What I'm saying with this statistic is just that something is happening in the 4 years of undergrad that leads to a difference in interest between mathematics as a major and mathematics as a graduate concentration. That's happening while the students are, as it were, under the influence of the mathematics community. I therefore hope that I can have an impact on that number by making changes to the environment, and to certain decision-making processes.

@ClarkBarwick In my undergrad, the female math students were largely interested in going into teaching, where a higher degree would not be helpful.

Now, I do believe that such interventions, uniformly applied at all levels, will end up in demographic equity. That's not a scientific claim; it's a judgment call, which I'm making on the basis of my own experiences. It's also something of a default position: to expect something different, I'd have to have a good reason.

I disagree @ClarkBarwick

As for the question of whether MO is perpetuating discrimination, I don't feel qualified to speak to that. I don't have a very global view of this website, I don't know anything about the demographics of its users, and I'd prefer to hear from women about their experiences here.

Yeah, but I want those experiences to be backed up by the record.

Everything on here is a matter of public record, for good or for ill.

@ClarkBarwick I disagree with your statement that demographic equity will come from changing the environment. I think this is demonstrably false. Look at Sweden, one of the most egalitarian countries in the world, and compare it to India, a far less egalitarian country. There are actually MORE gender equity in India when it comes to major choice than in Sweden.

user, every time you ping him, it makes a noise on his computer. He sees what you're saying. Pinging him is not going to encourage him to answer you more quickly

Okay Harry

I didn't mean to pester or annoy, sorry if I did

@user658409 over all majors or for mathematics specifically?

Regarding pings there are different preferences; I have seen people get annoyed over not getting pinged too.

I have the inside scoop on Clark's preferences.

I would have to pull it up, I read this awhile ago. And I do not mind pings, if someone wants to ping me that is okay.

No worries. I'd be interested in learning more about the Sweden/India story, and how all those qualities are measured. The details would matter a lot to determine whether they invalidate my belief dramatically.

But it's worth saying precisely what happens if I am completely wrong: In this case, there was nothing I ever could have done to achieve demographic equity. I was powerless against larger trends. I will have wasted my time trying ­- and failing! ­- to make more folks feel a little more at home in mathematics.

Yeah, my concern is about people who have the same view but who aren't into using such anodyne methods

I asked specifically because the social context can influence such choices in various ways, and the same field can have different stereotypes attached to them when one changes the country.

I think trying to make people of all kinds feel more welcome in academia is sorely needed and I am glad you are trying to do so. I just don't think that all discrepancies are because of discrimination or chance.

But to return to the original topic, I understood David's proposal to be to have an ICM discussion on exactly the kinds of initiatives I'm talking about here. The approaches that Valian proposes in An Inclusive Academy (which, I know, I've already praised!) are, I think, entirely anodyne in your sense. They're correcting sometimes subtle environmental hostility and examples of unfairness in our decision-making processes.

(Hostility is not really the right word, but I hope you know what I mean. I just mean an less-than-friendly environment.)

Yeah, I dunno. I don't think the environment is unfriendly in a gendered way.

I think part of the ethic of this site (as opposed to MSE) is that we expect more from people here, and that's fine.

I did see an interesting poll, where people were just as likely to call the users of MSE bullies compared to MO

Oh you mean the environment on MO.

At the risk of repeating myself I find it excessively difficult to have this in a meaningful way at an ICM for I just do not think that the problems are sufficiently comparable over the world.

Yeah, I'm really invested in this place, so I take it personally when people trash talk it with no evidence.

I agree with you, @quid, and I think that is a very important point. (I hope you are okay with the ping)

It'll be hard for me to know whether MO in unfriendly is a gendered way.

I think if people are going to make the claim, it's fair to ask for evidence.

From time to time, I get glimpses of what some math people are saying on twitter, and there is a lot of rumor mongering going around, and never a single piece of evidence.

Then it seems to me all concrete proposals for speakers are US-related. Nothing against the US, but if the goal is to promote diversity on a global scale maybe one could at least give a platform to something else.

As for the ICM, again, I'm not trying to comment on the particular medium. I'm just too ignorant there. But what I am saying is that the general task of promoting diversity and a spirit of inclusivity in the mathematics community is, in my view, entirely worth my time and energy, and I'm keen to learn from anyone.

