[malanj]

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.

[sporkenfang]

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.

[avatarlite]

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.

[simion314]

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.

[Moshe_Silnorin]

Math is a high IQ game. Anyone who tells you otherwise is kidding themselves.

[hyperpape]

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).

[martindelemotte]

It would be more like "Basketball is about being in very good physical shape", which makes more sense.

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)

[hyperpape]

I very clearly said component and "close to", so I don't think what I said merits a correction.

[martindelemotte]

Then why would the g factor also apply to animals as stated on the Wikipedia page? You don't see that many doing mathematics.

[tnzn]

Nope, it's a high logico-mathematics IQ game (no shit ?), Which is only part of IQ.

[deepnotderp]

Except iq is a terrible metric....

[Moshe_Silnorin]

Why?

[ktRolster]

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.

[deepnotderp]

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.

[Moshe_Silnorin]

https://en.wikipedia.org/wiki/Raven's_Progressive_Matrices

[iklos55]

How do you define 'high IQ'? +30 from height of bell curve or how much exactly?

[dagw]

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).

[lutusp]

> 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.

[ZeroFries]

A 7ft tall pro basketball player resides within every one of us.

[throwaway5752]

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.

[ZeroFries]

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.

[dagw]

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]

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

[ktRolster]

Add to your point: the vast majority of 7' tall people are not very good at basketball.

[Tomminn]

Actually, if you are a 7' tall American, you have a >15% chance of playing in the NBA.

[madgar]

You are conflating genius with productivity. In so doing you are missing the point of both your parent and grandparent poster.

[lordnacho]

He is, and he's right to.

Every single example of a genius ever has become so because of high productivity.

[deepnotderp]

So there are many fields of math, and you find you're good at one type,and even be a genius in that field...

[ktRolster]

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

[Jillboy]

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)?

[RangerScience]

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]

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.

[RangerScience]

It's more like a correlation than a definition.

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?

[CuriousCosmic]

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.

[distances]

Surely you don't mean to suggest that we all start with equal chances of attaining any and all skills?

[Jillboy]

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

[ouid]

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.

[pharrington]

"Everybody cannot be the best." - Jason Charles Beck, 2000

[Jillboy]

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).

[zizzles]

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]

>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.