7 ms·

Mathematical genius is fragile

86 points by fjmubeen 10y ago

malanj 10y ago
The author lost me at "Mathematical genius resides within every one of us — most people just don’t know it yet." The movie Ratatouille captured the sentiment much better, "a great chef can be anyone". Which is not the same as "anyone can be a great chef". It seems the author is mixing up those two. I fully agree that gender, background, schooling, etc is not the key determination of genius. However, saying anyone could be a genius is disingenuous.
- ZeroFries 10y ago
  A 7ft tall pro basketball player resides within every one of us.
  - throwaway5752 10y ago
    Not every 7' tall person is a great basketball player, and not every great basketball player is 7' tall. With all due respect, what you say is a consummate example of "dangerously bad idea that makes a good sound bite". Most mathematicians out there are not Hilbert, Gauss, Riemann, or Euler. They are reasonably smart people that work hard over long periods of time to learn their craft and their field, and make incremental progress in the niches they specialize in. Most people can be productive mathematicians, they just don't believe in themselves.
    - madgar 10y ago
      You are conflating genius with productivity. In so doing you are missing the point of both your parent and grandparent poster.
      - lordnacho 10y ago
        He is, and he's right to. Every single example of a genius ever has become so because of high productivity.
    - dagw 10y ago
      not every great basketball player is 7' tall In fact look at any list of the greatest basketball players of all time. Very few of them are 7' tall. Now look at a list of pro basketball players over 7', most of them are middle of the road journeyman players most people haven't heard of.
      - ZeroFries 10y ago
        I feel like this is a trick of statistics. Very few people, in general, are 7' or taller, and very few people are the best at basketball. See (1), and replace "have disease" with "7' or taller", and "test comes back positive" with "good at basketball". 1: https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml
      - ktRolster 10y ago
        Add to your point: the vast majority of 7' tall people are not very good at basketball.
    - ZeroFries 10y ago
      I doubt most people have the desire to be productive mathematicians, which is as required to be a good mathematician as being 7' tall is for playing basketball (aka not actually required, but big help). "Most people can be productive mathematicians, they just don't believe in themselves." Most people can X if Y, where Y is not the usual case. Again, believing in yourself, having the desire to be great at something, etc, are all included in the extremely large set of factors which determine whether someone will be good at any given activity. To say a large portion of the population can be good at some activity, knowing full-while that they do not possess most of the helpful attributes, is disingenuous.
    - Tomminn 10y ago
      Actually, if you are a 7' tall American, you have a >15% chance of playing in the NBA.
- sporkenfang 10y ago
  Being a hard worker is easier than being seven feet tall, though. I know it's disingenuous to say hard work will get you everywhere, but working your ass off and being confident about it will get you pretty far.
  - simion314 10y ago
    It depends, so actual math problems involve creativity and not brute force, though most of the problems in schools involve trying known recopies/algorithms to solve something if you check the problems people solve on international competition all of those involve creativity. But of course without hardwork you will not have a solid base for your creativity to work with.
  - avatarlite 10y ago
    In my experience, qualitative arguments of the form above rarely change people's minds but a quantitative model will help. The question asked is the causal network that contributes to mathematical genius and the distribution of contributing causal factors within the population -- P(genius | factors) Various factors are clearly involved: P(genius | intelligence), P(genius | hard work), P(genius | self-confidence), and so on. If we accept that those functions are probably not uniformly distributed and that some have a stronger impact than others, we can see that most arguments can be reduced to describing those functions or describing the distributions of those factors among the population. Where most educated people's intuitions lead them astray is that the experience of segregation in higher education and employment has led them to vastly underestimate the actual variance in factors like intelligence, hard work and self-confidence among people. Vanishingly few individual actually possess the right combination of factors required for mathematic genius.
- Moshe_Silnorin 10y ago
  Math is a high IQ game. Anyone who tells you otherwise is kidding themselves.
  - deepnotderp 10y ago
    Except iq is a terrible metric....
    - Moshe_Silnorin 10y ago
      Why?
      - ktRolster 10y ago
        Because they are calibrated not to measure innate intelligence, but our own cultural norms. The canonical example might be, imagine you were lost in the Australian outback. Would you rather have Albert Einstein as your guide, or a skilled Aborigine? The Aborigine would likely get a low score on logic puzzles, but at highly skilled activities like way-finding and tracking game, he would beat Einstein hands down. IQ doesn't measure intelligence, it measures artifacts of intelligence that appear in our culture. Also, it's a mistake to think that IQ is static. There have been studies that show wild swings in IQ over time, especially in teenagers, and even changes in the collective IQ of a culture (the Flynn effect). In addition, it seems likely that a person could study and improve their IQ score. The counter-argument is that although IQ tests have flaws, they are still to some degree a predictor of success in life.
        Moshe_Silnorin 10y ago
        https://en.wikipedia.org/wiki/Raven's_Progressive_Matrices https://en.wikipedia.org/wiki/Raven's_Progressive_Matrices
