Mathematical genius is fragile
medium.com
medium.com
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.
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".
"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].
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
$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?).
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.
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.
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.
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.
[EDIT:] 'HeavenBanned's sibling comment should be restored; it's a good point that is seldom made about math.
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.
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.
... 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.