That gap also exists in the middle-school and high-school levels [0] (at least in the US), so it fully reduces to the simpler question of why that's true. We should be able to agree that by the time we're discussing professional mathematics there's no expectation that it would be randomly distributed among genders.

[0] https://economics.mit.edu/files/7598 (admittedly a bit old; maybe a lot has changed in ~10 years?)

Still true globally at the high school level. Found some quora answers with perspectives on IOI(programming olympiad) and IMO(math olympiad) which both have low single digit percentage female participants:

https://www.quora.com/Why-are-there-few-females-in-competiti...

https://www.quora.com/Why-do-boys-outperform-girls-in-math-c...

All it would require is just that the standard deviation for math ability in men (whether by nature or nurture, I am making no judgment either way) is only very slightly higher than for women. Since we are looking at the tail of the distribution, the result would not be surprising.

That hypothesis got Larry Summers in a lot of trouble.

https://en.wikipedia.org/wiki/Lawrence_Summers#Differences_b...

As Helena Cronin noted of men: "more dumbbells but more Nobels" [1].

[1] https://www.edge.org/annual-question/2008/response/10670

I once did some calculations to explore the expected effect of that difference in standard deviation: https://news.ycombinator.com/item?id=14997524

I'm on my phone right now and can't redo it for the gender ratio of Fields medalists, but I expect that the effect would cover most of the difference, since the cutoff for the award does seem quite high.

> If you accept the idea that a penchant for math is randomly distributed among all people

That would seem rather detached from reality.

Maybe he meant "Even if" ?

> penchant for math is randomly distributed among all people

Fields medals are not awarded based on "penchant for math" though. And it surely isn't exactly fault of the prize committee that there aren't very many female mathematicians to choose from.

Note: I don't know if 55/56 is "correct" from the point of the actual numbers.

For the last 30 years over 40% of graduating math majors where where women. That drops to 15% of tenure track mathematicians being women, but again that's a long way to sub 2%.

This is the exactly the pattern you would expect to see though if the variance of mathematical ability is higher in men than in women, even if mean ability is precisely identical.

The sex ratio gets progressively more extreme as you go further out in the tails.

Not really, you get a fat tail effect at extreme ability reducing the differences. A more likely cause are highly capable women bailing on the field.

EX: Women live significantly longer on average and the oldest women lived 6 years longer than the oldest man. Yet, the 16th oldest person was a man and 6% of oldest 100 people where men. And 6% of the top 100 living people are men https://en.m.wikipedia.org/wiki/List_of_oldest_living_people

I'm not sure what you mean—why would you assume there is a fat tail expect in the first place, and not something approximating a normal distribution?

And even if you presume something like a Pareto distribution, the likelihood ratio between two distributions grow through the tails if their variance is not identical.

edit: I see you bring up longevity, but I don't see why this is relevant to a discussion about variance in mathematical ability or intelligence? See: https://www.sciencedirect.com/science/article/pii/S019188690...

Based on a wide range of ability testing we see fat tails (edit: more black swans than expected), it would be more surprising if they where skinny.

Granted, we can't measure very high ability very well due to sampling bias. I am simply saying even if there is a modest bias that's not enough it would have to be huge to account for these numbers.

So, I am bringing up something else with the kind of distribution we are talking about which has more accurate data. Women live ~ 5% longer both looking at the average lifespans and oldest examples which is a very significant difference. Yet, the oldest population has more men in it than you would think.

Edit: Math: 6 year longer lifespan + 50% risk of death per year = you would expect ~1% of top 100 oldest people to be men.

Life span here is interesting.

If it’s affected by things like work place deaths because men are more likely to take on dangerous jobs, e.g. sea fisherman, military service, etc. would that overlap with the section of the population likely to be working on pure mathematics?

Suicide, another cause of that difference in average life span, would overlap though I guess.

It would be worth properly investigating as I suspect there’s a lot of complexity hidden here.

> Based on a wide range of ability testing we see fat tails

What kind of ability? Mathematical? IQ?

IQ, memory etc, in uncalibrated tests you see something close to a bell curve in raw scores but more people score very high 180+ than you would get from an actual bell curve. So, many tests are given a max score or compressed at the high end.

One argument that some have is that men have a more extreme distribution of IQ and mathematical ability and when it comes to things like the Fields medal it is the few extreme ones that make an impact.

I don't know how well done those studies are though.

EDIT: I doubt it is that big though.

I used to believe this, but now I think a confounding factor here is that girls are socialized away from extremes in general.

Ok, I can get you can somehow socialize a person to pretend be dumber than they are, but how do you socialize someone away from being dumb? And why does that not work for boys?

I think poor achool performance is more a function of behavioral issues than "being dumb" -- not because everyone is smart, but because the bar in your average American school is more about following directions than anything else. Boys lagging behind girls in social development is well-documented, right?

And at the Fields medal level it's less about "pretend you're not smart" and more about "we just don't think it's a good idea for you to skip grades".

> a penchant for math is randomly distributed among all people

As politically difficult as it is to say, intelligence is NOT distributed randomly among all people.

Not by sex, not by race.

Characterizing something as "politically difficult" is no evidence for a claim.

There's tons of evidence. You can google as easily as I can.

The hard part is not the evidence, it's dealing with the social result. Do we as a culture decide "Yes, it might be true, but it's too harmful, so we will act as if it's false?"

Give extra tutoring to those lower on the scale, and withhold it from those higher, to try to even the balance?

Give special advantage to those lower? Is there a way to do that without disadvantaging others? What sort of advantage?

Something else?

Each of those options has pros and cons.

It should be discussed, but like I said, it's politically difficult, so people try not to talk about it.

> You can google as easily as I can.