        deepnotderp 10y ago
        This^^. I think another great example would be IQ tests in the army during WWI (and I think II?) in which one of the questions asked about a type of gun, which no one today would know, and other questions were like that as well. The point is that it measures cultural perceptions of intelligence, ie during WWI knowing your guns was considered intelligence.
- deepnotderp 10y ago
  So there are many fields of math, and you find you're good at one type,and even be a genius in that field...
- Jillboy 10y ago
  Why is that? Why do you claim not everyone has the potential to become a math genius? Do you have any evidence to back that up (besides Ratatouille)?
  - distances 10y ago
    Surely you don't mean to suggest that we all start with equal chances of attaining any and all skills?
    - Jillboy 10y ago
      Any and all skills? No. Mathematical and other related intellectual skills? Why, yes, I do. Despite what most people say, I've never seen a genius who hasn't worked at least twice or thrice as hard as his peers. I've never seen a child that, without the help of any tutors at an early age, or without any influence from their parents, was simply spitting out non-trivial theorems from an early age. I have a hard time believing that some people are BORN better at math and logic than others, and I've yet to see any evidence to suggest that. Quite on the contrary, I've seen plenty of evidence to suggest that genius is at all not genetic, and that you can train children to become prodigies, and later, geniuses. Surely you've heard of Judit Polgár, universally considered the best female chess player of all time? She was made a genius, not born. Her two sisters grown to become Grandmasters as well. And here's Dr. Frankenstein: https://en.wikipedia.org/wiki/László_Polgár https://en.wikipedia.org/wiki/László_Polgár
  - RangerScience 10y ago
    I only have anecdotal plus a bit of thinking...? Talent is pursued interest; genius is pursued passion. Most people won't have passion for mathematics, even if such passions were heartily encouraged - at the very least, because there are so many other things to also be passionate about.
    - Jillboy 10y ago
      I can get behind that, if we defined genius to be pursued passion. Not everyone has a passion for mathematics, that is true. I just thought what the root post was implying is that even if you're passionate, you might not have the potential to achieve genius-level skill because that would somehow be genetically predetermined. If that was what he was implying, I'd love to see some evidence to support the claim.
- lutusp 10y ago
  > The author lost me at "Mathematical genius resides within every one of us — most people just don’t know it yet." An unfortunate hyperbolic opening line, the remainder of the article is much better. > However, saying anyone could be a genius is disingenuous. But genius isn't an identity, it's a possession. It's often a currency with limited utility. Consider Bill Shockley, Nobel Prizewinner, co-inventor of the transistor -- he possessed a narrow, specific area of genius, held by someone otherwise quite ordinary and even deplorable (he was a racist who lectured on the imagined inferiority of black people). Consider Henry Ford, inventor of efficient factory methods, but a rabid anti-Semite. Identifying genius as a possession, not an identity, greatly clarifies its role in our lives. It can keep us from expecting a person to be smart about more than one or two specific things.
- zizzles 10y ago
  I got just a little further than you, until I reached "women make the best mathematicians" where I instantly ALT-F4'd Google Chrome and added 'medium.com' to a permanent blacklist. Truth of the matter is, math IS a high-IQ game, albeit average intelligence specimen can become semi-competent with time and practice (the payoffs of this pursuit are negligible)
  - ricree 10y ago
    >where I instantly ALT-F4'd Google Chrome and added 'medium.com' to a permanent blacklist Medium.com is essentially just a blog host, isn't it? Seems a bit harsh for one story you didn't like.
- ktRolster 10y ago
  The movie Ratatouille captured the sentiment much better, "a great chef can be anyone". Which is not the same as "anyone can be a great chef". The movie Ratatouille presented that statement without any evidence, and imo it is incredibly misleading, the preponderance of psychological evidence goes against it. This paper is a good starting place: http://cogprints.org/656/1/innate.htm http://cogprints.org/656/1/innate.htm
alimw 10y ago
The author backs up his assertion that mathematical genius is fragile by ... listing a bunch of people whose genius was apparently rather robust.
naranana 10y ago
To the author of the article—you have a very tiny typo, garderning instead of gardening.
watwut 10y ago
The thing about first example is that the speed of brain development in child and adulthood geniality/iq/whatever are only loosely related. It is perfectly possible for a child to be bad in math in first few grades and good later on. It did not had to be test, it is perfectly possible for him to be slower at that age or him having lower attention span. (That assumes school systems that wont give up on such child as bad early on.) The situation of women now is a lot better then it was in 19 century. There is some bias and unequal expectation toward gender, but nowhere near as was at the time. While all the kids now know what is supposed to be girly toy/profession and what is boyish, there is no particular stigma facing working females nor female mathematicians. The 'it could easily play out like that now' is far from being accurate. I don't think you are helping equality when you compare stigma of being women who knows stuff with unequal representation of genders now. One, you are lowering her achievement and strength of will which had to be huge. I would say she was anything but fragile. Two, you are not doing service to women now - our situation is not the same as situation hundreds years ago and talking about it as it would helps no one.
