As a rule, I do not discuss math with mathematicians if I can at all avoid it. I would like to tell you why, but it’s complicated. You can never make assumptions about a marginalized person’s character based solely on behavior. Oppression creates behaviors that wouldn’t otherwise be there, and if you are not going through the same oppression, you can’t know how you would behave. People have made a lot of assumptions about me because of my actions with respect to math.
I must not like math. I must not like math enough. I don’t find math research interesting. Maybe I should be doing something else. It’s okay if it’s just too hard. It’s okay if academia is not for me. If I really want to make a difference, I should work for NSF.
When you give off the impression of struggle people really expect you to Totally Understand Yourself And Your Motivations And Precisely What You Want Out Of Every Experience. I know plenty of mathematicians who have waned in their desire to be in academia, but their presence was never scrutinized and their worth was always taken for granted.
I can count on zero hands the number of times I was asked “Tell me, who or what crushed your mathematical curiosity?” When I stopped talking about math, not a single friend said “Have I done something to make you uncomfortable talking with me?” Nobody questioned whether I felt safe asking questions. They just built up their assumptions and their judgments. It became a thing. That thing they knew about me, you know, how I don’t talk about math. Whatever my problem is.
I hated it, but even still, it was better than discussing math.
It’s not that my friends had terrible intentions. Nobody was mean to me, nobody consciously laughed at me. There’s just a way that mathematicians have been socialized (I guess?!) to interact with each other that I find oppressive. If you have never had someone mansplain or whitesplain things to you, it may be hard for you to understand what I’m going to describe.
Usually, friendly conversation involves building a shared perspective. Among other things, mansplaining and whitesplaining involve one person of privilege forcing a marginalized person into a disagreeable perspective against their will, and not allowing them a way out. If you are someone averse to negative labels, it can be silencing. My experience discussing math with mathematicians is that I get dragged into a perspective that includes a hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent. Maybe I would’ve successfully assimilated into this way of thinking if I had learned it at a time where I was at the same level as my peers, but as it was it was just an endless barrage of passive insults I was supposed to be in on.
I got used to bracing myself. I got used to analyzing my self-consciousness. I prepared for every meeting with my advisor with a list of pre-approved mathematically sound sentences and questions. I got used to explaining that I wasn’t fluent in math. That I was different from everyone else. I let them win, because the alternative was too big an emotional sacrifice.
In preparation for my defense, I gave a talk in a friend’s class to a group of graduate students. It was my first ever math talk. At one point, my friend asked a fairly simple question about what I’d said (based on something she’d misheard) and the foundations of all my knowledge shattered and I was basically like “Maybe everything I’m doing is wrong and/or illegal, I don’t know.” Did that happen because it’s an essential part of my personality that would be with me no matter what? Did it happen because I’m a woman who was raised as a girl in a misogynistic society that expects women not to know things and to apologize for existing? Did it happen because I am a person of color who went to school with white people and learned that I don’t get to define my own experiences and my own knowledge? Did it happen because I learned that mathematicians believe some mistakes are morally reprehensible? I don’t know. I can’t know.
I can only wonder if there are people out there who think the way I think who are suffering in math or who got pushed out or never tried, and what a loss that is.
Thanks for sharing this, Piper. I have a lot of reactions to it, but I’ll stick with three things:
1. I am terrified to talk about math with people. Seriously. Somehow I’m not so scared to “give a talk.” But to sit around a just shoot the shit about math? I am always afraid. That I won’t be able to follow, that I won’t have anything to contribute, that they’ll figure out I don’t really know anything. It’s something I actively work on, because the truth is that I really do like math, and I really do want to be good at it, and the only way for me to get there is to talk to people. I know this about myself and how I learn. It doesn’t make it any easier though… it just means I do it.
(FWIW, my grad school experience was not so different from yours. I had a really good undergrad math major, but I took so much time off before my PhD program that I was really, really rusty. I didn’t remember most of what I needed. So who knows… does the fear come from being a woman in math or from having a non-traditional background when you enter grad school or some combination?)