Unsure. But you're the one making the claim.

> If you accept the idea that a penchant for math is randomly distributed among all people

Is there any experimental support for such an assumption?

If.

You also need the assumption that the judges are unbiased and that people have equal opportunities.

Lots of room for explanation from many angles here.

The penchant for math is probably randomly distributed between men and women.

But all that is overshadowed by the fact that culturally and societally women are heavily discouraged from entering and succeeding in fields like math. This begins right from childhood, where an abacus may make a good toy for a boy, while the appropriate toy for a girl would be a mini kitchen set.

Fortunately a lot of this is changing, however, the benefits of no longer discouraging 50% of the population from entering science/engineering won't be felt for another couple of generations.

  > The penchant for math is probably randomly distributed
  between men and women.

Source?

  > But all that is overshadowed by the fact that culturally and
  > societally women are heavily discouraged from entering and succeeding
  > in fields like math.

Source?

  > This begins right from childhood, where an abacus may make a good toy for a boy, 
  > while the appropriate toy for a girl would be a mini kitchen set.

This is often repeated, but I doubt that's true.

> Source?

You mis-quoted; the original comment said:

> If you accept the idea that a penchant..

which was a response to:

> why is it shocking?

i.e. It answers the question, "Why might [someone] find this shocking?" - Note that user 'Hasz' was not the user that found it shocking.

If you think about it, a 55/56 ratio (.98) is only commensurate with a distribution of mathematical talent by which the vast majority of women can't add 2 and 2 together.

Like, it would not even justified by women being "somewhat" less good at maths at the high level than men. Women would have to be really, really bad at maths for that to be a natural result.

To see why this is not true think about the average difference in men and women’s height and the relative prevalence of men and women among people 1.6, 1.7, 1.8, 1.9m tall, etc.

The difference with height is that you can train mathematical skill. For women to be trying, presumably as hard as the men, to become good enough to be elligible for a Fields medal, but (almost) never achieving it- they have to really suck at maths to begin with.

Mathematical skill can be trainable without a huge difference in male/female representation implying women are unable to add two and two, your original bar for sucking at math.

There are many, many obviously trainable skills where the best men are very obviously superior to the best women, sports and athletics providing endless examples. I would be very happy just to finish a marathon but the Irish men’s world record is almost ten minutes faster than the woman’s world record.

Malright. That was a dumb argument. Mine I mean.

Nature vs nurture.

> One of the reasons is, half their cells are using one X chromosome and half are using the other, so they're more likely to get their performance dragged down by deleterious mutations.

This statement is wrong 2x.

1. Lyonization is a process of inactivation that happens early in embryotic development so only one X is dominant in all somatic cells.

2. The chromatin packed X is not completely inactive, so if the dominant X has a deleterious variant the other X can sometime confer protection. Without a good copy of an X allele men getting X-linked disorder is a foregone conclusion. Women on the other hand suffer from X-linked disorders approximately 50-25% as often.

Also there is no evidence linking any of this to math ability

It's not "disorders" but anything that affects math ability. This is plain regression to the mean. If half your cells would make you capable of being an IMO gold medalist, if the whole brain were made from them, but the other half would make relatively stupid so that you could only barely qualify for the USAMO (~top 300 in USA or so), guess what making a brain from the combination of the two will get you.

Like I pointed out above, thats not how it works. And if it were, then women would be at an advantage. If genetics confers any difference in math ability, it's due to the Y chromosome. Period.

What isn't how it works? Why would women be at an advantage? There's clear evidence that different groups of cells are using one X chromosome versus the other. You can see this in cats, and you can see this in mammals' brains using fluorescent genes. If you want to claim it makes women more likely to be in the top 0.001%, you're by all means welcome to explain why. But you haven't.

Edit: You know, it occurs to me maybe you aren't trying to put together statements that make any sense, because when you said "1. Lyonization is a process of inactivation that happens early in embryotic development so only one X is dominant in all somatic cells," you were acting like that's a support for your argument when it's in fact just a description of X-chromosome inactivation. Unless you meant that all cells pick the same chromosome, in which case you're just wrong.

In any case I direct the readers to this New York Times article which has a picture of a slice of the brain with different X chromosomes inactivated. Readers can draw their own conclusion about how this affects the probability of being in the top 0.001% of ability at anything.

https://mobile.nytimes.com/2014/01/21/science/seeing-x-chrom...

I read your response yesterday evening, and was just going to take the lesson and move on. But that wouldn't be fair to you.

You are right. I was wrong.

I was taught that X inactivation happens so early in development (I think pre-neural tube, no?? if so, that's like what, 200 total cells?) that all neurons, or at least all neural subtypes (e.g. Purkinje, pyramidal, basket, etc) all have the same dominant X chr.

When I saw the picture in the NYT article you linked, I was immediately like- no. fucking. way! Well, anyway. I'm sorry about that; and I appreciate the enlightenment.

That said, you should check out figure 8 in the original article. I'd be interested to know what you think. Here's a direct link:

https://www.sciencedirect.com/science/article/pii/S089662731...

(the paragraph just above the figure is helpful to read)

>> One of the reasons is, half their cells are using one X chromosome and half are using the other, so they're more likely to get their performance dragged down by deleterious mutations.

That sounds like something has been severely misunderstood by someone, possibly even me. Are you a biologist?

See https://en.m.wikipedia.org/wiki/X-inactivation

With respect, this does not answer my question: are you a biologist?

The fluorescent proteins don't lie.

Yes, I'm sure they were brought up proper and are very honest, but in order to understand them you need the relevant training. Looking at your profile I can't see that you have that sort of background. So I don't think your confidence that you know what's going on is justified.

Or, like the saying goes- a little knowledge is a dangerous thing.