I am, in point of fact, a particularly haughty and exclusive person, of pre-Adamite ancestral descent. You will understand this when I tell you that I can trace my ancestry back to a protoplasmal primordial atomic globule. Consequently, my family pride is something inconceivable. I can't help it. I was born sneering.

One issue I have with people pushing for diversity and talks like these is the following. People hold all sorts of extreme positions (a faculty member who was head of graduate admissions says that he accepts literally every female applicant regardless of qualification, which is legally and morally discrimination), but then when you ask questions they always are vague and retreat to things that no reasonable person could disagree with. "Making the culture more welcoming" etc.

Not saying you are doing this, Clark. But these types of talks etc. do trojan horse extreme views including literal discrimination.

If an individual faculty member wants to take on only female grad students, I don't see a problem. That's academic freedom.

As soon as it becomes a directive from on high, then it's a big problem for me.

If all people did was make the culture more welcoming, help fight hostility in subtle and unsubtle ways, etc. I don't think anyone would disagree. But the issue is it's impossible to tell what people actually believe. People start off saying something more extreme and then when questioned retreat to something that no reasonable person could disagree with. When people talk about diversity, I mostly don't trust what they say. It's hard to get people to even commit to what they really want.

I disagree completely for example with everything on the Inclusion/Exclusion AMS blog

More than that. I find most of what they say morally repellent.

The thing is, that is just what they are posting publicly. I don't trust that those are their real/private views and how they actually behave towards people. And the people posting on there have a lot of power. If you were to question any blog post they would retreat to something reasonable. But their real views are even more extreme.

No, the people on Inclusion/Exclusion are very publicly saying what they want, and it's horrible.

What they want is more extreme than what they are posting on that blog.

I'm not sure I've seen the kinds of extreme positions you're describing. Among academics, I mostly know mathematicians, and among those I know maybe two or three more a little more "extreme" than I am. None would ever accept "literally every female applicant" for anything, unless somehow they were all fabulously brilliant. Now, you may think that they aren't revealing to me their true positions, but I hope you're wrong about that.

Yeah, the really extreme people are in Math-Ed

They're incredibly extreme.

Why does this matter? It matters because I'm worried you're arguing against straw men. One of the problems with this particular cultural moment is that everything either is or is seen to be a dog whistle of one kind or another ­- that is, that they are trying to indicate an allegiance to ideas or groups above and beyond what they are actually asserting. I think that's a widespread phenomenon, but it's perceived even more widely. That's why I'm taking pains here to say exactly what I believe.

"they" there should have been in scare quotes.

I'm also trying to be careful to indicate clearly what I'm certain of, what I strongly suspect but can defend, and what I'm just guessing at.

Yeah, I'm talking specifically about a particular group of people centered around the Inclusion/Exclusion blog and twitter. I won't name names in a public place, but I am arguing against a very specific point of view that is being pushed by a specific group.

I strongly suspect that there are far more people in mathematics whose views are extreme in the opposite direction to the direction you're describing. (I refuse to comment on Twitter, as it's dreck. The whole of Twitter could vanish tomorrow, and the world would improve noticeably.)

I was hoping they could find a legal pretext to shut it down.

It's the devil.

What I'm trying to suggest, though, is that it isn't good enough for us to tell each other what we're against. It looks to me as though we're both against unfairness, and we're both against prejudice. Ok, great. What are we for? And I'm guessing (but I'm not really sure) that where we disagree is that I think that we have more problems with prejudice than we do with attempted solutions to prejudice.

Now, I don't know anything nontrivial about the blog that you're talking about, but I think you way overestimate the power of the internetted word. What matters is not to be found on the internet. It's what happens in committee meetings. It's what happens when people decide on who should be invited to seminars. And let me emphasize: very little of this is explicitly sexist, or racist, or prejudiced in other ways.

@user658409 I really really don't want to get bogged down in a discussion here, but have you ever considered why women interested in academics are pushed towards high school teaching, and if it is something college should, at least a little bit, fight against? I understand there are some preexisting societal trends but "not my fault so I shouldn't do anything about it" is not an attitude I can get behind.