2. I’m so sorry that my question in your talk brought all that stuff up for you. I don’t know if it helps, but I honestly only ask questions in a talk when I’m super interested in what’s being talked about. I’m not a person who asks a question just to have a question be asked. When I give talks, I just work on the assumption that everyone functions this way. I know it’s not true, but it’s better for my sanity that way.
3. I really hope you’re not done with math. The response your thesis has been getting… it’s pretty obvious you have something important to say to this community. We need you here. If you want to practice talking about math with people, I volunteer. We can be uncomfortable and nervous together.
thanks!!!
re your question, I needed the practice!
I am definitely wary of talking to people about math. Everyone (seriously, everyone) says incorrect things sometimes when talking about math, but I’ve notice that if you fit people’s ideas of what a mathematician looks like (white, male, wearing either a button-down or a free math t-shirt), saying wrong things isn’t really a problem. I mean everyone makes mistakes, right? You really meant this, didn’t you? If you don’t fit that image though, far too many mathematicians take it as a confirmation of their assumption that you couldn’t possibly know what you are talking about.
We (the ones who don’t `look like mathematicians’) get less practice talking about math in the places that are supposed to be lower stakes in part because it is never lower stakes for us (we are constantly having to defend our right to be there, and making even small mistakes in so-called friendly company feels like it could our position in jeopardy).
great points!
Piper, your article is interesting. I have worked in academia, and I have my doctorate. I also have been marginalised by established Professors. Yet your article leaves me wondering; why won’t you discuss math with people?
it is painful to talk to people who give off the vibe that my level of knowledge (or manner of thinking/speaking) is not okay, even if it’s unintentional.
when i said: “My experience discussing math with mathematicians is that I get dragged into a perspective that includes a hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent. Maybe I would’ve successfully assimilated into this way of thinking if I had learned it at a time where I was at the same level as my peers, but as it was it was just an endless barrage of passive insults I was supposed to be in on.”
i was talking about “people” (ie other grad students), not “established Professors.”
i am fine teaching calclus and holding office hours. and now that i no longer feel obligated to fake proper math speak, i’m okay talking math to non math people. but i essentially haven’t had any positive experiences talking research math with mathematicians. over the years my husband and i have figured out how to have conversations about math… but still not casually.
Just wanted to say that I and so many of my friends have identified with your post, especially “My experience discussing math with mathematicians is that I get dragged into a perspective that includes a hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent. ” I realize you quoted it in your comment but it’s so good it deserves requoting.
I thought that feeling was something that I just had to burn through and burn out of myself and that no one else ever felt, so it’s good to know that I’m not alone (and it turns out a lot of my friends feel the same way!). Thanks for giving a voice to a problem we all try to hide- perhaps it’s mathsplaining in a condescending, patronizing way (but maybe there’s no other way to talk math, which is so didactic? Unclear? I guess this is why you don’t talk math…) I can tell you that what we’ve done in a small seminar is force everyone to give talks the first time they attend, and inevitably the first talk is horrible and embarrassing and awkward and sweaty, but everyone goes through the gauntlet and understands. However, I can see that putting someone through this awful experience who has had loads of previous awful experiences could turn them off from ever coming to seminar again, whereas putting someone through it who hasn’t actually helps them if they come to seminar again (generally they’re less mathhole-ish after doing the first talk). In sum I don’t have answers but I like conversations, so thank you for starting one in so many disparate places.
yenergy suggests that maybe “mathsplaining” is necessary, but as someone who has worked as a (Ph.D.) math professor for eighteen years, I can assure you that it is not. It is simply the dominant paradigm, particularly in the research community. Once you find your true math friends, the people you can really trust, the ones with whom you can really let down your defenses and say what you do and do not know, then you will find out how great true mathematical communication can be and how it should work. It can be tremendously difficult and frustrating to try to explain concepts that you now only sort of remember, but once understood very well, to someone who wants to understand deeply. (But it’s worth it!) This is when you will begin to understand why the other people act as they do. They simply do not have the patience to have a mathematical conversation with someone who is not on the same wavelength with them. Therefore, they are enforcing the mathematical social convention that what we don’t remember clearly enough we go home and look up (or figure out again for ourselves) so that the conversation can proceed without getting bogged down. The key is probably to realize that even though it is a terrible way to treat others, it happens to everyone. So while I don’t excuse the behavior, I recognize that it isn’t personal to me or to you. Try to hang in there. And when it’s your turn to speak, just try not to perpetuate the problem.
