two people who are both “generically smart”.
My personal intuition is that this really comes down to a brain wiring functionality that is peculiar to mathematical talent, since doing mathematics and doing proofs has such specific, strenuous requirements on serial logic processing, memory, symbolic representation, and so on. These constraints aren’t that specific in nature, but they are much more about just doing ordinary things at a very high level of functionality. For example, mathematicians have to have a very high capability in learning new definitions and inserting them into their knowledge base, reminiscent of language, but it’s essentially a task that all of us are able to do already, just not as well or as speedily. Hanging around mathematicians, you just start to get the feeling their minds are acting a lot more like computers than the rest of us, for example, just performing basic serial logic at an unusually high frequency.
I’ve been in the collegiate environment for a while now and spent a lot of time around various people in academics, but I have consistently noticed a striking difference in people gifted in mathematics. I find that people with serious mathematical talent have an extremely propensity for thinking about mathematics. It’s the most striking example of the sort of thing you’re mentioning that I have ever come across. It’s frequently given me the impression that mathematical talent is the academic talent that is most like athletics or sportsmanship in terms of just weird, unusually demonstrable performance characteristics.
It’s difficult to be more specific than that, but when I started noticing this, it made me extremely interested in the sort of topic you’re discussing. One of the ways this became apparent to me was when I realized that it wasn’t just the difference between someone being stupid and smart, or something generic like that. I think at first I was disconcerted by this level of mathematical aptitude in some people, but then eventually after getting to know a lot of people like this I realized I could still hold my own with them, the aptitude wasn’t some kind of signal for all around mental supremacy. I’m sure many people in my profession and people in various other areas of academia (biology, chemistry, all the engineering areas, philosophy, etc.) are just as “generically smart” as pure mathematicians, but when it comes to high level mathematics, it’s astonishing what kind of massive gap you can observe between two people who are both “generically smart”.
My personal intuition is that this really comes down to a brain wiring functionality that is peculiar to mathematical talent, since doing mathematics and doing proofs has such specific, strenuous requirements on serial logic processing, memory, symbolic representation, and so on. These constraints aren’t that specific in nature, but they are much more about just doing ordinary things at a very high level of functionality. For example, mathematicians have to have a very high capability in learning new definitions and inserting them into their knowledge base, reminiscent of language, but it’s essentially a task that all of us are able to do already, just not as well or as speedily. Hanging around mathematicians, you just start to get the feeling their minds are acting a lot more like computers than the rest of us, for example, just performing basic serial logic at an unusually high frequency.