A Mathematician's Secret: We're Not All Geniuses(bloomberg.com)
bloomberg.com
A Mathematician's Secret: We're Not All Geniuses
https://www.bloomberg.com/view/articles/2017-06-07/a-mathematician-s-secret-we-re-not-all-geniuses
137 comments
Genius has nothing to do with IQ. Genius is a level of creative thought that appears magically simple once you behold it, but yet was beyond people up to that point. The things that IQ tests for are almost orthogonal to this. Sure, there are probably geniuses with high IQs, but I'd be very surprised if high IQ has any predictive ability to detect genius.
In one sense, I think you're correct: the term "genius" should be reserved for people who produce extraordinary output in some field -- whether that's math or science, literature, music, visual art, etc. Even if we restrict ourselves to scientific geniuses, the idea that everyone who gets above a certain score on an IQ test should be labelled a genius seems, frankly, small-minded. Not everyone with an IQ >= X should be labelled a genius because not everyone with a very high IQ has the other qualities required to produce genius-level work.
But in many fields, such as mathematics, high IQ seems to be a necessary but not sufficient condition for genius. This makes sense -- doing well in mathematics courses requires the same logical and analytical skills required to score high on an IQ test. In that sense, it obviously has some predictive value.
But in many fields, such as mathematics, high IQ seems to be a necessary but not sufficient condition for genius. This makes sense -- doing well in mathematics courses requires the same logical and analytical skills required to score high on an IQ test. In that sense, it obviously has some predictive value.
I agree with everything you say, but if >140 IQ accounts for the 99.5 percentile and true genius (in my estimation) is closer to 1 in 100000, then, even if every genius is within that IQ percentile, the predictive value is still essentially worthless.
Using those numbers, a random person has a 0.001% chance of being a genius. After they score >140 on an IQ test, this improves to a 0.2% chance. That's a big increase, but it isn't high enough to predict that an individual is a genius with any degree of certainty.
But, we can use the IQ test to predict who isn't a genius, or to make large scale predictions. For example, if a state has 100,000 students entering middle school per year, there's approximately one genius in that group. If you can afford an intensive math program for 7,500 students, the IQ test would let you predict that any potential geniuses get enrolled with high probability. That raises issues of fairness, discrimination, etc., but that's another topic.
But, we can use the IQ test to predict who isn't a genius, or to make large scale predictions. For example, if a state has 100,000 students entering middle school per year, there's approximately one genius in that group. If you can afford an intensive math program for 7,500 students, the IQ test would let you predict that any potential geniuses get enrolled with high probability. That raises issues of fairness, discrimination, etc., but that's another topic.
> I'd be very surprised if high IQ has any predictive ability to detect genius.
This is the most ridiculous thing I have read for a while.
This is the most ridiculous thing I have read for a while.
Why? High IQ means you are very good at solving the IQ test problems, not that you are intelligent or genius. I don't think these problems represent anything else, or if there are examples of high IQ people that made actual, genius contribution to humanity. Do you?
Are you familiar with modern intelligence research? IQ test is reliable (get the same score when you test multiple times) and valid (correlate with things we actually care about, not just being good at solving IQ test problems).
Intelligence: All That Matters by Stuart Ritchie is a good summary of modern intelligence research. https://www.amazon.com/Intelligence-That-Matters-Stuart-Ritc... To quote:
"The scientific evidence is clear: IQ tests are extraordinarily useful. IQ scores are related to a huge variety of important life outcomes like educational success, income, and even life expectancy, and biological studies have shown they are genetically influenced and linked to measures of the brain. Studies of intelligence and IQ are regularly published in the world's top scientific journals."
Intelligence: All That Matters by Stuart Ritchie is a good summary of modern intelligence research. https://www.amazon.com/Intelligence-That-Matters-Stuart-Ritc... To quote:
"The scientific evidence is clear: IQ tests are extraordinarily useful. IQ scores are related to a huge variety of important life outcomes like educational success, income, and even life expectancy, and biological studies have shown they are genetically influenced and linked to measures of the brain. Studies of intelligence and IQ are regularly published in the world's top scientific journals."
My mum, after getting her PhD (and having taught herself through A-levels because her Yorkshire school stopped at O-levels, and got into Oxford) decided to take her first-ever IQ test. She rated mentally subnormal.
Astonished, she thought about what it was trying to test and took another test: now genius.
None of us think that either was right...
Astonished, she thought about what it was trying to test and took another test: now genius.
None of us think that either was right...
Up until I was eight they thought I might be deficient. So they poked and prodded and eventually some people came to school and took me to the library and gave me an IQ test. Then they came back and gave me another one. And I believe another one after that, by which point I was a little disgruntled. Didn't I already take one of these? Did you lose my answers?
Turns out that the test can be tuned to a range. If you take the wrong one it loses some accuracy at the low and high end of the range, so they had to retest me. They had assumed I might be dim and gave me the wrong one. The real problem was that I was so insufferably bored all the time that I wouldn't engage. But I liked puzzles and the test had a bunch I'd never seen before, so by the last one I was taking it in the spirit it was given.
My guess is in two parts. Either your mother took the wrong one(s), or took a bogus one, or you're thinking of elements of a successful adult that the test can't measure, like common sense and social graces.
In any group of peers at that level there are bound to be people who can certainly do the work, possibly better than you, but who are painfully, even cringingly, bad at certain other life skills. It gets a little uncomfortable to acknowledge these people as geniuses. And there are people who seem not to be all that, but on occasion surprise the hell out of you by coming through in a clutch.
Turns out that the test can be tuned to a range. If you take the wrong one it loses some accuracy at the low and high end of the range, so they had to retest me. They had assumed I might be dim and gave me the wrong one. The real problem was that I was so insufferably bored all the time that I wouldn't engage. But I liked puzzles and the test had a bunch I'd never seen before, so by the last one I was taking it in the spirit it was given.
My guess is in two parts. Either your mother took the wrong one(s), or took a bogus one, or you're thinking of elements of a successful adult that the test can't measure, like common sense and social graces.
In any group of peers at that level there are bound to be people who can certainly do the work, possibly better than you, but who are painfully, even cringingly, bad at certain other life skills. It gets a little uncomfortable to acknowledge these people as geniuses. And there are people who seem not to be all that, but on occasion surprise the hell out of you by coming through in a clutch.
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I'm not sure genius is correlated with income, life expectancy, and even educational success, though. Never mind poor, miserable geniuses like Dostoevsky; even Alan Turing was considered a rather mediocre student (and was also pretty miserable and quite unsuccessful by many measures). I'm pretty sure there is some statistical correlation between IQ and genius, but the correlation is certainly not absolute. In other words, genius and very high IQ are certainly not the same thing.
http://www.pnas.org/content/109/2/425.full.pdf (Schooling in adolescence raises IQ scores)
Summary: "The quasiexperimental results suggest that the reform increased the average IQ score for Norwegian men by a statistically significant 0.6 IQ points."
This paper shows two things, although only one is surprising enough for publication. The surprising part is that "schooling in adolescence raises IQ scores", which is the title of the paper. Another is that IQ is so reliable that increase of 0.6 IQ points is statistically significant.
This paper shows two things, although only one is surprising enough for publication. The surprising part is that "schooling in adolescence raises IQ scores", which is the title of the paper. Another is that IQ is so reliable that increase of 0.6 IQ points is statistically significant.
agree...IQ correlates with a lot. It's not just a measure of "how well someone does on IQ tests".
My impression is that IQ test roughly measures g [0], which does correlate with intelligence.Note that this is not my research area by any stretch.
[0] https://en.wikipedia.org/wiki/G_factor_(psychometrics)
[0] https://en.wikipedia.org/wiki/G_factor_(psychometrics)
I'm quite sure Van Gogh's IQ wasn't that high...
Why?
because... history?
he was a Genius, but his IQ was probably average, according to what we know about him
he was a Genius, but his IQ was probably average, according to what we know about him
I don't know the history, that's what I was asking. I googled before I asked but everything I could find seemed relatively split with many sources implicitly or explicitly referring to him as a genius.
Hard to say. He was nearly as good a writer as a painter and presumably wasn't even trying at that craft. He would be remembered for his letters even if he never painted a thing, and they were purely accidental because Theo wasn't always in town. But you still have a point.
> Genius has nothing to do with IQ. Genius is a level of creative thought that appears magically simple once you behold it, but yet was beyond people up to that point.
Not sure why the downvotes. While discounting the relationship of genius with IQ is specious in light of their point, this person offers a possible nugget of truth on an alternative understanding of genius.