- stale2002 10y ago
  It is better for women now than it was before, but it is still far from perfect. Just look at the turn over rate and exit rate of women in these fields. Even the women who objectively "make it" are being driven out of the industry in droves.
  - whenwillitstop 10y ago
    Driven out by who? A mass group of secret conspirators?
    - psyc 10y ago
      Women report being driven out by men hitting on them and sexually harassing them.
      - alimw 10y ago
imakecomments 10y ago
There are other examples of mathematical late bloomers. Check out https://en.wikipedia.org/wiki/Stephen_Smale https://en.wikipedia.org/wiki/Stephen_Smale He almost got kicked out of graduate school. Later went on to win the Fields Medal.
- osti 10y ago
  I read somewhere that hes incredibly smart, but very lazy. Just because he didnt do too well ealier on dosent mean he's not a genius. Most people no matter how much they work, still won't achieve 1/100th of what he did.
psyc 10y ago
This can be, and IMO ought to be, generalized to "People have a lot of potential, and society needs to stop being a lottery".
carsongross 10y ago
With common core, math is mostly now word problems, which makes them as much reading comprehension as abstract mathematical problems. This is going to be especially brutal for boys, who typically trail girls in reading skills early on. I expect in a decade the current 2-1 female-male ratio in higher education is going to reach such crisis levels that even our media will be unable to ignore it, as they do currently.
- HeavenBanned 10y ago
  It's not just that: introductory Calculus at even community colleges is designed to weed students out instead of emphasizing on teaching and comprehension. With tactics like curves, rushed test-taking, unrelated material on exams, poor lectures, and a "learn it yourself or die" attitude it's clear that many types of different learners are not given a fair shake. That is to say, many bright students who may be good at Math someday (like Hadamard) are unceremoniously kicked out of Math fields because of the sink or swim nature of teaching today either through lack of confidence or simple inability to muster the proper grades. This makes you wonder: how many potential geniuses in Mathematics or other STEM fields are we losing due to darwinian teaching tactics? I suspect many more than we're willing to admit.
- jessaustin 10y ago
  It will be shocking if there's a 2:1 female:male ratio at the bleeding edge of math anytime in the next century, even if word problems are required at lower levels. As for the rest of the fields, I suspect the media as currently constituted to celebrate rather than lament, when they can no longer ignore the situation entirely. [EDIT:] 'HeavenBanned's sibling comment should be restored; it's a good point that is seldom made about math.
  - jimhefferon 10y ago
    At the (not-BE) college college where I teach, the math majors who are female significantly outnumber those who are male. We don't have any program or special selection. We just find that the students who succeed at math are female, in the great majority.
tnzn 10y ago
Fallacious first paragraph. Not everyone has the potential to become a genius en math, or any other discipline for that matter.
- davesque 10y ago
  I think it's a bit pointless to get hung up on that wording. It seem to me that his point is more that people are often so bad at spotting genius that we may as well assume everyone is a genius.
vivekd 10y ago
His last point about poverty destroying genius was what really struck me. I remember reading that 71% of the world's population lives on less than $10 a day. That doesn't seem to be enough to get a decent education and contribute meaningfully to any field. This means that the world is working at 30% capacity. Our species only gets innovations from the 30% of inventors, entrepreneurs, politicians, scientists who were born in circumstances that allow them to contribute. How many more Srinivasa Ramanujans are there scattered throughout the world who simply didn't run into an obscure textbook or write to all the worlds top mathematicians. What would our species be like if we were working at closer to 100% capacity in terms of scientific innovations and discoveries.
- joe_the_user 10y ago
  I would mention that statistics like "$10/day" don't necessary capture the average living conditions of people. $10/day may yield a room over your head, a dull but acceptable meal and a somewhat austere routine in one place (whatever third world nation) but may yield a chaotic struggle for survival in another area (the USA). Which is not to say that poverty isn't eating a lot of people but rather that guarantees of food, cloth and shelter can be more useful metrics than median income in various places (world median income is rising but does that mean an increase people's ability to realize their geniuses, visions, passions etc?).
- deleted 10y ago
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deepnotderp 10y ago
I'd just like to note that math in early years is taught as rote memorization problems and doing things over and over again like memorization. Contrast this with higher level math which is highly creative...
- 0xFFC 10y ago
  This is my exact problem. For my whole life i was afraid of math, after i (i had to took it, it was not my choice) took real Analysis class and watched Francis Su Real Analysis videos, I realized i like math more than CS (and cs was my only love in my entire life.). Right now i am starting abstract Algebra and i have plan to took probability and number theory after that. I am literally in love with math. It does feelit is the only reason i was born in the first place. I sometimes think i have to change my career to math. And something i am really feel is brain plasticity. It may not have proven.But i can feel in my self, as much as i go deeper into math, i do realize it makes more sense, i can feel its effect on my day to day life, the way i think, the more effective way I Analysis circumstances.
  - deepnotderp 10y ago