1. thanks yen! i don’t think there’s ever a solution that works for everyone. if you’re working within a broken system, whatever choice you make is still going to be partially messed up, you know? i think the only thing you can ever do is just be honest (and even labeling a problem can be extremely useful psychologically).
2. the discussion of whether it’s possible to talk math without being inappropriately mathsplainy comes off to me as analogous to wondering whether humans are capable of being generous or if they are inherently selfish. if selfishness is dominant in your environment, it’s easy to bring up examples and suppose it’s only natural, but then someone can point out that actually in these particular situations people are generous, so let’s not lose hope, just try to stick with it til you find the generous spaces.
i understand that point of view, but it also makes me a bit angry. and i want to yell Of Course Humans Are Capable Of Being Generous!!
people are naturally generous. as long as they feel safe. and there is no reason to take insecurity for granted as a necessary evil, in life or in math.
what i want is for mathematics to be safe. because, unlike living, math is optional. i believe the current environment of math pushes people out and that makes math worse.
and it pushes out the exact people who would help make it better!
Dear Ms Piper,
I have recently become aware of your thesis at Princeton via a friend’s link to an interview you gave on mathbabe.org. This led me to your blog. In your latest post above, you include the following sentence: “Among other things, mansplaining and whitesplaining involve one person of privilege forcing a marginalized person into a disagreeable perspective against their will, and not allowing them a way out.” The terms “mansplaining” and “whitesplaining” are, taken literally (and apparently you like to take things literally) explicitly sexist and racist respectively. Yet, in your interview you describe how you became “consciously anti-racist”. Can you explain this to me ?
Sincerely,
Peter Hegarty.
I am happy to answer this question, but I will not debate the answer. I would like this to be an oppression free zone and part of that means not forcing marginalized people to defend their humanity or their expressions of their own experience.
in order to understand oppression, you need to understand power. you need to believe in power structures. casually racist/misogynist people I’ve encountered on the internet generally do not believe in race/gender/etc based power structures. they do not believe they live in a white supremacist patriarchy (and would probably lol if I said heteronormative. the one word for everything is kyriarchy).
I am not going to prove white supremacy etc to you, as you have access to the internet, and because it’s emotionally troubling to have to prove that sort of thing.
so, if you take racist and sexist (and homophobic, transphobic, ableist…) power structures as a given, then you get that oppression only flows from someone in a dominant group to someone marginalized. wrt gender, a man cannot be oppressed by a woman. a woman cannot be sexist against a man. even if she hates all men simply for being men, she is not oppressing them. she cannot spread her hate to a network of good old girls who will make sure some man isn’t respected or can’t get hired. if she assaults a man, she can’t count on the media to drag her victim through the mud trying to figure out to what extent he deserved to be assaulted.
similarly a black person can’t be racist. now there is intersectionality. a person can be an oppressor in one area and oppressed in another.
for easy to read information on this, I highly recommend Everyday Feminism.
back to power. aside from the fact that I can be marginalized by white men, but can’t marginalize them in return (think boss-employee, or terrorist-hostage relationships), it is also important to note that looking at race/gender is not inherently wrong. people only think it is because traditionally white men used these categories to oppress others. but the problem wasn’t the categorizing, it was the oppressing.
today race gender and other things determine what kind of life you can expect, ignoring that only perpetuates the problem.
any person in a dominant group who is offended by the notion of taking someone’s race/gender/etc into account would be wise to work to dismantle their own supremacy. once our access to health and wealth ceases to be related to race/gender/etc then we can talk about how to be fair to white people, men, cis gendered people, straight people, mainstream US Christians, able bodied people… but we’re far far from there.
feel free to ask more questions, but I will not necessarily “approve” a post that denies white supremacy etc.
