Social and Emotional Problems Affecting Mathematically Gifted Children
There is no question on both the intelligence and competence in mathematics for most students/users here in Brilliant. But as I pursue my career as a teacher (teaching mathematics), I figured out already several issues underlying children's giftedness and that includes social and emotional breakdown as they seek more knowledge about the particular discipline they like most. The symptoms associated with this are obsession and frustration.
Lets take for example Ted Kaczynski. He was a child prodigy in mathematics. Kaczynski excelled academically, but found the mathematics too simple during his sophomore year. Sometimes he would cut classes and write in his journal in his room. During this period of his life, Kaczynski became obsessed with mathematics, spending prolonged hours locked in his room practicing differential equations. Throughout secondary schooling, Kaczynski had far surpassed his classmates, able to solve advanced Laplace transforms before his senior year. He was subsequently placed in a more advanced mathematics class, yet still felt intellectually restricted. Kaczynski soon mastered the material and skipped the eleventh grade. With the help of a summer school course for English, he completed his high school education when he was 15 years old. He was encouraged to apply to Harvard University, and was subsequently accepted as a student beginning in 1958 at the age of 16. While at Harvard, Kaczynski was taught by famed logician Willard Van Orman Quine, scoring at the top of Quine's class with a 98.9% final grade.
Kaczynski graduated from Harvard University in 1962, at age 20, and subsequently enrolled at the University of Michigan, where he earned a PhD in mathematics. Kaczynski's specialty was a branch of complex analysis known as geometric function theory. His professors at Michigan were impressed with his intellect and drive. "He was an unusual person. He was not like the other graduate students", said Peter Duren, one of Kaczynski's math professors at Michigan. "He was much more focused about his work. He had a drive to discover mathematical truth." "It is not enough to say he was smart", said George Piranian, another of his Michigan math professors. Kaczynski earned his PhD with his thesis entitled "Boundary Functions" by solving a problem so difficult that Piranian could not figure it out. Maxwell Reade, a retired math professor who served on Kaczynski's dissertation committee, also commented on his thesis by noting, "I would guess that maybe 10 or 12 men in the country understood or appreciated it."
Despite of his fruitful careers and pure mathematical intelligence, at the later part of his life was spent behind bars. He was imprisoned for bombing structures and killing people. He was aliased as UNABOM (UNiversity and Airline BOMber). He was anti-social and Neo-Luddist (anti-technological thinkers). For more infos.....
This time I would not ask more about mathematics. As a future techer I am concerned on how other aspects of human such as social and spiritual are also developed aside from the mental and cognitive aspects. There is no more question with regards to your mental capability but the question here, how's your attitude, how you interact with other people, do you still feel being a normal person?
Please don't take it as a negative connotation, but I am just willing to know what are your stands for this.
Note by
Mharfe Micaroz
7 years, 11 months ago
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I am not enamored of imprecise reasoning and the drawing of parallels and causation on the basis of infamous anecdotes. That is not an evidence-based approach; it is not scientific to put it kindly, and it is sloppy thinking, to put it honestly.
If you are going to put forth the thesis that mathematically gifted individuals exhibit a higher incidence of social dysfunction than the population at large, then spending most of your argument describing Dr. Kaczynski's background is unpersuasive. Would you say the same of John Allen Muhammad or Timothy McVeigh, neither of whom were "mathematically gifted?" My point is that your citation is a form of confirmation bias. That is a mistake I would not expect someone who is proficient in mathematical thinking to so readily make.
A starting point to any actual evidence that you would need to furnish to support your claims might come in the form of a randomized psychological study of a reasonably large sample of people who have received their advanced degree in the pure or applied mathematical sciences, and compare those results with a control group. Otherwise, you are simply making assumptions on the basis of stereotypes and impressions. In my experience, the vast, vast majority of my colleagues are no more or less well-adjusted socially than anyone other educated individual--if anything, it has been my experience that it is the lack of education which is correlated with inappropriate behavior and antisocial viewpoints.
I will conclude my response with a question, to test one's understanding. Let G represent the event that a randomly chosen individual is mathematically gifted. Let A represent the event that a randomly chosen individual exhibits some form of antisocial disorder. Which is the more appropriate conditional probability to consider, Pr[A∣G] or Pr[G∣A]?
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And of course, this relates to Conditional probability and Bayes' Theorem
I have such good timing!
I like your perspective. I also want to add to your thoughts this: why exactly does this social stereotype exist?
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That's a good question to ask. I can only make a speculative answer, based on interactions I have had in the past, as well as what I have observed in social situations involving other people.
But before I get to that, I would like to point out that being socially awkward does not necessarily correlate or cause sociopathy. One can be remarkably inept at handling social situations but have no interest in blowing up federal buildings. In fact, as the example of John Allen Muhammad shows, one can be so charming that it is possible to manipulate others into being accomplices. It is far more reasonable to postulate that other factors are much more influential in predicting sociopathy than one's mathematical talent.