The truth is that there are many talented women that don't even consider academia as a plausible career choice, and we should find ways to at least limit the damages while we work to reform the wider society. I don't have solutions but "the problem is hard so let's not even bother" is not the kind of sentences I view kindly

(I"m talking about women because of the extreme visibility and almost universality of the situation -- I'm sure the same could be said of other minorities)

Said that I'll bow out of the conversation

Clark: "I strongly suspect that there are far more people in mathematics whose views are extreme in the opposite direction to the direction you're describing." This is the whole disagreement, the whole argument and why many people oppose any type of diversity lecture. I strongly disagree with this statement. There are far, far more left wing ideologues in academia than far right. Even, most people in academia are liberal.

Most people in academia are liberal. If you wanted equity across all areas, you would want to increase the number of conservatives in academia. (I am not advocating for this)

@DenisNardin I disagree with your premise that women are pushed towards high school teaching. I just don't believe that. Just because more women than men go into high school teaching doesn't mean anyone pushed them.

@user658409 Well, it is a fact that women tend to do teaching careers more than men, and that math departments have, on average, an abysmal quantity of women. You might shrug your shoulders and chalk it up to some innate differences, but I'm not prepared to do that

(also please can we try to make this not a US-centric discourse? The ICM is not a US-centric event in any shape or form. In particular, pay attention to how you use words like "liberal", it doesn't have the same meaning as you think across the world)

@DenisNardin I am not "shrugging my shoulders" and I have spent a lot of time thinking about these things. I have simply come to different conclusions than you. I don't believe that women are being pushed into teaching careers more than men.

Ok then, why are there significantly less women in academia?

(this is not a rethorical question -- if you have a reasoned opinion on the topic I genuinely want to hear it)

By the way, I count "biological differences involving childbirth" as a negative externality that we should compensate for, if that clarifies my position somewhat

That is a complicated question with complicated answers. First of all, of course there is some level of hostility, sexism, etc. that exists and should be eliminated. I have supervised female students who have experienced harassment and the perpetrators I find disgusting. So to be clear, I do agree that there are some issues with inclusivity that should be remedied and I do support those trying to improve those.

But primarily, men and women are different. There are differences in personality between men and women which lead to differences of interest. It is well backed up by research that men and women differ in statistically significant ways on several personality traits. I do not believe these are purely cultural, which is also backed up by research. These differences in personality lead to differences in vocation. One piece of evidence for this is that:

I also do not want to get bogged down in the discussion here, but two things came to my mind when I read your messages from the last few hours:

firstly, the topic of gender-specific differences in preferences (the "Sweden/India story") reminded me of a paper that was published by Science two years ago and that is at least interesting to look at: Falk & Hermle, Relationship of gender differences in preferences to economic development and gender equality, Science, Vol. 362, Issue 6412.

Secondly, the whole discussion here is always framed in such a way as if having a research career is the most desirable thing one could strive for if one has a certain talent and passion for mathematics.

But what if it isn't? I mean there are clearly many downsides of this path in life, like e.g. not really being able to decide where one will live. It could well be that there are disproportionally more women who decide early (like before finishing their undergraduate studies) that this is not the life they want.

In more egalitarian countries (Nordic countries), the discrepancy in major choice is actually higher than in less egalitarian countries (say, India). I believe that in an environment where women are more free to choose what they want to do, they are actually more likely to choose what they really want to do.

@JensReinhold Thank you for the link to the paper, and I agree wholeheartedly with your other points.

Two points and then I'll go back to working: (1) I'll try to read that paper when I have time, but I'll need a lot of evidence before I believe in innate differences -- it's just very very far from my experience (2) I of course do not consider a research career as the only life worth living, but my experience is that many people don't consciously reject it, rather it is not even something on their radar, and this I consider a negative situation

While perhaps interesting in an abstract sense I find the discussions around whether there might be statistical or innate differences at best a distraction and at times unhelpful, it I think it is not really relevant in practice where one deals with individuals.

@JensReinhold this just moves the question though to why this might be the case. (Granted one then is arguably outside of a domain specific to mathematics.)