Not sure why the downvotes. While discounting the relationship of genius with IQ is specious in light of their point, this person offers a possible nugget of truth on an alternative understanding of genius.
mathematicians probably have a much higher standard for what constitutes 'genius' than do regular people. For a layperson, a genius may be someone who understands elliptic integrals, but to a mathematicians such a concept is rather ordinary.
My senior year of undergrad, there were 4 of us living together who were math majors. There were so many things that we laughed or argued about that when non-math major friends were over, they sort of just stared at us because nothing we were saying made sense to them, even though it made perfect sense to us.
Part of it, I think, is because of the sheer knowledge threshold: much of higher level maths has its own specialized language, so when you start discussing isomorphisms between Z_p and geometric structures, and you don't know what those words mean, your eyes can't help but glaze over. So I don't know if it's so much that there's a higher standard of 'genius' so much as it is that it's a different standard, because much of maths is so far removed from the knowledge base of the layperson.
Part of it, I think, is because of the sheer knowledge threshold: much of higher level maths has its own specialized language, so when you start discussing isomorphisms between Z_p and geometric structures, and you don't know what those words mean, your eyes can't help but glaze over. So I don't know if it's so much that there's a higher standard of 'genius' so much as it is that it's a different standard, because much of maths is so far removed from the knowledge base of the layperson.
> Part of it, I think, is because of the sheer knowledge threshold: much of higher level maths has its own specialized language
Not sure if that's specific to math though... Certainly at a PhD-level there's going to be a specialized language.
But I'm trying to imagine undergrads of different majors having a conversation and seeing how far outside language of a layperson they'd be. Maybe most STEM majors would be incomprehensible? Math and physics may be the furthest outside. If you heard a bunch of chemistry students talking, your eyes may glaze over. Biology may be not too far outside. Once you get into psychology/sociology you might understand most of it.
I have a STEM PhD, so it's a difficult exercise. Essentially, "what would my mom understand?"
Not sure if that's specific to math though... Certainly at a PhD-level there's going to be a specialized language.
But I'm trying to imagine undergrads of different majors having a conversation and seeing how far outside language of a layperson they'd be. Maybe most STEM majors would be incomprehensible? Math and physics may be the furthest outside. If you heard a bunch of chemistry students talking, your eyes may glaze over. Biology may be not too far outside. Once you get into psychology/sociology you might understand most of it.
I have a STEM PhD, so it's a difficult exercise. Essentially, "what would my mom understand?"
Jargon certainly isn't unique to any field. In my view, jargon repackages conceptual or procedural knowledge into shorter phrases for the purpose of more efficient communication. The less familiar another person is with a particular set of jargon, the more it must be "un-packaged" into its fundamental ideas.
Of course, jargon can be nested, so this process may potentially be tedious. On the other hand, this jargon nesting problem can be avoided by approximating ideas with ones that the other party is assumed to be familiar with. An expert knows the jargon, the ideas behind the jargon, and many of the first- and second-order approximations of the ideas.
Of course, jargon can be nested, so this process may potentially be tedious. On the other hand, this jargon nesting problem can be avoided by approximating ideas with ones that the other party is assumed to be familiar with. An expert knows the jargon, the ideas behind the jargon, and many of the first- and second-order approximations of the ideas.
> Not sure if that's specific to math though... Certainly at a PhD-level there's going to be a specialized language.
That's a good point, and I don't think it even needs to be at the PhD level; just a 3rd yr u/g is probably sufficient. In poli sci, you can talk about phenomena like candidate emergence, for example, or voting systems like FPTP and the like. In phil, you have notions such as fallibility as a premise, phenomenology a la Heidegger, etc.
The big difference, I think, is that STEM tends to be less accessible because those fields tend to have knowledge bases that the average layman won't deal with in their lifetime, whereas with psych, soce, and most other liberal arts fields, people can always draw on personal experience to understand the jargon. There isn't really any such analogy, though, for homomorphisms in a metric space or thermo calculations.
To bring it back to the point I was trying to make: jargon is needed to discuss knowledge domains beyond what the layperson has been exposed to. So although jargon might give the impression of a higher "genius" standard, the standard isn't so much higher as it is different, because reasoning about stuff like the Riemann hypothesis is completely different from discussing the subtleties of, say, negotiation strategies.
That's a good point, and I don't think it even needs to be at the PhD level; just a 3rd yr u/g is probably sufficient. In poli sci, you can talk about phenomena like candidate emergence, for example, or voting systems like FPTP and the like. In phil, you have notions such as fallibility as a premise, phenomenology a la Heidegger, etc.
The big difference, I think, is that STEM tends to be less accessible because those fields tend to have knowledge bases that the average layman won't deal with in their lifetime, whereas with psych, soce, and most other liberal arts fields, people can always draw on personal experience to understand the jargon. There isn't really any such analogy, though, for homomorphisms in a metric space or thermo calculations.
To bring it back to the point I was trying to make: jargon is needed to discuss knowledge domains beyond what the layperson has been exposed to. So although jargon might give the impression of a higher "genius" standard, the standard isn't so much higher as it is different, because reasoning about stuff like the Riemann hypothesis is completely different from discussing the subtleties of, say, negotiation strategies.
> Part of it, I think, is because of the sheer knowledge threshold
That's common in every niche.
I don't get a third of what my weed expert friends say.
They don't get most of what I say about craft beer.
That's common in every niche.
I don't get a third of what my weed expert friends say.
They don't get most of what I say about craft beer.
> Maybe that's what she means by "geniuses", but usually the word tends to mean "who studied at Berkeley, Harvard and Princeton".
You made an excellent point here. I hope that more people who don't go to elite schools realize that many (most?) people who do are distinctly not geniuses either on the surface (e.g., if you talk to them) or in actuality (i.e., 140+ IQ).
You made an excellent point here. I hope that more people who don't go to elite schools realize that many (most?) people who do are distinctly not geniuses either on the surface (e.g., if you talk to them) or in actuality (i.e., 140+ IQ).
"Genius" is like "rich": as actually used, it's implicitly a comparative term. When someone talks about geniuses they usually mean "people much smarter than me" (either in general intelligence, in so far as that's meaningful, or in a particular area like mathematics or music or languages).
I think this sort of usage is so deeply ingrained that there's not much point in trying to counter it by adopting a fixed formal definition (e.g., someone elsewhere in the thread said something like "genius means IQ >= 140, get over it"). Instead, either pick a definition and say what definition you're using or use it informally and live with the fact that sometimes you'll be misunderstood.
In this particular case, it seems reasonably clear that what she means by "geniuses" is "people with the sort of ability the big names in mathematics generally have": her point is that mathematical progress depends not only on the Gausses and Thurstons and Ramanujans but also, just as much, on the ordinary mathematicians who, yes, are generally also extremely bright but are very conscious of the gulf between them and the famously-brilliant ones.
(Is it absurd to say "just as much"? No, because there are a lot more ordinary mathematicians than once-in-a-generation ones.)
I think this sort of usage is so deeply ingrained that there's not much point in trying to counter it by adopting a fixed formal definition (e.g., someone elsewhere in the thread said something like "genius means IQ >= 140, get over it"). Instead, either pick a definition and say what definition you're using or use it informally and live with the fact that sometimes you'll be misunderstood.
In this particular case, it seems reasonably clear that what she means by "geniuses" is "people with the sort of ability the big names in mathematics generally have": her point is that mathematical progress depends not only on the Gausses and Thurstons and Ramanujans but also, just as much, on the ordinary mathematicians who, yes, are generally also extremely bright but are very conscious of the gulf between them and the famously-brilliant ones.
(Is it absurd to say "just as much"? No, because there are a lot more ordinary mathematicians than once-in-a-generation ones.)
> This sounds ridiculous.
It sounds less so if you read the next sentence, and the one after that.
As a mathematician who studied at Berkeley, Harvard and Princeton, I’ve known geniuses. I got to hang out with Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture. They’re great guys, but they didn’t do it on their own. For each certified genius, there are at least a hundred other great people who helped achieve such outstanding results.
It sounds less so if you read the next sentence, and the one after that.
As a mathematician who studied at Berkeley, Harvard and Princeton, I’ve known geniuses. I got to hang out with Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture. They’re great guys, but they didn’t do it on their own. For each certified genius, there are at least a hundred other great people who helped achieve such outstanding results.
I think here are two things in play:
First the other end of the Dunning Kruger effect where competent people underestimate their competence rank.
Second, only good mathematicians[1] can recognize the massive gap between good mathematician and a real top class mathematical genius. For the mere mortals they both are so far that they look alike.