As for hypotheses regarding being socially awkward, I would guess that the stereotype exists in part because it is most commonly during childhood or adolescence when an interest in math and science becomes apparent, and our culture as a whole has something of a problem with intellectual pursuits. Thus, such activity is mocked as "nerdy." I could elaborate on this phenomenon further, but suffice it say I think this has consequences for one's social development.
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I agree. And the sad thing, as with all stereotypes, is that a few infamous examples occur and a lot of people get the wrong idea. They project these odd cases onto the normal population of interest.
I think that I have a unique perspective on this situation, insofar as I am completely enamored with mathematics, but I live a healthy social life. When I was in second grade, I had to move to a new school. Naturally introverted, I had no friends all of second grade. I wouldn't play at recess, I would just wait to go back inside. I then made a few successive groups of friends that were not the most caring in the world, but now I am at a better situation. With a strong and loving friend base, I even have a girlfriend! Even though I love math and could do it all day, none of my friends have an inclination towards math. I suspect that this has hindered my overall mathematical ability and drive (so thank god for brilliant), but that's not really the point. I just wrote all of this to show you that I have a working and valid understanding of society.
I'm also quite an obsessive person. I can easily see how someone would spend hours a day doing math. But many of the more ignorant in the world can't. Because they don't understand it, they dismiss it as weird. Thus, many of you "math geeks" are somewhat ostracized by society, and then you don't even try to make friends. It's logical, but unhealthy.
Some people are just natural recluses. "Only 10 or 12 men in the country can appreciate him" But they don't have to be. It's all about choosing your priorities.
I find myself, day in and day out, thinking about math. But since I know the people around me don't like to hear it, I keep my mouth shut and vent on sites like brilliant. I can assure you that I am the only student in my high school of 1600 kids that loves math this much. So even at school, I can't talk all I want to talk about math.
The fact of the matter is, there are very few gifted children out there. We don't get taught in normal school to the level we need, and much like Kaczynski, we feel a need to leave society and pursue our passion. Even though my mathematics has suffered, I'm thankful I didn't leave society and become a hermit. Sometimes you get the best insight from everyday people and things.
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I echo your sentiment. One aspect of the Brilliant community that we want to achieve, is to help students realize that they are not alone in their (obsessive) pursuit of math / science / etc, and to help them connect with others worldwide. It also helps for students to realize that there is always someone out there who is smarter than them in a particular area, and also possibly younger than them!
I was lucky to grow up in Singapore, with a land mass of 275 square miles and 3 million people, and hence the school systems could easily identity the talented students and connect them up, and we could even have almost daily interactions. In larger geographical regions, this becomes much harder to achieve, with such activity limited to weekly "math circles / math clubs" during the school year. Whereas, in Singapore, we could have a 6-week "camp" where the participants could return home everyday, instead of also providing room and board (and not to mention dealing with concerned parents).
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Right. I live in a more rural area of ohio, and my school doesn't even have any math related club (I plan to change that this coming year). The only mathematical enrichment my school offers is the amc. There was actually a time, last summer, when I had the opportunity to go to a math circle camp in NYC. It was a great experience, but a very humbling one! Back in ohio I am in the top of my class, surely the best at math, but as you said, there do exist those younger than me that are twice as good as me! Everyone needs to be humbled every once in a while.
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At my school, there are only olympiads for grade 8 and lower. I've always been (among) the best in maths and physics, but there was not too enjoyable, as the only thing we're taught is boring formulas and tricks, not interesting maths.
Online, I accidentily stumbled on the math olympiads, which you usually qualify for through school, and although my school didn't participate, I got in. I feel very lucky that I got a last shot at the olympiads, as next year, I'll be too old. Due to the previous years without any awareness of the olympiads, I fell behind on olympiad topics, which I especially noticed when I discovered AoPS and Brilliant.
On the one hand, the fact that some people are so much better at maths than I am, makes me question whether I will be able to qualify for the 2014 IMO (which is my ultimate goal), but it also gives me something to strive for, as I didn't really have any competition at high school.
The math circles (or anything alike) in The Netherlands are very limited: only if I make it to the best 25 of the country, I'll be part of a math group preparing for the IMO, but that's mostly through internet, as we would only be physically together just a few times in the whole year.
This is such an intriguing story. I agree with most of Kaczynski's views of the society, although he thought he could change everything by sheer force
It is the general vibe among most(not all) people to enjoy life to the fullest, not caring about how their activities could have repercussions that could harm the environment around them. Not that they are wrong, but sometimes I get the feeling that humans think they are something very important and, then there is all the unhealthy competition that forces people to get obsessed with what they do. If competition could be replaced with co-operation after a certain level of development of an individual, I think it would eliminate the feelings of superiority and inferiority to some extent. We can spend more time thinking about the environment around us rather than outclassing and demeaning others. Not that competition is bad altogether.
I don't know why but I limit my social interactions as much as possible. The more you talk, the more you have to follow the rules and systems of the society. It is better to lock yourself in your room and study math. I don't dislike people but sometimes I really wonder, why are we humans always so keen on our own career, goals? Why do we have to care so much about emotions, just because we think they exist?