Hello, this is an interesting explanation of oppression/oppressor relations. Especially the comment on intersectionality I find very interesting. Thanks for sharing this thought.
One need only be in a position of power to oppress. A person can belong to the dominant group on one level and not on another. As a kid I was bullied by whites, blacks, Mexicans, boys, girls. It’s always a laugh to see people claim that members of one group can’t oppress members of another group. All it takes is being in a position of power or the then dominant group. A 10 year old white boy is not in the dominant group when the group consists of him, two teenage black boys, and an adult black male, not at the scale of the event.
I once told a manager of mine about being attacked by those two boys with a belt and chased with a knife as the adult sat by and laughed his ass off. My manager, also black, said, “You must have done something or were about to do something.”
When a department that consists primarily of one gender and hiring committees for that department always have members of the department of said gender on them isn’t there a risk of sexism, particularly when the person with the final approval is a manager from said gender?
Yes, racism and sexism exist. Yes whites and males enjoy unfair advantage in the U.S. No, it isn’t so simple as to say being a member of an oppressed group means one cannot oppress members of the dominant group.
There’s a difference between abuse and oppression. There’s a difference bewteen person-to-person bigotry and institutional racism, for example.
One need only be in a position of power to abuse. A diverse group of bullies may abuse any child for any reason. If the bullied child is black, they will be impacted differently than if they are white. They will be impacted more if they are LGBT than if they are straight/cis. By impact I don’t mean physically in the moment, I mean emotionally and long-term.
White supremacy is a system that puts white people on top. It makes them normal (not, as some think, special). If a diverse group of children bully a black kid, white supremacy is certainly invoked in the different way the child is impacted because they’re black. Furthermore you can imagine that the children are part of the system. There’s no rule in white supremacy that says people of color can’t help whites oppress others. I’m sure plenty of slaves felt the best way for them to have some amount of security was to gain the favor of the slaveowners by helping enforce slavery. That doesn’t make those slaves racist. It doesn’t make slavery not racist. White supremacy is very complicated. So having POC in on the bullying isn’t enough to say it’s not about white supremacy.
I don’t know whether POC can oppress each other. Again, anyone can abuse anyone, but I’m not sure about oppress. I’m still learning these things. If a latinx person says some crap to me, it’s not the same as if it comes from a white person. The latinx has their own stuff to deal with; it’s not coming from a place of privilege. Either they’re parroting some white supremacy nonsense or they’re saying their own thing which is probably a reaction to white supremacy. On the other hand, I suspect that non-native POC can be complicit in the oppression of natives. All non-native North Americans benefit from their erasure. It’s complicated.
Piper,
Thank you for even discussing this with me.
I suspect that we have different definitions of racism. What you’ve said is similar to what was taught in one of my classes. The teacher and the text book author both said that there were other definitions but never addressed them. I consider racism to be something that existed on an individual level first and only later emerged at an institutional level. I imagine it is rooted in some biological function that has been twisted. It existed all over the globe long before whites and blacks made it to this continent. It seems to me that any theory of racism that fails to take that into consideration is flawed. It is just an opinion, but it is my opinion.
Regarding the existence of white supremacy and privilege, it is not my intent to deny their existence. The problem is very real and has to be addressed. Nor am I beating the “Whites are victims too!” drum. I enjoy many advantages, one being that when cops have been rude and abused their power, I’ve been able to speak up and walk away (still glad I had witnesses though). I’ve never been pulled over for being white and being in the ‘wrong’ neighborhood or car.
In the end I don’t know. Theory is like a map, useful but limited. Differences in theory shouldn’t prevent people from agreeing on reforms they would agree on otherwise or considering strategies that they might not readily derive from their own model.
