5 ms·

Colin Percival wrote one of my favorite response to a question about mathematicians here: https://news.ycombinator.com/item?id=228233 https://news.ycombinator.

Colin Percival wrote one of my favorite response to a question about mathematicians here: https://news.ycombinator.com/item?id=228233 https://news.ycombinator.com/item?id=228233 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.

Bahamut 9y ago
This is a supremely accurate quote - mathematicians often encounter this when teaching undergrads in lower level courses. I remember encountering some very smart people while teaching in grad school, but the people themselves did not recognize themselves as smart or gifted in the discipline due to their upbringing. It was a sad thing to see, and I would encourage them that they could be successful in mathematics if they wanted to & that they possessed the gift of intelligence to succeed. I hope I left a mark on their lives, although I am not able to see how they turned out (after all, I was just a TA for their one semester with me).
williamstein 9y ago
Colin's response nails it on the head (but also, some of the people Cathy is talking about are really, really scary smart). For what it's worth, around 15 years ago, I personally had a "traumatic" and relevant experience involving the author (Cathy O'Neil) of the article we're discussing here, which I've never told anybody about. We are both number theorists, with a similar educational track (Berkeley, Harvard, etc., at similar times). She and I were hanging out in a pub in Cambridge, MA, and I was showing her a list of research projects I was very excited about and working on. First, some background about me. In grad school at Berkeley, I had changed from worrying about "being a genius", to just being completely obsessed with doing mathematics research all the time, and actively simply not thinking about myself or social things. I had many clear experiences when working on research problems in which if I thought at all about myself and whether or not I was "smart" (or anything social), my progress would completely stop; however, if I could clear my mind of such worries -- about myself or others, then I could prove theorems and do good mathematics. So at the time I really embraced mathematics research itself over social concerns. Anyway, Cathy and I were in a bar, and I was showing her (on my laptop), my list of projects. I really hoped she would find some of them interesting, and we might coauthor a paper together, since her thesis research was closely related to mine, but approached things from a completely different (more geometric) direction, which I personally found extremely difficult (at least, I didn't have the "interest" to master that approach, in the sense of Colin's comment). Well this is not at all what happened! Instead, of getting excited by any of the projects I proposed, Cathy got really, really angry at me for (I guess) intimidating her (?). I was never sure. I genuinely meant no harm. For me personally at least, somehow worrying about the social aspects of research mathematics too much would make it impossible for me to actually do mathematics. I wonder if some of the other people Cathy alludes to in the article are similar, and if this has consequences. Anyway, it was a lesson to me at the time of the extent to which having a sense of "being in the zone" and not thinking about oneself (or social and emotional issues at all), can simultaneously be very conducive to research mathematics and also really piss off certain people. I make no claims to be a genius or "emotionally mature" at the time, and I'm a different person today than I was then. However, there is (at least for me) a real psychological conflict between the social aspects of thinking about research and actually doing research; it is a very difficult challenge to balance the two.
- psyc 9y ago
  Oh wow. I've had this exact thing happen a few times. I'm way in the zone, making thrilling progress on something and perceiving my own state of mind as rather egoless. I see that if I could collaborate with certain people, the result would be incredible. But instead of catching my excitement they get angry, tell me my work is garbage, and say don't speak to them again. It seems obvious that it must be an ego thing, because if the problem was simply that my work was bad, they could tell me nicely. Such people seem very territorial. It doesn't always happen this way. I've also approached people and had them respond enthusiastically. But when you're in that state of pure excitement about the objective, it doesn't occur to you that a colleague could feel threatened, and it can be quite crushing to get slapped back into that social plane.
  - kem 9y ago
    I've published in mathematical/statistical areas as well as applied ones, and my sense is that interpersonal difficulties are more acute, but also more transparent, in math and statistics, for lack of a better way of putting it. My sense is that people tend to hold views more absolutely, because they see their positions as more logic-based, and so have a more difficult time recognizing unrealistic assumptions they're making, or outright errors in their derivations or thinking. An applied researcher can shrug and dismiss something as sampling error, or ambiguity in a study design, but in math, it's harder to invoke such excuses or pressure relief valves. A threat, of whatever real or misperceived magnitude, seems to take on greater significance in math and statistics.
- watwut 9y ago
  It is possible that she went to bar with completely different expectations - drinking beer and having fun. She probably did not expected to be pushed into passive role of "listen about cool things I have done". I don't mean to say that you have done sonething wrong, you did not. But if I can choose who I would cooperate with, I would choose someone I can have more two way conversation with. If the discussion between you and me is about your projects only, I would assume that our cooperation would be primary about your ideas and plans (since I have hard time make myself being listened to now).
thearn4 9y ago
It rings true to me. I have a math PhD, and taught at various levels. Something I can say is that while I'm not sure that everyone is capable of groking advanced math, a person who can do that could actually come from anywhere, at least. And our system isn't really all that great at seeking that capability out. Unless you are in a fairly privileged group.
- kem 9y ago
  There's kind of "converse" problems too, that I think is the focus of the linked article, in that there's an epidemic of hype in academics, math, and the sciences. So it's not just that people of high ability are being missed, but some individuals of high ability are being over-hyped to an extreme. The signal to noise ratio is very poor due to multiple types of errors. People have been writing about this for a long time; it's nothing new but little seems to change (https://www.theatlantic.com/magazine/archive/2002/12/our-genius-problem/308435/ https://www.theatlantic.com/magazine/archive/2002/12/our-gen...).