[1] Mathematician can be replaced with any other talent/competence. Actually I realized this phenomena first in sports. The world's ultimate top and a very good amateur look perfectly as good to a complete beginner. But when you get to the very good amateur level, you start to realize the massive amount of work (and maybe talent) that makes the difference between you and the ultimate top.
First the other end of the Dunning Kruger effect where competent people underestimate their competence rank.
Second, only good mathematicians[1] can recognize the massive gap between good mathematician and a real top class mathematical genius. For the mere mortals they both are so far that they look alike.
[1] Mathematician can be replaced with any other talent/competence. Actually I realized this phenomena first in sports. The world's ultimate top and a very good amateur look perfectly as good to a complete beginner. But when you get to the very good amateur level, you start to realize the massive amount of work (and maybe talent) that makes the difference between you and the ultimate top.
Someone has to build the confusion matrix for the geniuses "> 130 IQ" classifier.
I mean, if you have a definition for "a genius" that likely ends up excluding Bach, Escher, Darwin - then something's fishy about your definition.
In terms of communicating with the others, that's akin to having a definition for "great basketball player" to which Jordan doesn't fit.
I mean, if you have a definition for "a genius" that likely ends up excluding Bach, Escher, Darwin - then something's fishy about your definition.
In terms of communicating with the others, that's akin to having a definition for "great basketball player" to which Jordan doesn't fit.
Darwin was something of a plodder who get's a lot of great press. He did not really come up with the idea of evolution, just came up with more support, a convincing argument, and most importantly communicated this to a wide range of people. https://en.wikipedia.org/wiki/History_of_evolutionary_though...
It's kind of the great man argument taken to the extreme.
It's kind of the great man argument taken to the extreme.
Remember in a stadium of 80,000 people there are 320 people who have an IQ of >=140.
Only true if the distribution of people going to a stadium is not biased to below average intelligent people, or biased in some other way, which I suspect might be the case.
Above average, considering the cost of a ticket.
She names specific people who she met at Berkeley as geniuses:
As a mathematician who studied at Berkeley, Harvard and Princeton, I’ve known geniuses. I got to hang out with Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture.
I don't think she means that everyone she met at Berkeley was a genius.
As a mathematician who studied at Berkeley, Harvard and Princeton, I’ve known geniuses. I got to hang out with Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture.
I don't think she means that everyone she met at Berkeley was a genius.
I’m not saying we shouldn't have high hopes and standards for our children. But by focusing our attention on the kids who get the top SAT scores, we reinforce the fixation on genius to the detriment of everyone else
No amount of idealism will change the fact that mathematicians , with virtual certainty, tend to score very high on such tests. To find the next generation of mathematician, look to kids who are getting ceiling scores on the math part of the SAT at the age of 13. Sometimes 'late boomers' exist, but still they exhibit preciosity at youth and then later decide to turn to mathematics and learn the material very quickly due to having a high iq. If genius is defined by having a high IQ (which according to the Stanford Binet Intelligence scale it is) and standardized test scores, virtually all mathematicians are geniuses, regardless of how much recognition they later get in their careers.
No amount of idealism will change the fact that mathematicians , with virtual certainty, tend to score very high on such tests. To find the next generation of mathematician, look to kids who are getting ceiling scores on the math part of the SAT at the age of 13. Sometimes 'late boomers' exist, but still they exhibit preciosity at youth and then later decide to turn to mathematics and learn the material very quickly due to having a high iq. If genius is defined by having a high IQ (which according to the Stanford Binet Intelligence scale it is) and standardized test scores, virtually all mathematicians are geniuses, regardless of how much recognition they later get in their careers.
What research are you referring to?
He didn't mention any research. Lets not start the 'prove that there is such a thing as smart people' debate again.
I meant: "Mathematicians, with virtual certainty, tend to score very high on such tests".
This seems easily tested or refuted, and I'd be surprised if nobody has done it. However, I haven't figured out a good search query yet.
This seems easily tested or refuted, and I'd be surprised if nobody has done it. However, I haven't figured out a good search query yet.
Every test has false positives and true negatives. The problem with any standard like the SAT or a generalized IQ test is that it has general accuracy, sure, but it's hardly a true north.
And people prescribe too much value to numbers anyway. By creating a standard, you lock out or diminish the types of genius less selected for in that standard.
And people prescribe too much value to numbers anyway. By creating a standard, you lock out or diminish the types of genius less selected for in that standard.
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.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.
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-gen...).
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-gen...).
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).
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).
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.
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.
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.
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.
>Instead, of getting excited by any of the projects I proposed, Cathy got really, really angry at me for (I guess) intimidating her (?).
I've had similar experiences to this, across work, academia, friends, and online gaming. My thought is that you made her question her personal identity as a mathematician, and this doubt created a state of cognitive dissonance.
Cognitive dissonance gets dealt with in many ways. Some people simply shut down and try to purge the event from memory, and pretend as if it never happened.
Others will deflect and do everything to convince themselves and those around them that their perception of reality is the truth. It seems like few people are actually capable of re-evaluating their current position and coming to some sort of internal compromise.
In the case of dealing with harsh truths about oneself, this can be coupled with some sort of plan or goal to improve and get to the point that they initially believed themselves to be at, and/or that they believe that they deserve to be at.
I think what you experienced is a variant of the former, where her inner turmoil was channeled as anger and projected onto you, because you (inadvertently) made her question her identity, and I've learned that this can cause certain people to experience a complete collapse of how they view themselves.
You can see this happen all the time with people who tie their perception of being "good" at something to their identity, and who have completely exaggerated and inappropriate reactions when something that contradicts that perception happens.
A short-term example of this is the way that people who dedicate lots of time to online team-based videogames and consider themselves "good" players blame their teammates for losses in order to absolve themselves and maintain their identity.
A long-term example is how people react to unwillingly losing their career, due to factors like injury, legal issues, money (when self-employed), or the job simply ceasing to exist due to economic collapse or technology. Something like this is completely devastating for most, and they irrecoverably fall into depression.
I've had similar experiences to this, across work, academia, friends, and online gaming. My thought is that you made her question her personal identity as a mathematician, and this doubt created a state of cognitive dissonance.
Cognitive dissonance gets dealt with in many ways. Some people simply shut down and try to purge the event from memory, and pretend as if it never happened.
Others will deflect and do everything to convince themselves and those around them that their perception of reality is the truth. It seems like few people are actually capable of re-evaluating their current position and coming to some sort of internal compromise.
In the case of dealing with harsh truths about oneself, this can be coupled with some sort of plan or goal to improve and get to the point that they initially believed themselves to be at, and/or that they believe that they deserve to be at.
I think what you experienced is a variant of the former, where her inner turmoil was channeled as anger and projected onto you, because you (inadvertently) made her question her identity, and I've learned that this can cause certain people to experience a complete collapse of how they view themselves.
You can see this happen all the time with people who tie their perception of being "good" at something to their identity, and who have completely exaggerated and inappropriate reactions when something that contradicts that perception happens.
A short-term example of this is the way that people who dedicate lots of time to online team-based videogames and consider themselves "good" players blame their teammates for losses in order to absolve themselves and maintain their identity.
A long-term example is how people react to unwillingly losing their career, due to factors like injury, legal issues, money (when self-employed), or the job simply ceasing to exist due to economic collapse or technology. Something like this is completely devastating for most, and they irrecoverably fall into depression.
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).
You seem to be attempting to validate and excuse behavior that is, frankly, extremely inappropriate and arguably cruel. When I was in my early 20s, something like this would make me very wary of approaching other people in the future, because I would have felt like I did something wrong. It would be legitimately traumatizing, and I am not using that word lightly. You agree that the person you are replying to did nothing wrong, but you are still blaming them.
Reverse the genders in the scenario, and think about it again. Would you still be defending a man who got angry at a female academic peer with no reasonable explanation? Do you still see the dynamics in the same light? Do you still make the same assumptions in regards to the intentions of both parties, and their subsequent reactions?
Reverse the genders in the scenario, and think about it again. Would you still be defending a man who got angry at a female academic peer with no reasonable explanation? Do you still see the dynamics in the same light? Do you still make the same assumptions in regards to the intentions of both parties, and their subsequent reactions?
He talked with her once in pub, she got angry so it did not worked out and that is cruel? Seriously? Reverse gender, a girl got long monologue to dude not allowing him to speak who failing to get his turn got angry and left (or whatever). Normal encounter between two people, nothing to sugest it had anything to do with gender.