    Haha, that's great, good job :) Side note: Su's real analysis videos are great aren't they?
    - 0xFFC 10y ago
      They are excellent, literally. I start to love math after I understand math, and he was the one showed me how to understand math. Every one of those proofs was enjoyable, more than anything i have ever done. P.S. if he was accessible for me , I would go to every class he goes, every office hour he has. I would just stick to the guy until I can find my way in mathematics.
    - 0xFFC 10y ago
      The only problem i have across is speed of my brain, i want to understand faster, for example i want to complete a whole material of abstract algebra (for 2,3 year ungradate math students) in one week or less. But my brains says nah. I keep pushing it, but after 7,8 hour a day, its performance hits a block and i have to play game or talk to a friend to start again.
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jankotek 10y ago
> Mathematical genius is fragile; society needs to stop destroying it ... but there are too many men in this field. Just love this marxist logic.
- hiddencost 10y ago
  s/too many men/not enough women/ Suddenly it makes perfect sense. Why on earth do you choose to frame it the first way? Getting more women into math by having male mathematicians be less shitty people doesn't decrease the total number of mathematicians.
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  - jankotek 10y ago
    Do you know any 'shitty mathematician' in person, or is it just another stereotype?
    - GFK_of_xmaspast 10y ago
      > Do you know any 'shitty mathematician' in person I certainly do.
      - jankotek 10y ago
        That talk to individuals, do not blame entire field or entire gender.
lordnacho 10y ago
I find it hard to accept the "you must be 7ft tall to play basketball" story about why people become good at something. My own view is more something like what bodybuilders say. Some people find it harder to grow than others, but everyone can do it. And people who put effort into it will definitely be separable from people who don't, regardless of endowment. Now as for who gets to be written into history books, there's a fair bit of randomness about that. A hard working person can well find that the only phd advisor who will take them wants them to work on some dead end. Or you may work on something hot, but other people will know it's hot, too, and they may well beat you to publication. Doesn't make you any dumber, but your name will not be enshrined in that theorem. There's also a necessary confluence of factors that depends very much on your parents, specifically whether they figure out how to manage your development. Look at the current first-in-most-people's-minds genius, Terence Tao. Not only did his parents figure out that he was good at math, they somehow got him the right guidance. I'm guessing very few parents, even quite well educated ones, would know what to do if a guy like that turned up in their house. There's also the sheer randomness of whether you'll end up doing things that encourage the kid. Most parents, myself included, have very little idea of how to get a kid to do what's good for them. You laugh, unless you are a parent.
- ZeroFries 10y ago
  Isn't a part of a person's endowment their ability to work hard and put in effort where it's required, when it's required? The 7ft tall thing is an example of an easy to see factor, which some people have, and some don't. In reality, as you say, there are unlimited factors going into a person's greatness (or lack-of). By the way, there was a study where, given the same weight lifting program, a couple people gained tons of muscle, most gained some, some gained none, and a few even lost muscle. Not everyone can gain appreciable muscle, and not everyone can get good at math (although most can, and the average person underestimates their ability to do so).
  - ktRolster 10y ago
    there was a study where, given the same weight lifting program, a couple people gained tons of muscle, most gained some, some gained none, and a few even lost muscle. Not everyone can gain appreciable muscle This is a non sequitur. A reasonable follow-up study would try to figure out why those people didn't gain muscle, and how that can be changed (the first things to look at would be diet and sleep. If they're not getting enough food, of course they will lose muscle).
robertk 10y ago
Very similar to what I wrote years ago: https://deconstructinggenius.wordpress.com https://deconstructinggenius.wordpress.com
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stupidcar 10y ago
I think these sort of anecdotes about genius mathematicians are rather disheartening. For many students, math is a struggle, even with the advantages of a good education. Hearing about how such-and-such a person derived the whole of number theory from an old Sesame Street book they found in the trash just makes me feel dumb in comparison. If anything, the examples given suggest that mathematical geniuses will find a way to contribute whatever the obstacles in their way. But what about the majority of students who are turned off the subject because they don't have the same drive and natural ability? What's fragile isn't the abilities of savants, but the belief of the average person that math is something they can do, rather than the preserve of the super-intelligent.
aphextron 10y ago
>Tests can serve a profoundly useful purpose in providing feedback and diagnosing students’ learning needs. But as blunt labels for students’ abilities, they can be devastating. This is so spot on. I've recently started taking college math courses for the first time, and I'm astounded by how little actual "teaching" goes on in these classes. My entire term grade for Precalculus was determined by 5 tests of 8 questions each, and the class consisted of a professor reading from a text book for an hour a week with zero feedback or help. I think experiences like this lead to a lot of people becoming completely frustrated and feeling worthless at math, while also outwardly validating that feeling with an unfair poor grade.