The twin towns of Emmerdahl and Efferdahl each have their own elementary schools, which have been operating continuously since the early 1800s. They are roughly of equal size. Children from these towns are educated at one of these two schools till age 14 or so, and then sent off to the big shared High School between the two towns.

Historically, the Emmerdahl School has been a place of love and support. The students are constantly reminded that they can do anything they put their minds to. Back in the 19th century, they were explicitly told that as Emmerdahl Kids, they were superior, and destined to dominate the Efferdahl Kids.

At that time, the Efferdahl School was, by contrast, quite cruel to its students. The kids were punished harshly for small infractions, and the students were regularly reminded that as Efferdahl Kids, they were fit only to serve the Emmerdahl Kids.

As you might expect, in those days, the Efferdahl kids were generally not successful as students in the High School, and most dropped out long before graduation. Effectively none of the graduating class had any Efferdahl Kids.

This was the case right up to the early 20th century, when reforms started to be implemented. The reforms were introduced slowly — first they stopped the regular beatings of the Efferdahl kids; they introduced rules that said that that the punishments need to be the same in both elementary schools; etc. Each time the reforms were met with arguments, and sometimes hostility, and each time it was hard work (often of the former Efferdahl Kids) to bring to light the injustice.

Still today, there are differences. Less dramatic than in the 19th century, to be sure, but they persist. Efferdahl's halls are adorned with posters of successful Emmerdahl students. Most of the instructors at the high school and both elementary schools are Emmerdahl kids who left before the most recent reforms.

In meetings to see who should get the prizes, the files of Efferdahl Kids are scrutinized a little more harshly, and sometimes a suggestion is made that an Emmerdahl Kid had helped with a hard project, etc.

Nevertheless, each year since the reforms started, the percentage of Efferdahl kids in the graduating class has risen. Today, the Efferdahl Kids make up about a third of the graduating class. Some folks think that suggests that the reforms are working, and more are needed. We'll call these the reformists.

Others say that it's pretty obvious that everything is fair now, and that the differences in outcomes are not going to be significantly changed by further reform. We'll call these the anti-reformists.

Perhaps 30 or 40 years ago it would have been common to hear an anti-reformists explicitly comment that the Efferdahl kids were just intrinsically less smart or hard-working than the Emmerdahl kids, but these days virtually no one would ever say that, at least not out loud.

Now, instead, the argument has softened to the claim that Efferdahl kids are 'just different.' Perhaps they're intrinsically less interested in the work, or maybe they see the value of not winning prizes or doing the kind of work that would merit a poster of them on the walls.

The anti-reformists admit that there are a few areas where the two schools are not quite equal, and they have heard stories of cruel or dismissive behavior toward the Efferdahl students, but they say that is inadequate to explain the differences in High School graduation rates.

The reformists point to all the progress that has been made, and suggest that we might reasonably expect it to continue, if only we keep making things better and fairer at the two elementary schools.

The anti-reformists respond that they have very good data that in fact the inequality is just the result of the inherent difference between Emmerdahl kids and Efferdahl kids. The reformists point out that the same 'inherent difference' arguments were made back when there were NO Efferdahl students graduating, and they had studies to back those claims up too.

Those old studies, the anti-reformists say, were unscientific, of course. But today the studies are very scientific and robust. We have arrived, they say, at as much equality between the two towns as we can expect, and the reforms aren't really going to help so much anymore.

The reformists observe that data show that simple reforms can have more equitable outcomes, and that's a nice thing. The anti-reformists call into question the seriousness of that data. And in any case, they argue, the burden of proof rests with those who seek equitable outcomes. And in fact, isn't all this focus on reform just a way to sneak in some radical agenda? Why, just last week they heard a reformist say something that sounded extreme.,,

I can't map any of the groups or institutions in this parable neatly onto anything where I'm from.

(Central NJ shore)

At least the dynamic of the two schools you mentioned doesn't really exist where I'm from, since there was never any official segregation. There was, after all, only one local public highschool.

I heard that texas is in a bit of a different situation

Also, I think for boys and girls, we already see that in terms of highschool grades, girls already outperform boys pretty much everywhere in the entire world where women are entitled to an education (and have lower levels of disciplinary problems and later criminality), so in that case, I don't think this parable even relates to that question.