For that matter, I don't see dudes being blamed for being angry. It is normal emotion. At worst, it is assumed that they are either alpha or on the spectrum. But you brought up gender which has nothing to do with anything here, not me. She was not friendly to girls who would act the same.
Academic peer has nothing to do with anything. And I did not blamed him. I provided interpretation that does not rely on her being "intimidated".
For that matter, I don't see dudes being blamed for being angry. It is normal emotion. At worst, it is assumed that they are either alpha or on the spectrum. But you brought up gender which has nothing to do with anything here, not me. She was not friendly to girls who would act the same.
Academic peer has nothing to do with anything. And I did not blamed him. I provided interpretation that does not rely on her being "intimidated".
williamstein never told anyone about this event, despite the fact that it bothered him enough to be a clear and distinct memory 15 years later. I am presuming that he did not tell anyone because he did not have any sort of dependable support group to turn to. I want you to think hard about why that may have been the case.
>For that matter, I don't see dudes being blamed for being angry. It is normal emotion.
Do you live in the United States? It is completely unacceptable for anyone to display anger in a public, academic, or professional setting unless they are in a position of power and/or authority. And just because it's acceptable for someone with status to do it doesn't make it okay either. In the case we are discussing, getting angry at someone else is EXTREMELY inappropriate.
>For that matter, I don't see dudes being blamed for being angry. It is normal emotion.
Do you live in the United States? It is completely unacceptable for anyone to display anger in a public, academic, or professional setting unless they are in a position of power and/or authority. And just because it's acceptable for someone with status to do it doesn't make it okay either. In the case we are discussing, getting angry at someone else is EXTREMELY inappropriate.
You are adding own fiction to the story. His own interpretation was thay there is for him conflict between focusing at math and social. That makes people come across sdifferently then they intended - because they don't think about others at the moment. Duh.
As anger goes, u have seen angry American managers and academics and journalists and random friends whether in position of authority or not.
And I dont know why you imply she did not had social status to display anger (as only higher status can do that according to you). His story implies opposite - except again you are adding that aspect. OP did not cared about status not anything else social. He was overly excited about his research.
Nevertheless, if you think anger it self is bad thing, then it is very unhealthy way of living. Such people tend to end up passive aggressive. Anger does not excuse unethical acts nor rude acts, but none such act is mentioned here. Just her being angry.
As anger goes, u have seen angry American managers and academics and journalists and random friends whether in position of authority or not.
And I dont know why you imply she did not had social status to display anger (as only higher status can do that according to you). His story implies opposite - except again you are adding that aspect. OP did not cared about status not anything else social. He was overly excited about his research.
Nevertheless, if you think anger it self is bad thing, then it is very unhealthy way of living. Such people tend to end up passive aggressive. Anger does not excuse unethical acts nor rude acts, but none such act is mentioned here. Just her being angry.
Just a shot in the dark, but from your setup you and another person were meeting up at a bar, and then they got mad when you were only interested in talking about work... Maybe she was interested in you and kept dropping hints and you were impossible to derail from your number theory laptop notes?
As a side note a girl once asked me to help fix her computer in college (both of us majoring in math), and she was slightly annoyed when I came over and couldn't find anything wrong with her computer. It was a laptop, but she said it only caused problems in her dorm room.... I later felt extremely stupid!
As a side note a girl once asked me to help fix her computer in college (both of us majoring in math), and she was slightly annoyed when I came over and couldn't find anything wrong with her computer. It was a laptop, but she said it only caused problems in her dorm room.... I later felt extremely stupid!
"In short, we over-reward those at the top and dismiss the rest. It’s an unhelpful and unnecessary bias that facilitates hero worship, undermines the goal of nurturing creativity and discourages valuable contributions to communities, worthy causes and scientific projects"
I don't think "the rest" are in any way "dismissed", but certainly it's much more interesting to read about a Feynman, Saussure or Pascal, than the more mediocre people around them. Reading about a hard working and helpful but relatively average group of helpers seems profoundly boring, and our attention is quite limited, so naturally all coverage focuses on the more interesting luminairies at the apex.
Besides, it's not even true that all these people were heavily dependent on big teams of helpers, especially not before the mid last century or so.
Did Leibniz get much help? Did Newton rely on dozens of graduate students? Did Dostoyevskiy have a team of writers? Hardly. The geniuses of old worked pretty much alone.
But coming back to the main point, isn't it precisely this "hero worship" that makes the teams work so hard for these geniuses? And why would this focus necessarily discourage any creativity? I don't see why it would. It's not like people, when they inevitably discover that they are not Einstein, give up science completely. The situation is the same in sports, most people are not going to set any records, but they don't stop training, despite the total focus on a few individual top level athletes.
If the author feels that things should be different, why not try writing a book about these teams, and see if people are actually interested in hearing about them.
I don't think "the rest" are in any way "dismissed", but certainly it's much more interesting to read about a Feynman, Saussure or Pascal, than the more mediocre people around them. Reading about a hard working and helpful but relatively average group of helpers seems profoundly boring, and our attention is quite limited, so naturally all coverage focuses on the more interesting luminairies at the apex.
Besides, it's not even true that all these people were heavily dependent on big teams of helpers, especially not before the mid last century or so.
Did Leibniz get much help? Did Newton rely on dozens of graduate students? Did Dostoyevskiy have a team of writers? Hardly. The geniuses of old worked pretty much alone.
But coming back to the main point, isn't it precisely this "hero worship" that makes the teams work so hard for these geniuses? And why would this focus necessarily discourage any creativity? I don't see why it would. It's not like people, when they inevitably discover that they are not Einstein, give up science completely. The situation is the same in sports, most people are not going to set any records, but they don't stop training, despite the total focus on a few individual top level athletes.
If the author feels that things should be different, why not try writing a book about these teams, and see if people are actually interested in hearing about them.
The issue is the expectations this builds.
If the only mathematicians you hear about are apparently the smartest fucking people ever, you might think math isn't for you even though you enjoy it. The message needs to get out that you don't need to be that exceptional to do math. Mostly, its about being interested.
Note that I don't mean interested in the results of math. You need to find the intricacies of a proof interesting (at least some of the time).
If the only mathematicians you hear about are apparently the smartest fucking people ever, you might think math isn't for you even though you enjoy it. The message needs to get out that you don't need to be that exceptional to do math. Mostly, its about being interested.
Note that I don't mean interested in the results of math. You need to find the intricacies of a proof interesting (at least some of the time).
Now do you also think that the average kid starting out in basketball will be put off by, rather than inspired by, the likes of Michael Jordan?
> In short, we over-reward those at the top and dismiss the rest. It’s an unhelpful and unnecessary bias that facilitates hero worship, undermines the goal of nurturing creativity and discourages valuable contributions to communities, worthy causes and scientific projects.
This happens in every research community. The hero worship also tends to over-fund certain areas because of how the agenda is effectively set by a few researchers.
One way that may help fix this is if there's a way to generate a crowd-sourced network of links whose purpose is to plot as a graph the current gaps and challenges of the field. It's perhaps easier in fields with clear subject boundaries like physics.
We could then observe how individual knowledge contributions have helped (are helping) progress the growing knowledge "surface." Young researchers could also observe areas of neglect and attack those instead of going where everyone else is. Reward people who grow the knowledge surface, irrespective of their background.
This happens in every research community. The hero worship also tends to over-fund certain areas because of how the agenda is effectively set by a few researchers.
One way that may help fix this is if there's a way to generate a crowd-sourced network of links whose purpose is to plot as a graph the current gaps and challenges of the field. It's perhaps easier in fields with clear subject boundaries like physics.
We could then observe how individual knowledge contributions have helped (are helping) progress the growing knowledge "surface." Young researchers could also observe areas of neglect and attack those instead of going where everyone else is. Reward people who grow the knowledge surface, irrespective of their background.
I wish companies also realized this. We need to recognize and reward effective groups, not super good individuals. It doesn't matter how brilliant an individual is if they aren't in a group that will leverage that genius. Whatever, still somewhat mysterious, factors make that group work overall are the things the company needs to not trample on.
Amen to that friend. Many have observed this before, but culture trumps everything. Teams that establish viable cultures become engines of value, the mechanisms of corporate life seem to me to be especially designed to prevent that from happening and to dismantle it arbitrarily.
If you want to do math and can and do, then fine. Else, still fine. There's no sense in inserting genius into the situation.
Bluntly, there's only one way to know if someone can do math: They want to and try. If their efforts result in some math, then necessarily they can do math. That's really the only way to know.
Bluntly, there's only one way to know if someone can do math: They want to and try. If their efforts result in some math, then necessarily they can do math. That's really the only way to know.