86 points by fjmubeen 10y ago

The author lost me at "Mathematical genius resides within every one of us — most people just don’t know it yet." The movie Ratatouille captured the sentiment much better, "a great chef can be anyone". Which is not the same as "anyone can be a great chef". It seems the author is mixing up those two. I fully agree that gender, background, schooling, etc is not the key determination of genius. However, saying anyone could be a genius is disingenuous.

ZeroFries 10y ago
A 7ft tall pro basketball player resides within every one of us.
- throwaway5752 10y ago
  Not every 7' tall person is a great basketball player, and not every great basketball player is 7' tall. With all due respect, what you say is a consummate example of "dangerously bad idea that makes a good sound bite". Most mathematicians out there are not Hilbert, Gauss, Riemann, or Euler. They are reasonably smart people that work hard over long periods of time to learn their craft and their field, and make incremental progress in the niches they specialize in. Most people can be productive mathematicians, they just don't believe in themselves.
  - madgar 10y ago
    You are conflating genius with productivity. In so doing you are missing the point of both your parent and grandparent poster.
    - lordnacho 10y ago
      He is, and he's right to. Every single example of a genius ever has become so because of high productivity.
  - dagw 10y ago
    not every great basketball player is 7' tall In fact look at any list of the greatest basketball players of all time. Very few of them are 7' tall. Now look at a list of pro basketball players over 7', most of them are middle of the road journeyman players most people haven't heard of.
    - ZeroFries 10y ago
      I feel like this is a trick of statistics. Very few people, in general, are 7' or taller, and very few people are the best at basketball. See (1), and replace "have disease" with "7' or taller", and "test comes back positive" with "good at basketball". 1: https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml
    - ktRolster 10y ago
      Add to your point: the vast majority of 7' tall people are not very good at basketball.
  - ZeroFries 10y ago
    I doubt most people have the desire to be productive mathematicians, which is as required to be a good mathematician as being 7' tall is for playing basketball (aka not actually required, but big help). "Most people can be productive mathematicians, they just don't believe in themselves." Most people can X if Y, where Y is not the usual case. Again, believing in yourself, having the desire to be great at something, etc, are all included in the extremely large set of factors which determine whether someone will be good at any given activity. To say a large portion of the population can be good at some activity, knowing full-while that they do not possess most of the helpful attributes, is disingenuous.
  - Tomminn 10y ago
    Actually, if you are a 7' tall American, you have a >15% chance of playing in the NBA.
sporkenfang 10y ago
Being a hard worker is easier than being seven feet tall, though. I know it's disingenuous to say hard work will get you everywhere, but working your ass off and being confident about it will get you pretty far.
- simion314 10y ago
  It depends, so actual math problems involve creativity and not brute force, though most of the problems in schools involve trying known recopies/algorithms to solve something if you check the problems people solve on international competition all of those involve creativity. But of course without hardwork you will not have a solid base for your creativity to work with.
- avatarlite 10y ago
  In my experience, qualitative arguments of the form above rarely change people's minds but a quantitative model will help. The question asked is the causal network that contributes to mathematical genius and the distribution of contributing causal factors within the population -- P(genius | factors) Various factors are clearly involved: P(genius | intelligence), P(genius | hard work), P(genius | self-confidence), and so on. If we accept that those functions are probably not uniformly distributed and that some have a stronger impact than others, we can see that most arguments can be reduced to describing those functions or describing the distributions of those factors among the population. Where most educated people's intuitions lead them astray is that the experience of segregation in higher education and employment has led them to vastly underestimate the actual variance in factors like intelligence, hard work and self-confidence among people. Vanishingly few individual actually possess the right combination of factors required for mathematic genius.
Moshe_Silnorin 10y ago
Math is a high IQ game. Anyone who tells you otherwise is kidding themselves.
- deepnotderp 10y ago
  Except iq is a terrible metric....
  - Moshe_Silnorin 10y ago
    Why?
    - ktRolster 10y ago