I know some people (all white) that I’m reluctant to talk with about this because they just try to twist it to justify an abusive/oppressive ideology that I just don’t get (I’ll have to think more about the abusive/oppressive distinction). I’d say that the oppression whites in the U.S. as a group experience is due to classicism and religious bias. Once again its the one’s that are oppressive that are screaming that they are being oppressed. Then there are those that are oppressed and defend their oppressors.
I have started reading your thesis! I’ve only gotten up to my B.S. in applied math. Yeah, its over my head. Very cool though. I appreciate your decision to say it in your own way. Sometimes I enjoy mathspeak, but I think it is very easy to lose sight of it being very specialized.
Oh! I’m going to cut this short. I could ramble on (actually I did and still am, but decided to edit myself). I’ll say this your thesis, your emphasis on recognizing that people come to math with all sorts of different experiences, that we communicate and experience it differently; it touches my heart and brings up a lot of memories and emotions. I think a lot of people in our culture have have suffered because of the way math and math education have been viewed in this country. Some cope with it by saying it isn’t important,some by locking it up, and some by saying “I managed it you should too.”
That I managed to get my B.S. in math is a strange thing to me. I’d talk with my class/study mates about why we were interested in math. Sometimes I’d add that I was doing it because it was hard. They’d say something to the effect that that was admirable. What I really meant was I was trying to prove to myself that I wasn’t stupid, because that is how much of my experience with math left me feeling. Don’t get me wrong, I love it. I may not be very good at it, but I love it now. The experience has left me craving more; at the same time I wish I’d done a minor in something else, building on other abilities that came easier to me.
Thanks Piper.
– Alex
i’m going to reply in chunks b/c i’m supposed to be working right now.
first, your definition of racism.
the idea that racism is old and somehow natural is inaccurate ahistorical white supremacist rationalizing. 🙂
okay so, i’m not saying it’s *your* white supremacist rationalization. or that it is wrongheaded. what you’re saying is a perfectly reasonable opinion to have from within the white supremacist fishbowl we all live. it’s an opinion i used to have. it is what a reasonable person would think if they didn’t support racism but didn’t know the relevant history. and the relevant history is not taught in school.
whiteness was not a thing before there was a financial incentive to whiteness. people weren’t racist until after racism was carefully constructed over a long period of time. i can maybe look up some links later. there’s a really nice video that may have been called “race baiting 101” i forget but it’s on youtube. also read all the things by Ta-Nehisi Coates and you will see the depths/layers of racism.
always think about who benefits. who benefits from various definitions of racism. who benefits from thinking that racism is probably natural. think about why we haven’t been taught the history of racism we’re just left to our opinions. etc.
more later (perhaps much later).
Race Baiting 101 video on youtube
Invention of the White Race <-- i haven't read this, but someone shared it elsewhere.
whatever else I thought I was going to talk about, I’ve forgotten…
question: why do white people get to have opinions on what racism is?
it always helps me to think about a situation which is obviously oppressive. like in the days of chattel slavery. if a slave owner says they aren’t racist because they take care of their slaves like family, does that make it true? do you ask the slaveowner for their “objective” view on racism? if non slaveowners say they aren’t racist because they don’t support slavery, but they still don’t welcome blacks into their society as equals, should we accept that definition?
when white people can’t concede to let black people define their own experiences… how is that not the work of white supremacy?
You actually think you aren’t biased. Interesting.
i don’t think i’m “not biased” i think there is no such thing as an “objective” opinion on oppression. you side with the oppressors, in which case you are an oppressor, or you side with the oppressed. that is it. i am biased; i empathize with the oppressed.
Adding to what Piper said (all of which I agree with) I find that certain people on the Internet confuse “racism” (resp. “sexism”) with “noticing that racism (resp. sexism) exists”. The term “mansplaining” acknowledges a fact about the way men interact with women in our society. This is a fact that can be empirically verified (for example, men are much more likely to interrupt women than vice versa) and I can’t think of any useful or reasonable definition of sexism in which noticing facts about inequality is sexist. On the contrary, if it was sexist to notice that we had inequality of this kind, how would non-sexist people ever go about fixing it?