The press likes to reinforce this "one hero who did it all my himself" myth. They are big part of the problem.
It's not really the press that does this, it is the human psyche. It is why we have celebrities, in any field. Humans love to idolize others, for various reasons that have been deliberated upon for centuries by those in philosophy and psychology.
There is nothing fundamental about this. It stems from a lack of understanding, not human nature.
The concept of a single genius coming up with everything exist mostly to people who don't know any better, not to people who actually have extensive study of the field.
The concept of a single genius coming up with everything exist mostly to people who don't know any better, not to people who actually have extensive study of the field.
Well there are a lot of musings in the field of psychology about why society creates celebrities from a fundamental need to have living idols.
I think you underestimate how much influence media has on people.
I think you underestimate how fundamentally human the actions of the media are.
I see a lot of comments stating that mathematicians have high IQ and high test scores. Is there any data to confirm that or is everyone just speculating?
Mathematicians aren't forced to take IQ tests. This could cause self-selection bias.
The IQ test has a predictive correlation to academic success. How should one be classified if one has a high IQ but is stuck in a poor educational environment (i.e. uninteresting/unmotivational teachers or lack of interest in the area of study)?
https://www.quora.com/What-college-majors-have-on-average-st...
You could use GRE test scores to compare across subject majors. There may be saturation at the top where further differentiation between majors could be possible if the exam material were sufficiently more difficult.
You could use GRE test scores to compare across subject majors. There may be saturation at the top where further differentiation between majors could be possible if the exam material were sufficiently more difficult.
For the perspective of someone to whom the label "genius" hsa often been applied: https://terrytao.wordpress.com/career-advice/does-one-have-t...
Terry Tao is genius, so what does he know :)
His brother, Nigel Tao, who is not quite as genius as him and works in Google has IQ of 180.
His brother, Nigel Tao, who is not quite as genius as him and works in Google has IQ of 180.
Elitism is a form of social stupidity but egalitarianism is socially dangerous when it comes to STEM-based endeavours.
Agreed, unlike other administration-heavy fields such as academics and government, STEM really can't sustain a net-negative contributing subset who are a natural baggage of egalitarianism. Considering the dangers in fields such as engineering and medicine and the many important systems that software fuels there are serious consequences when competency filters are devalued in the name of some idealized form of equality or other social hierarchies or attempting to fulfill some artificial processes in the name of risk aversion.
But in a more practical sense life is too short to be a smart person without having a bit of elitism. Which is both a result of optimization and a bit of cynicism.
You can indeed be a mathematician without being a genius. In the sense you can understand the field and convince enough people of your value to keep you employed.
Every field has tons of busy work and not particularly challenging jobs but jobs that none-the-less need to be done and are ultimately an important piece of the puzzle. So it's true that any field, even STEM, shouldn't be hostile to the 9-to-5ers and the 'middling' bunch, merely because they aren't genius.
That said - if you're going to push those fields forward and make real progress like these two:
> Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture
you have to be top tier. Or close enough to it to feed off the top tier. These are typically the people pushing industries forward which generate work for the middling level tiers who weren't child prodigies. In math meaning the people to work out the details of proofs and finding real world applications.
Talent shortages are usually the result of the work of this tier. So it will always be a symbiotic relationship between the genius/elite and average person. The problem largely then isn't so much the elitism, or the fact their is an elite, but merely that the field was given a false image as being limited to only those types of people. Rather than one that needs (and welcomes) the average-person as much as any other field.
More of a marketing problem than a systemic one.
The people doing middling busy-work aren't going to fill pages of Bloomberg or fill the pages of books like 'Men of Mathematics'. But regardless the fact is there are a small subset at the top are doing pioneering work and that is what makes them interesting. Why else would New Yorker write an extend profile on Grigori Perelman and Shing-Tung Yau? They are interesting because they a small group at the top. If there were a bunch of them then Grigori wouldn't have a million dollar prize for his work nor would layman be praising them.
But in a more practical sense life is too short to be a smart person without having a bit of elitism. Which is both a result of optimization and a bit of cynicism.
You can indeed be a mathematician without being a genius. In the sense you can understand the field and convince enough people of your value to keep you employed.
Every field has tons of busy work and not particularly challenging jobs but jobs that none-the-less need to be done and are ultimately an important piece of the puzzle. So it's true that any field, even STEM, shouldn't be hostile to the 9-to-5ers and the 'middling' bunch, merely because they aren't genius.
That said - if you're going to push those fields forward and make real progress like these two:
> Andrew Wiles, who is credited with solving Fermat’s Last Theorem, and I met Grigori Perelman, who solved the Poincare Conjecture
you have to be top tier. Or close enough to it to feed off the top tier. These are typically the people pushing industries forward which generate work for the middling level tiers who weren't child prodigies. In math meaning the people to work out the details of proofs and finding real world applications.
Talent shortages are usually the result of the work of this tier. So it will always be a symbiotic relationship between the genius/elite and average person. The problem largely then isn't so much the elitism, or the fact their is an elite, but merely that the field was given a false image as being limited to only those types of people. Rather than one that needs (and welcomes) the average-person as much as any other field.
More of a marketing problem than a systemic one.
The people doing middling busy-work aren't going to fill pages of Bloomberg or fill the pages of books like 'Men of Mathematics'. But regardless the fact is there are a small subset at the top are doing pioneering work and that is what makes them interesting. Why else would New Yorker write an extend profile on Grigori Perelman and Shing-Tung Yau? They are interesting because they a small group at the top. If there were a bunch of them then Grigori wouldn't have a million dollar prize for his work nor would layman be praising them.
I thought "genius", properly defined, was an ability to perceive things before the general public can. They discover not only what we know is difficult, but completely change how we think about that aspect of the world. Intelligence is important, but only one part of that quality, and does not have to necessarily be among the highest, as traditionally measured. As Nietzsche is often quoted, it lies on a line very close to madness.
Something I skimmed in a random book recently is that "genius" and "genie" have the same root and origin.
https://en.wikipedia.org/wiki/Genius_(mythology)
https://en.wikipedia.org/wiki/Genius_(mythology)
I regret not getting more into Math in college; only got as far as Linear Algebra even though I was pretty good at it, even relative to people in the class. For some reason, I did believe you had to be really exceptional to major in Math. I think it was, in part, because there were a couple really talented kids in high school and everyone including the teachers put them on a huge pedestal. I never felt like I measured up, and if you were smart but not the type to dominate math league, something like Chemistry or Biology were more suitable. Having since met many math majors and even phds, I know know my assumption was kind of false. I look at those talented kids; they're doing advanced degrees or research at top tier universities, and I realize that wasn't the route you had to be on. Oh well.
I like the idea of genius as derived from genus, and meaning something like a particular kind of excellence, an exemplar of its kind, something's characteristic disposition. One can think of there being not one class of geniuses, but think of it as excellence of a particular kind, in a particular activity, that is related to the intrinsic and highly developed talents or disposition of the genius. So, Rafael Nadal is a clay court genius, because he is a great tennis player, and in addition he puts maximum effort into the kind of tennis that requires it, and his physical, top-spin heavy tennis is ideally suited to the surface.
My first week of grad school at Harvard, Ted Slaman was freaking out a bit, wondering whether he (or any of us) was good enough to succeed at math. I replied (more or less in these words):
"Look. You're brilliant. I'm brilliant. We're all brilliant, or we wouldn't be here. We may not be brilliant ENOUGH to make it, but we have nothing to feel inadequate about."
He calmed down, and eventually went on to have what may have been the best math career of any of us (at least judging by the stature of the department where he wound up tenured).
"Look. You're brilliant. I'm brilliant. We're all brilliant, or we wouldn't be here. We may not be brilliant ENOUGH to make it, but we have nothing to feel inadequate about."
He calmed down, and eventually went on to have what may have been the best math career of any of us (at least judging by the stature of the department where he wound up tenured).
> In short, we over-reward those at the top and dismiss the rest.
This is standard tournament theory: big rewards at the top to provide a strong incentives for excellence. Look at the prize structure in sporting events and at the three-medal rewards at the Olympics. Paradoxically the decline in quantity and quality typically seen after tenure suggests that it works in academic circles: post-docs and assistant professors are doing outstanding work because that's what it takes to "win".
This is standard tournament theory: big rewards at the top to provide a strong incentives for excellence. Look at the prize structure in sporting events and at the three-medal rewards at the Olympics. Paradoxically the decline in quantity and quality typically seen after tenure suggests that it works in academic circles: post-docs and assistant professors are doing outstanding work because that's what it takes to "win".