      Because they are calibrated not to measure innate intelligence, but our own cultural norms. The canonical example might be, imagine you were lost in the Australian outback. Would you rather have Albert Einstein as your guide, or a skilled Aborigine? The Aborigine would likely get a low score on logic puzzles, but at highly skilled activities like way-finding and tracking game, he would beat Einstein hands down. IQ doesn't measure intelligence, it measures artifacts of intelligence that appear in our culture. Also, it's a mistake to think that IQ is static. There have been studies that show wild swings in IQ over time, especially in teenagers, and even changes in the collective IQ of a culture (the Flynn effect). In addition, it seems likely that a person could study and improve their IQ score. The counter-argument is that although IQ tests have flaws, they are still to some degree a predictor of success in life.
      - Moshe_Silnorin 10y ago
        https://en.wikipedia.org/wiki/Raven's_Progressive_Matrices https://en.wikipedia.org/wiki/Raven's_Progressive_Matrices
      - deepnotderp 10y ago
        This^^. I think another great example would be IQ tests in the army during WWI (and I think II?) in which one of the questions asked about a type of gun, which no one today would know, and other questions were like that as well. The point is that it measures cultural perceptions of intelligence, ie during WWI knowing your guns was considered intelligence.
deepnotderp 10y ago
So there are many fields of math, and you find you're good at one type,and even be a genius in that field...
Jillboy 10y ago
Why is that? Why do you claim not everyone has the potential to become a math genius? Do you have any evidence to back that up (besides Ratatouille)?
- distances 10y ago
  Surely you don't mean to suggest that we all start with equal chances of attaining any and all skills?
  - Jillboy 10y ago
    Any and all skills? No. Mathematical and other related intellectual skills? Why, yes, I do. Despite what most people say, I've never seen a genius who hasn't worked at least twice or thrice as hard as his peers. I've never seen a child that, without the help of any tutors at an early age, or without any influence from their parents, was simply spitting out non-trivial theorems from an early age. I have a hard time believing that some people are BORN better at math and logic than others, and I've yet to see any evidence to suggest that. Quite on the contrary, I've seen plenty of evidence to suggest that genius is at all not genetic, and that you can train children to become prodigies, and later, geniuses. Surely you've heard of Judit Polgár, universally considered the best female chess player of all time? She was made a genius, not born. Her two sisters grown to become Grandmasters as well. And here's Dr. Frankenstein: https://en.wikipedia.org/wiki/László_Polgár https://en.wikipedia.org/wiki/László_Polgár
- RangerScience 10y ago
  I only have anecdotal plus a bit of thinking...? Talent is pursued interest; genius is pursued passion. Most people won't have passion for mathematics, even if such passions were heartily encouraged - at the very least, because there are so many other things to also be passionate about.
  - Jillboy 10y ago
    I can get behind that, if we defined genius to be pursued passion. Not everyone has a passion for mathematics, that is true. I just thought what the root post was implying is that even if you're passionate, you might not have the potential to achieve genius-level skill because that would somehow be genetically predetermined. If that was what he was implying, I'd love to see some evidence to support the claim.
lutusp 10y ago
> The author lost me at "Mathematical genius resides within every one of us — most people just don’t know it yet." An unfortunate hyperbolic opening line, the remainder of the article is much better. > However, saying anyone could be a genius is disingenuous. But genius isn't an identity, it's a possession. It's often a currency with limited utility. Consider Bill Shockley, Nobel Prizewinner, co-inventor of the transistor -- he possessed a narrow, specific area of genius, held by someone otherwise quite ordinary and even deplorable (he was a racist who lectured on the imagined inferiority of black people). Consider Henry Ford, inventor of efficient factory methods, but a rabid anti-Semite. Identifying genius as a possession, not an identity, greatly clarifies its role in our lives. It can keep us from expecting a person to be smart about more than one or two specific things.
zizzles 10y ago
I got just a little further than you, until I reached "women make the best mathematicians" where I instantly ALT-F4'd Google Chrome and added 'medium.com' to a permanent blacklist. Truth of the matter is, math IS a high-IQ game, albeit average intelligence specimen can become semi-competent with time and practice (the payoffs of this pursuit are negligible)
- ricree 10y ago
  >where I instantly ALT-F4'd Google Chrome and added 'medium.com' to a permanent blacklist Medium.com is essentially just a blog host, isn't it? Seems a bit harsh for one story you didn't like.
ktRolster 10y ago
The movie Ratatouille captured the sentiment much better, "a great chef can be anyone". Which is not the same as "anyone can be a great chef". The movie Ratatouille presented that statement without any evidence, and imo it is incredibly misleading, the preponderance of psychological evidence goes against it. This paper is a good starting place: http://cogprints.org/656/1/innate.htm http://cogprints.org/656/1/innate.htm

