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.
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.
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.
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.
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.
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.
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.
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.
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.
Since mathematical skills (broadly defined) are a component of IQ, this is dangerously close to "Basketball is a getting the ball in the hoop game. Anyone who tells you otherwise is kidding themselves." True, but less informative than you might think...
(This is not to comment on the underlying question of whether everyone has the potential to be a great mathematician, just a particular type of reasoning).
Mostly in the same way the basket ball is a tall persons game. Yet there have been a lot of very good basketball and quite a few brilliant players below 5'10" (the US median height).
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
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.
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.
I feel as if it is also somewhat true in that regard. I have been extremely passionate about music for more than half my life yet I am still horrible. I believe the same applies with many other skills in life.
But to be a genius, you don't have to be the best, only one of the best.
The article also never claims that everyone IS a mathematical genius, only that they have the potential to become geniuses. Whether or not the achieve this potential in their lifetimes is another matter entirely that doesn't contradict what your quote implies (that only a small percent of the population can be among the "best" at any given time, by definition).
Not everyone who wants to be a math genius is. Desire is not sufficient for mathematical aptitude, and I'm not sure how you can honestly define potential to yield a case where both potential and desire can exist without achievement.
> 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.
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)
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
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.
Many women are not attracted to work in fields populated 90% by males. I believe this to be a more subtle problem that you suggest; you might eliminate all sexual harassment and it would still be the case.
What I am saying, is that the two biggest complaints that women who have worked in this industry have stated to me, are being hit on, and being harassed. Not as a single incident, but as a pattern. The only argument you could make against this is that I'm lying, and women haven't actually said these things to me.
> The only argument you could make against this is that I'm lying
First, that's lacking in civility, you've been here long enough to know that tone isn't appropriate.
Now then. The fact that your experience is not statistically significant isn't a possible counter argument? In order for you to be right, you would need evidence not only that most female mathematicians were harassed, but that they left the field because of if. If you have exit interview data for a random sample of former mathematicians, there are a lot of people here who would probably love to talk to you.
This is an especially unfortunate stance given that this is an article about math.
Edit: I make no claims one way or the other, I'm only talking about statistical validity.
Lets do the math, there are about 3.6 Million software engineers. Software engineering is 90% male. There should be 1.8 Million women to fill that demand, but there is about only 360,000.
1.8 M - 360,00 = 1.44 Million cases of sexual harrassment and other gender based discrimination, across the whole country, and across all groups of men.
Is that logical to you? Does that sound real? Do you have a low IQ?
Question: had they worked in the same company or same geographical area? I found that there is big difference between how companies and groups treat people.
Men in specific industries have a higher likelihood to sexually assault women, so much so that it pushes 90% of the women out of an industry with greater than 10M people. Do you understand how delusional that is?
Could you please post some data about those rates? I'm working on a visualization project and that would be perfect. I've only been able to find college-level data, professional mathematician data has been elusive so far.
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.
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.
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.
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.
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.
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.
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.
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?).
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...
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.
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.
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.
Hey, just want to chime in and say keep at it. I don't come from a highly educated family nor was I especially fond of maths, but one good advanced math course with a really brilliant professor in my undergrad made me switch majors. And yes, I also started to feel like everything around me was falling in its place; it's quite a rush, huh? I haven't read the article yet, but no matter what anyone else says or what you read I hope you continually pursue your love of math. :)
I did almost exactly the same thing. I was one of those kids that was always 'good' at math, but somewhere during high school they managed to effectively kill any interest I'd ever had in math. I went into university with the intention of studying computer science and a plan to try to take as few math classes as I could get away with. However after my first 'real' math course at university I instantly realised that I actually loved math (always had) and switched from CS to math at the end of the semester.
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.
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.
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).
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).
Good nutrition can frequently change the height of whole populations. Yet, we say height is part of a person's endowment. One might say potential is largely determined at birth, but how that potential unfolds is determined over the course of an organism's life.
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.
>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.
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[ 3.1 ms ] story [ 180 ms ] threadThe 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.
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.
Every single example of a genius ever has become so because of high productivity.
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.
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
"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.
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.
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.
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.
(This is not to comment on the underlying question of whether everyone has the potential to be a great mathematician, just a particular type of reasoning).
IQ (or more precisely the g factor) correlates not only with math but also with language skills and music[1].
[1] https://en.wikipedia.org/wiki/G_factor_(psychometrics)
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
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.
But more - it's the only reasonable-sounding argument for that part of the "Myth of a Meritocracy".
The caveat for the real argument is: People are more complicated than animals, and there's way more to it than genetics.
The real argument is: If everyone was capable of everything, evolution wouldn't work as a process.
The addendum of: of course this is inaccurate, poorly phrase, etc etc - the idea is still "new" enough to be unpolished.
Thoughts?
The article also never claims that everyone IS a mathematical genius, only that they have the potential to become geniuses. Whether or not the achieve this potential in their lifetimes is another matter entirely that doesn't contradict what your quote implies (that only a small percent of the population can be among the "best" at any given time, by definition).
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.
Medium.com is essentially just a blog host, isn't it? Seems a bit harsh for one story you didn't like.
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
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.
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.
EDIT: not calling anyone a liar.
First, that's lacking in civility, you've been here long enough to know that tone isn't appropriate.
Now then. The fact that your experience is not statistically significant isn't a possible counter argument? In order for you to be right, you would need evidence not only that most female mathematicians were harassed, but that they left the field because of if. If you have exit interview data for a random sample of former mathematicians, there are a lot of people here who would probably love to talk to you.
This is an especially unfortunate stance given that this is an article about math.
Edit: I make no claims one way or the other, I'm only talking about statistical validity.
1.8 M - 360,00 = 1.44 Million cases of sexual harrassment and other gender based discrimination, across the whole country, and across all groups of men.
Is that logical to you? Does that sound real? Do you have a low IQ?
Men in specific industries have a higher likelihood to sexually assault women, so much so that it pushes 90% of the women out of an industry with greater than 10M people. Do you understand how delusional that is?
Just because your coworkers aren't literally raping you doesn't mean that there aren't men out there who will be huge assholes to women.
He almost got kicked out of graduate school. Later went on to win the Fields Medal.
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.
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.
[EDIT:] 'HeavenBanned's sibling comment should be restored; it's a good point that is seldom made about math.
$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?).
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.
Side note: Su's real analysis videos are great aren't they?
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.
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.
... but there are too many men in this field. Just love this marxist logic.
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.
I certainly do.
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.
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).
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).
No this is largely a malleable set of traits.
Good teachers can frequently change them in whole populations of students.
We're still barely tapping into people's potential, but people still act form arguments on the assumption that we are.
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.
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.