Or is it that faculty are diverted into keeping the roof on the lab that the post docs and assistant professors work in?
TLDR: "I'm special too, give me more credit for whatever I'm doing."
Egregious logical errors throughout. Would not recommend others read this article.
Egregious logical errors throughout. Would not recommend others read this article.
Maybe one or two of you living are geniuses. At least I can think of two in my lay-man's opinion.
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Everyone is always calling me a genius, but I've learned that they apply the term too loosely, and thus I support much of this article's points. For example, when socializing with my colleagues a couple weeks ago, a very pretty girl asked me at the bar if I wanted a drink. I already had one in my hand, so I told her, "I already have one in my hand." My colleagues, as they often do, said to me after she walked away, "Good to point that out, genius." I will admit that it is very hard to be a genius, and I empathize with others in my same position.
That sounds more like they're making fun of you or mocking you for being an idiot and not realizing that a very pretty girl was interested in you. I will say I've a noticed a lot of book-smart people can be total idiots in social situations.
Like being at a conference and helping an attractive person with a problem on their laptop, and they say "we could take this up to my room so you can work better" and you reply "nah, the WiFi is better in the lobby"?
And they reply, "Hm, good idea, I like it when people watch." And you reply, "Me too, I sometimes get a new client out of it." And their eyes widen, impressed, asking, "How many clients do you have?" And you reply, "In total? I've probably had a few hundred." And in shock they admit this is more than was even mentioned in the autobiography of Casanova himself, at which point you reply, "Casanova was in IT?!"
The author is referring to genius without defining it.
You might say that being 1/1,000,000 in intelligence qualifies as a genius. However, that would still leave around 8000 people smarter in the world. This author seems to limit the word 'genius' to the people that those 8000 people look up to.
When this author talks about genius, she means a genius among geniuses. The population she's calling not-geniuses are in the top 1/10th to 1/100th of 1%.
You might say that being 1/1,000,000 in intelligence qualifies as a genius. However, that would still leave around 8000 people smarter in the world. This author seems to limit the word 'genius' to the people that those 8000 people look up to.
When this author talks about genius, she means a genius among geniuses. The population she's calling not-geniuses are in the top 1/10th to 1/100th of 1%.
Genius itself is a slippery social construct, defined by social position rather than any actual objective ranking.
(Also, the author's a she, genius.)
(Also, the author's a she, genius.)
Are height and eye color also social constructs?
Height and eye color are measurable and meaningful. Intelligence is neither.
what is particularly meaningful about eye color?
Its meaning is evident and reflexive.
Intelligence is measurable and meaningful.
It astonishes me that people can claim with a straight face that it is not. I suspect it is sour grapes or something?
If intelligence isn't measurable, then you would agree that the average frog cannot be reliably distinguished from the average human in terms of intelligence?
Ok, so lets move on from that, and don't give me some painful story about how there are different kinds of intelligence and frogs are 'smarter about eating bugs' or something, please?
Maybe with the benefit of the doubt, you are trying to say that human's are genetically not very diverse, and so you can't find significant differences in intelligence. To that I would say you are certainly not claiming this in good faith, and you have some quasi-political reason to deny something that is obviously true to anyone who has interacted with more than 3 people. (and we can skip the lecture along the lines of 'you can't trust what is obvious and have to pretend that all your beliefs are properly cited or they are invalid')
It astonishes me that people can claim with a straight face that it is not. I suspect it is sour grapes or something?
If intelligence isn't measurable, then you would agree that the average frog cannot be reliably distinguished from the average human in terms of intelligence?
Ok, so lets move on from that, and don't give me some painful story about how there are different kinds of intelligence and frogs are 'smarter about eating bugs' or something, please?
Maybe with the benefit of the doubt, you are trying to say that human's are genetically not very diverse, and so you can't find significant differences in intelligence. To that I would say you are certainly not claiming this in good faith, and you have some quasi-political reason to deny something that is obviously true to anyone who has interacted with more than 3 people. (and we can skip the lecture along the lines of 'you can't trust what is obvious and have to pretend that all your beliefs are properly cited or they are invalid')
Intelligence is somewhat measurable, with some nice big error bounds and a big asterisk for the particularly stark replication problem in psychology.
You can define genius as a mark on the IQ scale, but that certainly isn't the definition being used when people use the word in conversation. That conversational form of genius is the social construct.
You can define genius as a mark on the IQ scale, but that certainly isn't the definition being used when people use the word in conversation. That conversational form of genius is the social construct.
So you really think intelligence can be accurately measured using a single number?
Do you not agree that different people have different talents? Some are good at constructing clever arguments, some can compose beautiful music, and some can solve partial differential equations in their heads.
Do you not agree that different people have different talents? Some are good at constructing clever arguments, some can compose beautiful music, and some can solve partial differential equations in their heads.
thats just being butthurt because we chose to call it intelligence, and somehow not being classically intelligent is understood as a personal insult.
the IQ simply doesnt measure creative genius. if it was called "the test that measures how good a persons brain is at pattern recogniton", you wouldnt care. you'd simply state that you're not particularly interested in logical reasoning.
intelligence, in terms of IQ, is a more or less well defined metric. in popular language, its conflated with "not being a mouthbreather". thats why people get pissy when they dont score above average on an iq test. its kinda pointless, really. people only care about iq tests because of the name.
the IQ simply doesnt measure creative genius. if it was called "the test that measures how good a persons brain is at pattern recogniton", you wouldnt care. you'd simply state that you're not particularly interested in logical reasoning.
intelligence, in terms of IQ, is a more or less well defined metric. in popular language, its conflated with "not being a mouthbreather". thats why people get pissy when they dont score above average on an iq test. its kinda pointless, really. people only care about iq tests because of the name.
It's possible to be a very able, erudite person and not do well on an IQ test. Conversely, it's possible to score highly and be incompetent.
Intelligence is an ill-defined, nebulous quantity. IQ is a precisely defined quantity. Since intelligence is hard to measure and IQ is easy to measure, it's tempting to use one as a proxy for the other. But I, and the other posters above me, just don't find that very convincing.
Intelligence is an ill-defined, nebulous quantity. IQ is a precisely defined quantity. Since intelligence is hard to measure and IQ is easy to measure, it's tempting to use one as a proxy for the other. But I, and the other posters above me, just don't find that very convincing.
Not even a little. But you won't get much respect on HN with that attitude.
Intelligence is meaningless? Do you seriously believe that statement?
Despite the difficulties involves in measuring it exactly, intelligence does exist objectively and is measurable in principle: https://en.m.wikipedia.org/wiki/G_factor_(psychometrics)
Despite the difficulties involves in measuring it exactly, intelligence does exist objectively and is measurable in principle: https://en.m.wikipedia.org/wiki/G_factor_(psychometrics)
She, and exactly. A 1-in-1,000,000 person (like Terry Tao) saying Math and Science need all the 1-in-10,000 people it can get and the focus on the 1-in-1,000,000 people is not helpful is not useful advice for K-12 policymakers. If 1-in-10,000 people say that the 1-in-100 don't receive enough attention, that would be important information to elite college admissions people. But these people have no relevant experience with average people and probably have nothing useful to say about how to educate average kids in average schools.
Personally I think I am at best 1-in-100 smart. I don't know if in the future there will be useful work for people only as smart as I am.
Personally I think I am at best 1-in-100 smart. I don't know if in the future there will be useful work for people only as smart as I am.
I know many mathematicians. Not a single one of them I'd refer to as "genius". Most are very bright. Some think fast.
But for the most of it, they've "just" persistently and wholeheartedly studied their field in mathematics.
Geniuses are rare. Art Tatum, Messi, Tesla, Mingus - those are people you'll have to wait another century to see the equal of. If at all.
But for the most of it, they've "just" persistently and wholeheartedly studied their field in mathematics.
Geniuses are rare. Art Tatum, Messi, Tesla, Mingus - those are people you'll have to wait another century to see the equal of. If at all.
I think you're missing her overall point by focusing on the "genius" label though. Our reward system is set up for those at the very top. But those top performers rely on a whole host of other good-but-not-stellar actors who never see a comparable reward for their efforts.
A genius is somebody shizophrenic enough to make connections where others are incapable off doing so, while still remaining sane enough to filter the results and only ocassionally walk the street naked at night, to escape the satellites tracking him/her with bugs embedded into buttons (lets call it sabatical).
To be this mad is nothing worthy to strive for. It comes with real cons.
Con A: Your family has usual several shizos who are "over the edge", meaning people who are in need of constant care.