alimw 10y ago

The author backs up his assertion that mathematical genius is fragile by ... listing a bunch of people whose genius was apparently rather robust.

naranana 10y ago

To the author of the article—you have a very tiny typo, garderning instead of gardening.

watwut 10y ago

The thing about first example is that the speed of brain development in child and adulthood geniality/iq/whatever are only loosely related. It is perfectly possible for a child to be bad in math in first few grades and good later on. It did not had to be test, it is perfectly possible for him to be slower at that age or him having lower attention span. (That assumes school systems that wont give up on such child as bad early on.) The situation of women now is a lot better then it was in 19 century. There is some bias and unequal expectation toward gender, but nowhere near as was at the time. While all the kids now know what is supposed to be girly toy/profession and what is boyish, there is no particular stigma facing working females nor female mathematicians. The 'it could easily play out like that now' is far from being accurate. I don't think you are helping equality when you compare stigma of being women who knows stuff with unequal representation of genders now. One, you are lowering her achievement and strength of will which had to be huge. I would say she was anything but fragile. Two, you are not doing service to women now - our situation is not the same as situation hundreds years ago and talking about it as it would helps no one.

stale2002 10y ago
It is better for women now than it was before, but it is still far from perfect. Just look at the turn over rate and exit rate of women in these fields. Even the women who objectively "make it" are being driven out of the industry in droves.
- whenwillitstop 10y ago
  Driven out by who? A mass group of secret conspirators?
  - psyc 10y ago
    Women report being driven out by men hitting on them and sexually harassing them.
    - alimw 10y ago

imakecomments 10y ago

There are other examples of mathematical late bloomers. Check out https://en.wikipedia.org/wiki/Stephen_Smale https://en.wikipedia.org/wiki/Stephen_Smale He almost got kicked out of graduate school. Later went on to win the Fields Medal.

osti 10y ago
I read somewhere that hes incredibly smart, but very lazy. Just because he didnt do too well ealier on dosent mean he's not a genius. Most people no matter how much they work, still won't achieve 1/100th of what he did.

psyc 10y ago

This can be, and IMO ought to be, generalized to "People have a lot of potential, and society needs to stop being a lottery".

carsongross 10y ago

With common core, math is mostly now word problems, which makes them as much reading comprehension as abstract mathematical problems. This is going to be especially brutal for boys, who typically trail girls in reading skills early on. I expect in a decade the current 2-1 female-male ratio in higher education is going to reach such crisis levels that even our media will be unable to ignore it, as they do currently.

HeavenBanned 10y ago
It's not just that: introductory Calculus at even community colleges is designed to weed students out instead of emphasizing on teaching and comprehension. With tactics like curves, rushed test-taking, unrelated material on exams, poor lectures, and a "learn it yourself or die" attitude it's clear that many types of different learners are not given a fair shake. That is to say, many bright students who may be good at Math someday (like Hadamard) are unceremoniously kicked out of Math fields because of the sink or swim nature of teaching today either through lack of confidence or simple inability to muster the proper grades. This makes you wonder: how many potential geniuses in Mathematics or other STEM fields are we losing due to darwinian teaching tactics? I suspect many more than we're willing to admit.
jessaustin 10y ago
It will be shocking if there's a 2:1 female:male ratio at the bleeding edge of math anytime in the next century, even if word problems are required at lower levels. As for the rest of the fields, I suspect the media as currently constituted to celebrate rather than lament, when they can no longer ignore the situation entirely. [EDIT:] 'HeavenBanned's sibling comment should be restored; it's a good point that is seldom made about math.
- jimhefferon 10y ago
  At the (not-BE) college college where I teach, the math majors who are female significantly outnumber those who are male. We don't have any program or special selection. We just find that the students who succeed at math are female, in the great majority.

tnzn 10y ago

Fallacious first paragraph. Not everyone has the potential to become a genius en math, or any other discipline for that matter.

davesque 10y ago
I think it's a bit pointless to get hung up on that wording. It seem to me that his point is more that people are often so bad at spotting genius that we may as well assume everyone is a genius.

vivekd 10y ago

His last point about poverty destroying genius was what really struck me. I remember reading that 71% of the world's population lives on less than $10 a day. That doesn't seem to be enough to get a decent education and contribute meaningfully to any field. This means that the world is working at 30% capacity. Our species only gets innovations from the 30% of inventors, entrepreneurs, politicians, scientists who were born in circumstances that allow them to contribute. How many more Srinivasa Ramanujans are there scattered throughout the world who simply didn't run into an obscure textbook or write to all the worlds top mathematicians. What would our species be like if we were working at closer to 100% capacity in terms of scientific innovations and discoveries.

joe_the_user 10y ago
I would mention that statistics like "$10/day" don't necessary capture the average living conditions of people. $10/day may yield a room over your head, a dull but acceptable meal and a somewhat austere routine in one place (whatever third world nation) but may yield a chaotic struggle for survival in another area (the USA). Which is not to say that poverty isn't eating a lot of people but rather that guarantees of food, cloth and shelter can be more useful metrics than median income in various places (world median income is rising but does that mean an increase people's ability to realize their geniuses, visions, passions etc?).
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deepnotderp 10y ago

I'd just like to note that math in early years is taught as rote memorization problems and doing things over and over again like memorization. Contrast this with higher level math which is highly creative...