Bahamut 9y ago

This is a supremely accurate quote - mathematicians often encounter this when teaching undergrads in lower level courses. I remember encountering some very smart people while teaching in grad school, but the people themselves did not recognize themselves as smart or gifted in the discipline due to their upbringing. It was a sad thing to see, and I would encourage them that they could be successful in mathematics if they wanted to & that they possessed the gift of intelligence to succeed. I hope I left a mark on their lives, although I am not able to see how they turned out (after all, I was just a TA for their one semester with me).

williamstein 9y ago

Colin's response nails it on the head (but also, some of the people Cathy is talking about are really, really scary smart). For what it's worth, around 15 years ago, I personally had a "traumatic" and relevant experience involving the author (Cathy O'Neil) of the article we're discussing here, which I've never told anybody about. We are both number theorists, with a similar educational track (Berkeley, Harvard, etc., at similar times). She and I were hanging out in a pub in Cambridge, MA, and I was showing her a list of research projects I was very excited about and working on. First, some background about me. In grad school at Berkeley, I had changed from worrying about "being a genius", to just being completely obsessed with doing mathematics research all the time, and actively simply not thinking about myself or social things. I had many clear experiences when working on research problems in which if I thought at all about myself and whether or not I was "smart" (or anything social), my progress would completely stop; however, if I could clear my mind of such worries -- about myself or others, then I could prove theorems and do good mathematics. So at the time I really embraced mathematics research itself over social concerns. Anyway, Cathy and I were in a bar, and I was showing her (on my laptop), my list of projects. I really hoped she would find some of them interesting, and we might coauthor a paper together, since her thesis research was closely related to mine, but approached things from a completely different (more geometric) direction, which I personally found extremely difficult (at least, I didn't have the "interest" to master that approach, in the sense of Colin's comment). Well this is not at all what happened! Instead, of getting excited by any of the projects I proposed, Cathy got really, really angry at me for (I guess) intimidating her (?). I was never sure. I genuinely meant no harm. For me personally at least, somehow worrying about the social aspects of research mathematics too much would make it impossible for me to actually do mathematics. I wonder if some of the other people Cathy alludes to in the article are similar, and if this has consequences. Anyway, it was a lesson to me at the time of the extent to which having a sense of "being in the zone" and not thinking about oneself (or social and emotional issues at all), can simultaneously be very conducive to research mathematics and also really piss off certain people. I make no claims to be a genius or "emotionally mature" at the time, and I'm a different person today than I was then. However, there is (at least for me) a real psychological conflict between the social aspects of thinking about research and actually doing research; it is a very difficult challenge to balance the two.

psyc 9y ago
Oh wow. I've had this exact thing happen a few times. I'm way in the zone, making thrilling progress on something and perceiving my own state of mind as rather egoless. I see that if I could collaborate with certain people, the result would be incredible. But instead of catching my excitement they get angry, tell me my work is garbage, and say don't speak to them again. It seems obvious that it must be an ego thing, because if the problem was simply that my work was bad, they could tell me nicely. Such people seem very territorial. It doesn't always happen this way. I've also approached people and had them respond enthusiastically. But when you're in that state of pure excitement about the objective, it doesn't occur to you that a colleague could feel threatened, and it can be quite crushing to get slapped back into that social plane.
- kem 9y ago
  I've published in mathematical/statistical areas as well as applied ones, and my sense is that interpersonal difficulties are more acute, but also more transparent, in math and statistics, for lack of a better way of putting it. My sense is that people tend to hold views more absolutely, because they see their positions as more logic-based, and so have a more difficult time recognizing unrealistic assumptions they're making, or outright errors in their derivations or thinking. An applied researcher can shrug and dismiss something as sampling error, or ambiguity in a study design, but in math, it's harder to invoke such excuses or pressure relief valves. A threat, of whatever real or misperceived magnitude, seems to take on greater significance in math and statistics.
watwut 9y ago
It is possible that she went to bar with completely different expectations - drinking beer and having fun. She probably did not expected to be pushed into passive role of "listen about cool things I have done". I don't mean to say that you have done sonething wrong, you did not. But if I can choose who I would cooperate with, I would choose someone I can have more two way conversation with. If the discussion between you and me is about your projects only, I would assume that our cooperation would be primary about your ideas and plans (since I have hard time make myself being listened to now).

thearn4 9y ago

It rings true to me. I have a math PhD, and taught at various levels. Something I can say is that while I'm not sure that everyone is capable of groking advanced math, a person who can do that could actually come from anywhere, at least. And our system isn't really all that great at seeking that capability out. Unless you are in a fairly privileged group.

kem 9y ago
There's kind of "converse" problems too, that I think is the focus of the linked article, in that there's an epidemic of hype in academics, math, and the sciences. So it's not just that people of high ability are being missed, but some individuals of high ability are being over-hyped to an extreme. The signal to noise ratio is very poor due to multiple types of errors. People have been writing about this for a long time; it's nothing new but little seems to change (https://www.theatlantic.com/magazine/archive/2002/12/our-genius-problem/308435/ https://www.theatlantic.com/magazine/archive/2002/12/our-gen...).