Con B: If you get the necessary education to contribute more then spynovellas and abstract art in this unstable family environment, which may include initially getting pushed into engineering/the sciences against your will - boy/girl are you lucky.
Con C: No drugs, no long partying, no chem-triggering yourself of any kind (no, coffee - what a world!)
Con D: Selfisolation tendencies- as perceiving other people as hostile, overinterpreting constantly on theire intent is very tiresome- thus, you end up self isolating to not feel the sting of beeing constant wrong (aka Mad) all along on your spouse.
Con E: Good Connections can also be had by normal people now, if they would go for that. There are several systems to make them and find exotic and interesting solutions. The real problem starts with normal people fighting against new ideas because they pose a risk to there career, there company, the process and there concept of self-worth.
Con F: You are not systematic, meaning for example, to set up a coherent list will be impossible.
Con 8: Martyrers of any kind, in religion become sort of very attractive- or was it the other way around, that martyrer religion produce more durable creative bonkers people? The irony is that israel, america and irans cultural looks very much alike to a bonkers inventor.
Con G: The real trouble starts, when the normal people run out of ressources, and start to vote the "geniuses" as war-chieftains to power, usually after a prolonged episode of "pulling up more Cash obsticles to actual archivers". If you are constantly in danger of beeing the guy/girl who the mob will turn to when they need a witch-streetlight, its a good quality to turn on the needle and point on any group guilty of beeing not part of the mob enough. Thus artists and geniuses- the worst group to look for integrity the day the madmen gets voted to power.
Con H: Sometimes people crash, like computers, and spend the rest of there days iterrating over a "topic" or "obsession" totally not worth it.
Con I: CEOs and Decisionsmakers constantly crowding in on "working" geniuses, trying to deduce the "process". Its laughable- but there is no process. There is no method to learn, there is nothing you can take home from that art-gallery-meetup. The process consist of a mind constantly recombining stuff that is not supossed to be recombined, throwing away metric tons of wrong stuff subconciously and sometimes putting out ideas, with a tacked on invented backstory how they came to be. Thats it. And as you are going to sit on those patents and stuff anyway, and live in constant fear, that all those incremental investments blow up, why fly towards the fire, little moth?
Pro A: Wir sind die Quelle, ihr seid die Senke.
To be this mad is nothing worthy to strive for. It comes with real cons.
Con A: Your family has usual several shizos who are "over the edge", meaning people who are in need of constant care.
Con B: If you get the necessary education to contribute more then spynovellas and abstract art in this unstable family environment, which may include initially getting pushed into engineering/the sciences against your will - boy/girl are you lucky.
Con C: No drugs, no long partying, no chem-triggering yourself of any kind (no, coffee - what a world!)
Con D: Selfisolation tendencies- as perceiving other people as hostile, overinterpreting constantly on theire intent is very tiresome- thus, you end up self isolating to not feel the sting of beeing constant wrong (aka Mad) all along on your spouse.
Con E: Good Connections can also be had by normal people now, if they would go for that. There are several systems to make them and find exotic and interesting solutions. The real problem starts with normal people fighting against new ideas because they pose a risk to there career, there company, the process and there concept of self-worth.
Con F: You are not systematic, meaning for example, to set up a coherent list will be impossible.
Con 8: Martyrers of any kind, in religion become sort of very attractive- or was it the other way around, that martyrer religion produce more durable creative bonkers people? The irony is that israel, america and irans cultural looks very much alike to a bonkers inventor.
Con G: The real trouble starts, when the normal people run out of ressources, and start to vote the "geniuses" as war-chieftains to power, usually after a prolonged episode of "pulling up more Cash obsticles to actual archivers". If you are constantly in danger of beeing the guy/girl who the mob will turn to when they need a witch-streetlight, its a good quality to turn on the needle and point on any group guilty of beeing not part of the mob enough. Thus artists and geniuses- the worst group to look for integrity the day the madmen gets voted to power.
Con H: Sometimes people crash, like computers, and spend the rest of there days iterrating over a "topic" or "obsession" totally not worth it.
Con I: CEOs and Decisionsmakers constantly crowding in on "working" geniuses, trying to deduce the "process". Its laughable- but there is no process. There is no method to learn, there is nothing you can take home from that art-gallery-meetup. The process consist of a mind constantly recombining stuff that is not supossed to be recombined, throwing away metric tons of wrong stuff subconciously and sometimes putting out ideas, with a tacked on invented backstory how they came to be. Thats it. And as you are going to sit on those patents and stuff anyway, and live in constant fear, that all those incremental investments blow up, why fly towards the fire, little moth?
Pro A: Wir sind die Quelle, ihr seid die Senke.
The definition of a genius is someone with an IQ >= 140. Sorry, that word is taken. Embiggen your vocabulary and apply your definition to a more cromulent term.
Eh, no. That's presupposing the conclusion. While the conclusion is correct and validity of IQ is one of the best replicated finding in all of psychology, by "genius" we certainly don't mean "being good at solving IQ test problems". "Being good at solving IQ test problems" happens to correlate with "being genius", but this is an empirical fact and not a logically necessary conclusion.
Well, any other definition is going to be mostly subjective and will not survive a rigorous logical definition that satisfies all parties. Genius and madness seem to be intricately linked. one man's genius can be seen as someone who was insanely obsessive and compulsive about a small domain of knowledge, eshewing every other part of life like experiencing sex (Thank god for Tesla and thank god I am not afflicted with his condition, no matter how much smarter I'd be).
That said, I think one of the hallmark's of genius is that they learn from first principles, maximizing their ability to context switch and apply inherent truths from one domain of knowledge to not only multiple others, but integrate it into their general world view...essentially polymaths.
Knowledge isn't artificially contained in one area, it is part and parcel of the entirety of reality. One detriment of the hyper-specialization promulgated by capitalism is that we may have missed out on some prodigious talents who were siloed away studying in one field.
Thankfully, we're seeing the pendulum swing back as multi-disclipinary approaches are becoming more popular, thanks in no small part to the rise of Information Technology. Being able to use a computer increases your ability to learn almost anything faster.
That said, I think one of the hallmark's of genius is that they learn from first principles, maximizing their ability to context switch and apply inherent truths from one domain of knowledge to not only multiple others, but integrate it into their general world view...essentially polymaths.
Knowledge isn't artificially contained in one area, it is part and parcel of the entirety of reality. One detriment of the hyper-specialization promulgated by capitalism is that we may have missed out on some prodigious talents who were siloed away studying in one field.
Thankfully, we're seeing the pendulum swing back as multi-disclipinary approaches are becoming more popular, thanks in no small part to the rise of Information Technology. Being able to use a computer increases your ability to learn almost anything faster.
I wasn't sure if this comment was fine irony, but apparently it was meant in seriousness. To me, your definition makes the notion of genius almost meaningless. True genius for me has to have an aspect of transcendence, of deep and abiding insight or beauty. Measuring it using IQ is completely beside the point.
A 140 IQ puts someone around the 99.5 percentile, but not even among mathematicians would I venture that 1 out of every 200 is a genius. If you're talking about the general population, then that's just even more incredible.
A 140 IQ puts someone around the 99.5 percentile, but not even among mathematicians would I venture that 1 out of every 200 is a genius. If you're talking about the general population, then that's just even more incredible.
I think the point he's trying to make is that the definition for the word "genius" is very clear. It's defined as an IQ >= 140. You can't say that _for you_ it means something different. That's like saying, _for you_ a convex function means something different than the mathematical definition. It's fine that you think it means something different, just use a different word, not the word "genius".
> I think the point he's trying to make is that the definition for the word "genius" is very clear. It's defined as an IQ >= 140.
Where did you find this definition of "genius"? Maybe someone decided that "genius" means someone with and IQ >= 140, but I haven't found any evidence that it's the definition.
For example, Merriam-Webster's definition [1] seems to be closer to tacomonstrous's usage. In fact, the only mention of IQ it makes is "a person endowed with extraordinary mental superiority; especially : a person with a very high IQ".
[1] https://www.merriam-webster.com/dictionary/genius
Where did you find this definition of "genius"? Maybe someone decided that "genius" means someone with and IQ >= 140, but I haven't found any evidence that it's the definition.
For example, Merriam-Webster's definition [1] seems to be closer to tacomonstrous's usage. In fact, the only mention of IQ it makes is "a person endowed with extraordinary mental superiority; especially : a person with a very high IQ".
[1] https://www.merriam-webster.com/dictionary/genius
No dictionary I'm aware of carries the IQ based definition of the word, so I'm not sure how anyone can claim with such authority that this is the case.