0xFFC 10y ago
This is my exact problem. For my whole life i was afraid of math, after i (i had to took it, it was not my choice) took real Analysis class and watched Francis Su Real Analysis videos, I realized i like math more than CS (and cs was my only love in my entire life.). Right now i am starting abstract Algebra and i have plan to took probability and number theory after that. I am literally in love with math. It does feelit is the only reason i was born in the first place. I sometimes think i have to change my career to math. And something i am really feel is brain plasticity. It may not have proven.But i can feel in my self, as much as i go deeper into math, i do realize it makes more sense, i can feel its effect on my day to day life, the way i think, the more effective way I Analysis circumstances.
- deepnotderp 10y ago
  Haha, that's great, good job :) Side note: Su's real analysis videos are great aren't they?
  - 0xFFC 10y ago
    They are excellent, literally. I start to love math after I understand math, and he was the one showed me how to understand math. Every one of those proofs was enjoyable, more than anything i have ever done. P.S. if he was accessible for me , I would go to every class he goes, every office hour he has. I would just stick to the guy until I can find my way in mathematics.
  - 0xFFC 10y ago
    The only problem i have across is speed of my brain, i want to understand faster, for example i want to complete a whole material of abstract algebra (for 2,3 year ungradate math students) in one week or less. But my brains says nah. I keep pushing it, but after 7,8 hour a day, its performance hits a block and i have to play game or talk to a friend to start again.

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jankotek 10y ago

> Mathematical genius is fragile; society needs to stop destroying it ... but there are too many men in this field. Just love this marxist logic.

hiddencost 10y ago
s/too many men/not enough women/ Suddenly it makes perfect sense. Why on earth do you choose to frame it the first way? Getting more women into math by having male mathematicians be less shitty people doesn't decrease the total number of mathematicians.
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- jankotek 10y ago
  Do you know any 'shitty mathematician' in person, or is it just another stereotype?
  - GFK_of_xmaspast 10y ago
    > Do you know any 'shitty mathematician' in person I certainly do.
    - jankotek 10y ago
      That talk to individuals, do not blame entire field or entire gender.

lordnacho 10y ago

I find it hard to accept the "you must be 7ft tall to play basketball" story about why people become good at something. My own view is more something like what bodybuilders say. Some people find it harder to grow than others, but everyone can do it. And people who put effort into it will definitely be separable from people who don't, regardless of endowment. Now as for who gets to be written into history books, there's a fair bit of randomness about that. A hard working person can well find that the only phd advisor who will take them wants them to work on some dead end. Or you may work on something hot, but other people will know it's hot, too, and they may well beat you to publication. Doesn't make you any dumber, but your name will not be enshrined in that theorem. There's also a necessary confluence of factors that depends very much on your parents, specifically whether they figure out how to manage your development. Look at the current first-in-most-people's-minds genius, Terence Tao. Not only did his parents figure out that he was good at math, they somehow got him the right guidance. I'm guessing very few parents, even quite well educated ones, would know what to do if a guy like that turned up in their house. There's also the sheer randomness of whether you'll end up doing things that encourage the kid. Most parents, myself included, have very little idea of how to get a kid to do what's good for them. You laugh, unless you are a parent.

ZeroFries 10y ago
Isn't a part of a person's endowment their ability to work hard and put in effort where it's required, when it's required? The 7ft tall thing is an example of an easy to see factor, which some people have, and some don't. In reality, as you say, there are unlimited factors going into a person's greatness (or lack-of). By the way, there was a study where, given the same weight lifting program, a couple people gained tons of muscle, most gained some, some gained none, and a few even lost muscle. Not everyone can gain appreciable muscle, and not everyone can get good at math (although most can, and the average person underestimates their ability to do so).
- ktRolster 10y ago
  there was a study where, given the same weight lifting program, a couple people gained tons of muscle, most gained some, some gained none, and a few even lost muscle. Not everyone can gain appreciable muscle This is a non sequitur. A reasonable follow-up study would try to figure out why those people didn't gain muscle, and how that can be changed (the first things to look at would be diet and sleep. If they're not getting enough food, of course they will lose muscle).

robertk 10y ago

Very similar to what I wrote years ago: https://deconstructinggenius.wordpress.com https://deconstructinggenius.wordpress.com

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stupidcar 10y ago

I think these sort of anecdotes about genius mathematicians are rather disheartening. For many students, math is a struggle, even with the advantages of a good education. Hearing about how such-and-such a person derived the whole of number theory from an old Sesame Street book they found in the trash just makes me feel dumb in comparison. If anything, the examples given suggest that mathematical geniuses will find a way to contribute whatever the obstacles in their way. But what about the majority of students who are turned off the subject because they don't have the same drive and natural ability? What's fragile isn't the abilities of savants, but the belief of the average person that math is something they can do, rather than the preserve of the super-intelligent.

aphextron 10y ago

>Tests can serve a profoundly useful purpose in providing feedback and diagnosing students’ learning needs. But as blunt labels for students’ abilities, they can be devastating. This is so spot on. I've recently started taking college math courses for the first time, and I'm astounded by how little actual "teaching" goes on in these classes. My entire term grade for Precalculus was determined by 5 tests of 8 questions each, and the class consisted of a professor reading from a text book for an hour a week with zero feedback or help. I think experiences like this lead to a lot of people becoming completely frustrated and feeling worthless at math, while also outwardly validating that feeling with an unfair poor grade.