Can someone give an example how a conversation in which someone does the mathsplainy behavior would sound?
This is by far the most important comment on this blog. If we as mathematicians and educators are to change our behavior, we need understand where we can improve. Concrete examples, help a lot to this end. Now, of course, this isn’t Piper’s responsibility to provide them, but I do hope that someone does. Especially useful are the more subtle/nuanced examples. Obvious examples allow us to say in our heads, “Oh I don’t do that, so I guess I can go about as usual.”
I’m making up an example in a field I know because I can’t think of a real recent one in my life. Suppose a group of grad students are studying/chatting about algebraic topology. And A might say something like “Okay, so if the fundamental group of the wedge of n circles is Z^n, what about the wedge of infinitely many circles?” B: “Oh, we know that’s the Hawaiian earring, so it has a nontrivial fundamental group. Anyways…” A: “How about the wedge of infinitely many spheres?” B: “Oh, that’s obviously trivial because each sphere has trivial De Rham cohomology.”
This example isn’t subtle, but hopefully it illustrates something. B is wrong, but trying to throw in big words/unknown terms to appear knowledgeable while subtly putting down A’s lack of knowledge with words like “obviously.”
Oh wait, isn’t the fundamental group of the wedge of n circles free product of n many Z?
Ha yes! Everyone is wrong in my example!
There is a tendency among mathematicians to assume that everyone knows everything, and to put forth the attitude that if you don’t know this basic thing then you’re way behind and you should have learned it in kindergarten and it’s trivial anyway so how can you have forgotten all logic? This makes men and women feel bad, it’s worse when you actually don’t know it or forgot it, and it’s really annoying when that’s the only way someone talks to you. I’ve learned to roll with the punches, but they really are punches when they’re coming from the most famous person in your field.
Another aspect of it is that mathematicians value that the truth (the precise truth) is known by everyone in the room. So when you speak to a mathematician about math, your conversation is interrupted every ten-fifteen seconds to make minor corrections about the things you just said. This is necessary to some degree, but nobody would ever do it when talking to, say, the world expert in the field because the assumption for them is that they’re sweeping the details under the rug on purpose. On the other hand, women are often talked to in the former sense, without the assumption of expertise and so with the continual corrections.
I guess this might count as an example
http://www.math.harvard.edu/~knill/mathmovies/swf/myturn_snake.html
(I actually just enjoy that short clip so much I want to share it.)
Ack! I just rescued a bunch of comments from spamland! welcome to the light, comments! I’ll figure this whole blog thing out one of these days.. months, maybe.
I don’t know that I can give concrete examples. for one, I stopped talking math. for two, it’s not necessarily the words said as it is the implications.
in general, when you’re talking to a marginalized person and you’re expressing a well established or mainstream point of view, your voice is amplified by the power you represent. you may think you’re having an individual disagreement or confusion, but you’re not. because you share many of the same ignorances or lack of experience as others in your dominant group, so you end up repeating the same things we’ve already heard possibly reinforcing things we’ve heard our whole lives.
one thing I’ve noticed, in general, not just about math, is that people never assumed they could learn from me. I didn’t notice until I started talking to anti racist whites and they would listen to me and ask me questions rather than just telling me their totally mainstream counterpoint. I felt like I’d been promoted! I wondered is this how it feels to be a white man??
so, when you’re talking to a woman or POC in math, try consciously assuming that you have something to learn from them. even if they’re asking you for help, try learning what they want from you. my background is unusual so I never know what is representative, but I struggle with people trying to force their solutions on me. trying to get me to think about math the way they do. and that drives me up several walls, because if they know enough to be a jerk about it, why can’t they bother to listen to me?? fair enough if neither of us knows enough to meet the other where they are, but if you’re going to act like you know the best way to think about it and all other ways are wrong, you should have the fortitude to meet me where I am and lead me to supposed enlightenment.
those are my first hastily thrown together thoughts.