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Exactly. I was just listing the technical definition. IQ tests are far from perfect, but they are an empirical measure
Where does that definition come from? The root of the word is from birth and creation, not problem solving. The word is often applied to artists and musicians - is Keith Richards blessed with an IQ of 140? I think that it is generally agreed that Keith Richards is a genius, but his ability to make decisions is... questionable. Van Gogh is another, a life of terrible decision making, huge creative transformations, interventions that turned painting forever. Do you deny that these people should be called Geniuses because they wouldn't (or could) score highly on a test?
The definition comes from the Stanford-Binet IQ test.
> is Keith Richards blessed with an IQ of 140? I think that it is generally agreed that Keith Richards is a genius, but his ability to make decisions is... questionable.
How do you feel about it? I don't really care for the Rolling Stones or that type of rock music in general, so I'm not qualified to make an opinion here
> Van Gogh is another, a life of terrible decision making, huge creative transformations, interventions that turned painting forever.
I'm not really a big fan of his work. It doesn't elicit a strong emotional response in me. Perhaps because of its ubiquity, it seems like "default art". Then again I don't know much about painting or art history to offer a strong opinion.
If we're going to be subjective, and I know this will be very controversial, I consider Arnold Schwarzenegger a genius in his field. He's the greatest bodybuilder of all time and will most likely remain so if the tradition of doing as many steroids as possible continues in the Mr Olympia competition. Arnold did steroids as well, but he sculpted his body to look like Hercules, as opposed to modern winners who look like Abomination( The Hulk's major foe).
Also, in a very narrow way, his acting is genius. He plays the role of an assassination robot better than anyone. Note, I'm not saying he's great at portraying a synthetic intelligence in general (like Ava from Ex Machina)
The point of having a technical definition is not to exclude those in the past, it is so that going forward it has a precise, empirical definition that everyone can all agree on. I'm not wedded to the word so it can also be brilliant, prodigy, virtuoso, etc. Many words in common parlance once had specific medical/clinical meaning like idiot, moron, etc.
> is Keith Richards blessed with an IQ of 140? I think that it is generally agreed that Keith Richards is a genius, but his ability to make decisions is... questionable.
How do you feel about it? I don't really care for the Rolling Stones or that type of rock music in general, so I'm not qualified to make an opinion here
> Van Gogh is another, a life of terrible decision making, huge creative transformations, interventions that turned painting forever.
I'm not really a big fan of his work. It doesn't elicit a strong emotional response in me. Perhaps because of its ubiquity, it seems like "default art". Then again I don't know much about painting or art history to offer a strong opinion.
If we're going to be subjective, and I know this will be very controversial, I consider Arnold Schwarzenegger a genius in his field. He's the greatest bodybuilder of all time and will most likely remain so if the tradition of doing as many steroids as possible continues in the Mr Olympia competition. Arnold did steroids as well, but he sculpted his body to look like Hercules, as opposed to modern winners who look like Abomination( The Hulk's major foe).
Also, in a very narrow way, his acting is genius. He plays the role of an assassination robot better than anyone. Note, I'm not saying he's great at portraying a synthetic intelligence in general (like Ava from Ex Machina)
The point of having a technical definition is not to exclude those in the past, it is so that going forward it has a precise, empirical definition that everyone can all agree on. I'm not wedded to the word so it can also be brilliant, prodigy, virtuoso, etc. Many words in common parlance once had specific medical/clinical meaning like idiot, moron, etc.
No, outside of some contexts (i.e. the technical jargon of some domain/field of research/community), the definition of genius is not "140+ IQ".
Yes, in one context that definition could be valid, but in general discourse something like the generic "Exceptional intellectual or creative power or other natural ability" from https://en.oxforddictionaries.com/definition/genius would be a much more relevant definition.
Yes, in one context that definition could be valid, but in general discourse something like the generic "Exceptional intellectual or creative power or other natural ability" from https://en.oxforddictionaries.com/definition/genius would be a much more relevant definition.
Outside of that context, it fails to have any consistent meaning, especially if relying on creative power.
The technical definition makes it so that
I'm not proclaiming that the Iq test is the measure, or even a good measure of intelligence. I happen to think it is heavily biased and what it really tries to measure, imprecisely, is your potential for success in the system in which it was created.
Doubtlessly, they were geniuses among people before the development of language and mathematics. For example, let's presuppose some genius hunter who had a knack for catching prey without breaking a sweat, made the best fishing lures and hunting traps, could predict migration patterns, could track any creature, can use his/her sense of smell to predict the weather, etc. It has been argued that hunter-gatherers were even more intelligent than modern humans as they had a larger skull, indicating a larger brain. However, the IQ test would not rate him well.
That still doesn't contradict the point I was trying to make. A technical definition means that being a genius becomes a matter of fact, not a matter of opinion. It could just as easily be another word. Otherwise, discussion just dissolves into subjective opinion.
The technical definition makes it so that
I'm not proclaiming that the Iq test is the measure, or even a good measure of intelligence. I happen to think it is heavily biased and what it really tries to measure, imprecisely, is your potential for success in the system in which it was created.
Doubtlessly, they were geniuses among people before the development of language and mathematics. For example, let's presuppose some genius hunter who had a knack for catching prey without breaking a sweat, made the best fishing lures and hunting traps, could predict migration patterns, could track any creature, can use his/her sense of smell to predict the weather, etc. It has been argued that hunter-gatherers were even more intelligent than modern humans as they had a larger skull, indicating a larger brain. However, the IQ test would not rate him well.
That still doesn't contradict the point I was trying to make. A technical definition means that being a genius becomes a matter of fact, not a matter of opinion. It could just as easily be another word. Otherwise, discussion just dissolves into subjective opinion.
The word "genius" in the modern sense (extraordinary inborn mental ability) is about 200 years older than the practice of IQ testing, and it went through at least two definitions before that. The common theme has been that genius is something innate to the individual. Nobody has a claim on the word, especially not the super dubious psychometric community.
Would you please not post unsubstantive comments to HN? At some point Cunningham's Law blends into trollery.
We detached this subthread from https://news.ycombinator.com/item?id=14532068 and marked it off-topic.
We detached this subthread from https://news.ycombinator.com/item?id=14532068 and marked it off-topic.
> Would you please not post unsubstantive comments to HN?
I take issue with this. How is the content unsubstantive? It wasn't untrue or misleading, it is just what the Stanford Binet IQ test classifies as genius. so that it being one becomes a matter of fact, not of opinion.
> At some point Cunningham's Law blends into trollery.
Now that I reread my comment, I see how it can be misconstrued as snarky. That was not at all the intention. It was meant to be self-deprecating and lighthearted, as I was using made-up words while criticize someone for not using made-up words. I thought about adding a smiley face so as to make my intentions clearer, but emoticons aren't really used on HN.
I'm about as anti-troll as you can get as I believe them to be parasites of the internet and a brief look at my comment history would elucidate than I am always if not I'm not earnest, helpful, or passionate in discussion, I am positive in tone.
Look at the amount of discussion it generated before being pruned and the varying opinions on what constitutes "genius". It's not that big a deal, but this is the first time I can ever recall having a comment moderated in my nearly 25 year history of using the internet. I see how it can be interpreted as snark, but when moderating, perhaps take the user's history into account.
For my part, I will make my intentions more obvious so that they will not be interpreted as negative or as an attack.
I take issue with this. How is the content unsubstantive? It wasn't untrue or misleading, it is just what the Stanford Binet IQ test classifies as genius. so that it being one becomes a matter of fact, not of opinion.
> At some point Cunningham's Law blends into trollery.
Now that I reread my comment, I see how it can be misconstrued as snarky. That was not at all the intention. It was meant to be self-deprecating and lighthearted, as I was using made-up words while criticize someone for not using made-up words. I thought about adding a smiley face so as to make my intentions clearer, but emoticons aren't really used on HN.
I'm about as anti-troll as you can get as I believe them to be parasites of the internet and a brief look at my comment history would elucidate than I am always if not I'm not earnest, helpful, or passionate in discussion, I am positive in tone.
Look at the amount of discussion it generated before being pruned and the varying opinions on what constitutes "genius". It's not that big a deal, but this is the first time I can ever recall having a comment moderated in my nearly 25 year history of using the internet. I see how it can be interpreted as snark, but when moderating, perhaps take the user's history into account.
For my part, I will make my intentions more obvious so that they will not be interpreted as negative or as an attack.
In terms of IQ, I think mathematicians are averaging something like +2 SD (>= 130). They are certainly "geniuses" (or "gifted"). But they themselves don't think they are geniuses, because by that word they mean +4 SD (>= 160) people.