@HarryGindi I went to college in central NJ (not the shore, sure) and I found it striking how many people I met there from Cherry Hill and how few people I met from Camden. Sure those are different towns with different high schools I think, but doesn't that just make the situation worse than the parable?

That's because Camden is iirc a city of nightmares and one of the most dangerous cities in America.

or at least it was up until very recently

(Camden is also among the districts receiving the most money per student in NJ)

The state court system has a large amount of say over school budget allocation. Anyway, the point I'm making is that if it weren't for the need for things like extra security, Camden would be among the most well-resourced districts in the state.

@HarryGindi What you say convinces me more than ever that I should be interested in learning about ways that I, in my daily life as a mathematician, can be part of the solution to inequities such as those between Camden and Cherry Hill.

The first thing you would need to do is figure out how to solve gang violence.

I didn't say it was my duty to take on my back all the problems and solve them myself. I said I feel I should be doing my part. Your attitude strikes me as defeatist.

It's not defeatist, but I eagerly await your proposals.

Right. Details, such as the groups involved or their stage of life, are changed. The reasoning suggested by those who oppose reform is however identical, and so if you are anti-reformist with respect to, say, women in mathematics, then you would have to either (a) feel as though the anti-reformist for the elementary schools in this parable seem reasonable, or (b) explain how the changed details have any impact at all on the arguments.

Great! I agree that we should listen to expert opinions about how we can all do our part.

I'm against the mathematics community trying to solve social problems that are insoluble within academia

That doesn't make me anti-reformist it makes me realistic

Give me a break, Harry. Are you against category theorists solving problems that are insoluble within category theory?

Give me a break I don't want to see mathematics politicized and wrecked. We have enough politics in our lives. Can't we be a sanctuary?

Not every human endeavor has to be aimed at saving the world.

Do you think that if we all just ignored inequity in mathematics that politics in mathematics would go away?

I think that pure mathematics as a discipline has nothing useful to say about inequality in safety and elementary education in urban new jersey.

Trying to make it fit into that role is an attempt to fundamentally change the focus of the field.

Nobody's asking you to change your research, Harry.

Not yet.

I also think that overtly politicizing academia is damaging public trust in academia.

I think this is undeniable if you look at surveys.

@HarryGindi What are you so paranoid about?

It's not paranoia I've seen it happen before.

There's virtue in being above the fray and apolitical. I firmly believe this.

@HarryGindi I'm all ears.

We can talk about it in private if you'd like.

We're connected on google hangouts, or you can contact me on discord at Harry Gindi#4480

The problem with the story above is that it leaves out so much nuance and detail that all content is lost. One could just as well write a different story that emphasizes something else and arrives at an entirely different conclusion.

As said earlier I am unconvinced that such discussions are helpful.

For example one could say that there are reformists now that claim things rather at odds with the reformists 30 or 40 years ago, but this time they are sure they got it right (as sure as were those 30 or 40 years ago). Etc.

I've placed some of the answers that I have seen on this page into a different context, and there, to me at least, they do not look reasonable. I didn't see nuance or detail in those answers, so I didn't put it in the story. If you're unhappy with my lack of nuance, then you ought to be equally unhappy with the lack of nuance in the answers on this forum.

So if there are nuances and details that are germane, then they can be named, and we can examine them.

My point is that the problem is with where the burden of proof is placed. One side says that the burden of proof rests with people who want equality, and the other side says that the burden of proof rests with people who do not want equality. I think the latter view is more reasonable.

My issue with the story is that it seems to pretend to be modeled from reality, while in actual fact it is just a story that is written to make a point. All the choices are made so as to make your point.

I'm not sure what the alternative is to having such discussions. Shall we all come to conclusions about the world at some early age and never have anything change our minds?

I mean, whether or not we should do that, it seems like most people do.

They've done studies on stability of political identity

Yes, I have a view and I'm defending it. I'm not feigning neutrality here. I don't think I did that.

I am lawful neutral =]

@ClarkBarwick What precise statement are you deciding burden of proof for?