In my life I have observed that children who are mathematically gifted tend to be more polite and helpful. My school was unable to quench my mathematical thirst because of mathematically non-gifted students. So, to prepare for IITJEE, I joined a coaching institute which trained me at math, physics and chemistry. There I was among the top students in my city. The people there were very good human beings (both teachers and students) apart from being proficient in studies.
The environment in my school is the opposite (there are a few good people, though). More annoying is the fact that some students discourage gifted students from studying by always making fun of them and discriminating them.
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see most of the people are like that .......its advisable not to mingle with them
I think that mathematically gifted kids are actually encouraged to be antisocial. It's a stereotype and if people know you're clever, they assume you'll be antisocial. When i was three, i was sent to a psychiatrist to see if i had Asperger's syndrome and my dad practically exploded when he implied it was obvious i would have some kind of social disorder given that my parents had both done degrees in maths. At school in maths i'm expected to sit in a corner working through a-level problems and so i don't know how to talk to people normally. I also read too much and most of my friends are the kind of people that don't mind if i don't talk, because no one ever understands what on earth i'm talking about. I'm also quite an obsessive person, mostly because all my family is clever so if you want to keep up self esteem, you have to work way hard, and i think it's very easy to just get so stuck in a niche that if you ever came out the world looks completely alien and it's too much effort to come back to it. I don't think it's so much the being good at something that's bad for you because from what I've observed, in my school,most slightly clever people just like excelling instead of making it a big part of their life- It's the reading too much that seems to be the trouble in my case. Maybe those are just problems that i experience, but most of my family seem to be antisocial in one way or another and it's the cleverest ones that are worst off so it does seem linked.
Well, I suppose I'm "mathematically gifted" to some extent, though attending a camp for math humbled me to the point that I actually felt idiotic in comparison to those who had done and learned much more math than me. I only really became more introverted once I realized how different my interests/intelligence (my perception of it) was from my peers. Anyways, I think the biggest problems facing gifted adolescents are depression and feelings of alienation. The depression comes when contemplating existential questions, like how good I am objectively in the world or if anything I learn really matters, and the alienation is felt both when I am among peers and can't talk how I want to and when I am among those who are smarter and my age or younger and I feel like I do not belong there either. Sorry for writing with such poor structure right now. I'd edit, but I have some proofs to do!
Well, i think there is no connection between maths and being antisocial. But actually I think that people start becoming antisocial, when people begin eliminating them from their own group or society.
As I experience today, here in Philippines, at a Science High School, I am mathematically talented and almost perfected all tests my teachers gave me but it came to this point that I have to prioritize math really... It's more than dedication... it's sacrifice... I sacrificed my whole academic career in a math subject only. I am currently 15 years old and I studied Calculus already and Discrete Maths. If time permits me, I would continue my learning even to the Complex Analysis level... In my school, most of my classmates tell me that I am a nerd in Math for learning a lot of things.... Whenever we have requirements in school, I feel being tortured by other subjects except math.. In short, I have an obsession on the subject matter.
I don't really know how to correlate the above incident. But the following paragraph describes a relation between math and social interaction . Although I don't judge whether its right or not but this is my perception. The reason why possibly social awkwardness is related to gifted mathematical capabilities is because the subject itself tells us not to eliminate every possibility. And this possibility factor which keeps our mind pondering over the issue of the best way to interact with society such that the outcome would be maximized to a factor which is almost equal to my effort. The question of making "the" move dictates over our brain and we end up not taking any action. But we never rule out the fact that time is moving while we are thinking and to other people this looks pretty annoying and uninteresting. The way we inculcate mathematical logic with our day to day life makes things quite rigid. Although this phenomena is due to a general tendency to avoid mistakes that every gifted mathematician is scared of in an unknown field. The social interaction is the field that makes him neurotic. And to know a certain field in a particular situation it performs certain awkward experiments to know the maximum and minimum talking with involvement with variety of factors. And so does some seemingly illogical things. That is my observation ,though I have no precise reason for this. And the above things may be crap but thats the only thing that stimulated when I read the title.I'm not gifted I'm just good at math so the possibly the above statements may be missing some elements .
is there are really 2 different type of people mathematically gifted and mathematically not gifted?
then how to identify them?
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Good idea.
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I think I might have been wrong.
pls reply.....
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mathematically gifted people are the people that have a click moment where they understand unlike most people i observe who memorize the function and working out format for each particular type of problem
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wow I don't even remember writing this.
Mao lagi nang giingon nila nga mabuang ka sa subraan ka brayt. Tanawa si Kaczynski mura nag rebelde. Kinahanglan jud nga average ra ang atong kabrayt arun average rapud atong pagkabuang... XD.. kasabot ka ani bisaya bitaw ka.
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Apir!.. Kasabot ko sa imuha..jejeje
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hahahaha.. lage sir.. maestro ka diba?
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ongoing pa kung kaluy-an.. im 4th year college..ikaw?
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aw... 1st year paku ya uie...
Given 2a3b=432, where a and b are positive integers, what is the value of a+b? how to answer ?
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You should create a separate discussion for this question.