The emphasis is on "such." A relevant discussion could be, and here we agree, what actually should or could be done. Most everyone is for making things "better" yet what exactly does this mean and in particular what exactly could or should be done.

I guess one thing is this: Maybe equality is good, but not at any price.

It is also noteworthy that you wrote "keep making things better and fairer at the two elementary schools" (my emphasis). A problem in some, not all, of these discussions is that one does not get away with the impression that the idea is to keep making things better for everyone. Instead one group is singled out as the root-cause of the problem.

"Is it reasonable to aim for relative equality in the relative populations of various groups (women, e.g.) at various levels of math education?" I claim that the answer is yes, and I think that the burden of proofs rests with those who say "no."

Not to be glib or dismissive of this, but why do you believe the burden shifts when we change from mathematics to e.g. being in prison or sanitation?

I think I have a perfectly good biological explanation for why young men are more likely to be in prison, which makes me at least agnostic to the idea that women might have on average different personalities and different preferences.

Young male aggression is a human universal.

quid, You say "most everyone," but I'm not sure of that yet. There are arguments being made here that (a) the differences in outcome are immutable, and (b) this is "just politics" and therefore should be avoided. I'm claiming that there is something here that is worth a professional mathematician's time.

@ClarkBarwick I think that the question, as you have phrased it, unfairly collapses a spectrum of answers through vagueness. "Aim for" is an entire process, and people may have objections at several steps in that process.

Harry, I agree that "equality is good, but not at any price."

I'm not sure what's unfair, exactly.

The unfairness comes in the idea that answers are simply "Yes" and "No", as implied by what you are saying about burden of proof.

@HarryGindi Im sure you've heard this before, but the answer to your question is no, we can't be a sanctuary because there are people within the community that can't just switch off who they are, and the politics of the outside world directly interfere with who is part of academia. This has been discussed before but two people born in different places will have different challenges to make it in math just because of their passports. Politics within and outside academia affect the actors.

But (a) is orthogonal to making things better at both schools.

@AngelTC Different people have different challenges getting up in the morning. I don't see your point

And if those challenges are a result of (unfair) social dynamics, policies, etc? You just dont care?

Taken to an extreme, we should hire people who are bad at math because they're underrepresented among mathematicians.

Angel, unfair social dynamics are not my area of study or expertise, nor are they yours, I assume.

Plus we're not politicians and we're not elected.

If we alienate a large proportion of the population pursuing political goals, we will be thrown out or defunded.

They aren't paying us to dictate politics to them. They're paying us to do math.

What about the people that are already alienated and broke and as a result have a harder time to make it in math? I repeat my question, do you, personally, dont care?

I think it should come down to a vote about what kind of country we live in.

Are you answering my question?

Are you asking my personal views, or if I think we should act on them?

Both if you want

because the first question is personal, and I won't answer it, and the second answer is no, not without consulting the public.

All right.

quid, I'm claiming that it isn't orthogonal. If we've decided a priori that one group of people is never going to be as successful on some metric as another because of biology, then we have an excuse not to implement further reforms to ensure fairness.

Render unto Caesar the things that are Caesar's, and unto the Mathematical Community the things that are ours

user44191 I don't see that as unfair. It's not the only question I want an answer to, but it's one of them. If you agree that the answer is yes, then we can have a discussion about how to achieve that, and we have plenty more opportunities to disagree.

Yet somebody might believe this and still be committed to make things better. I understood make things better as increasing the quality of the schools etc.

I think I said "better and fairer." Maybe "better" wasn't the clearest word there. My apologies.

Alright so making things better at both schools actually was not a goal of the reformists?

I'm taking it as read that both reformists and anti-reformists want things to be "better," but they may disagree on what "better" means.

That too, but there is a separate concern, in that making things more fair can also be obtained by making things worse for everyone (for some more for some less).

That's true. And I'm opposed to that.

There's the story of Boris and Igor, two communist-era farmers, both very poor. The main difference being that Boris has a sickly goat tied to a stick outside his shanty. Igor has no goat. A spirit visits Igor, offering him anything his heart desires in the world. Igor pauses and replies, "I wish that Boris's goat should die."

All this to say: I'm opposed to Igor-style equality.