I’ve had the same experiences around my peers as an engineering student! Coming to terms with the idea of inherent disadvantages–not growing up with a similar, problem-solving-oriented background or being unable to take on the same mindset despite having been in school for a decade and half–is incredibly unhealthy but seemingly unavoidable in conversation with anybody, and especially those peers, who never cite incorrect information and never have the wrong opinions.
Then I realized that I was taking them too seriously and being too sensitive, that then most conversations with them are competitions to prove who is more correct. Then I realized that I was making up excuses for myself not taking advantage of my family’s middle-class standing to explore engineering, planes, rockets, or spacecraft on my own when I was younger. Then that all led to thinking that I wasn’t meant for engineering, and that made me think that I was thinking too much about myself and should instead focus on my studies to get over it all.
I’m not comfortable with ignoring that contemporaries in the same field with similar aspirations can make another person who wants to learn feel inadequate for not already knowing some fact, or accepting that that is how engineers (mathematicians, a group of people knowledgeable in the same field) normally talk with each other, even though I’m sure it’s been that way for decades and won’t change.
Reading your post and finding someone else has been treated and feels similarly is relieving; yet figuring that this is an unchanging characteristic of the age of information is pretty troublesome. I can see how autonomously completing tasks, and disregarding the thoughts would help, but defective robots inherently can’t do as well.
Someone or something out there will help make that defective one useful, though. Sorry that was so long!
Tiffany Nguyen
Here’s a strategy I’ve employed for years in mathematical conversations: when I try to explain an idea to someone I like to start at a more basic level than I expect I need to, by telling them something that it’s likely they already know. So I start with a brief “review” if you will, though I prefer to do this without explicitly voicing any expectation that they “know this already.”
Frequently — and this still surprises me — this often leads to some resistance, as if I’ve offended the person I’m speaking with by talking about basic things. (I think this illustrates Piper’s point about mathematical conversations: that mathematicians are so used to using them as an opportunity to prove how smart they are, that we can sometimes forget that the real point is to communicate something.) But that’s not it at all. I just want to be understood! And I think it’s more likely I’ll get my point across if I work up to it slowly.
Regardless of the response, I still think this is good practice. Having been on the other side, even if I do ultimately know something about whatever it is that someone’s trying to tell me about, it often takes me a moment to get “oriented” to the language, worldview, etc, being employed in a particular instance. If the speaker had chosen to start more gently, with something I’m more likely to be familiar with, I’d have an easier chance of getting where we were going.
I love Emily’s approach to math conversations, and the opposite is a good example to answer Nick’s question.
One of the people I most love talking about math with is someone who does exactly what Emily suggests. I have never felt stupid talking to this person, because any conversation he initiates about a new topic starts out at a level where I’m very comfortable: he seems to always err on the safe side. This enables us to build the conversation on solid ground, and allows me to contribute ideas instead of battling self-consciousness. I really admire the ability to capture the essence of a complicated concept in simple terms. I think this is a great skill to cultivate, not just for the sake of talking to people in an inclusive way, but also for our own understanding.
I’ve often had the opposite experience as well, say I tell someone that I’d like to understand concept X but I don’t know much algebraic geometry. If their answer is something like “IC sheaves perverse raibow unicorns flying in the equivariant derived category of DG module stacks”, I come away feeling like I’m clearly not smart enough to have a conversation with this person (even if rationally I know that it may well be that they don’t understand concept X so well themselves). I don’t think anyone’s intention was ever to intimidate me, nonetheless I’m intimidated maybe 6 out of 10 times I talk to a new person.
perverse rainbow unicorns!!! haha. now, i’m having a flashbacks of sitting in the common room where i swear every other word was “cohomology.” i was ready to shatter glass. nobody was talking to me personally, so this is not totally on topic. just random memory.
I’d like to hear people here’s views on how condescention comes into it.
As an example, I was once at a science outreach thing and when I was wearing the baby I have the distinct impression that the explanations I was given were not at the same level as when I was not. The fact that these with-baby explanations started at a lower level was not a good thing.
Related by slightly different, in Piper’s thesis (which is awesome!), I loved the .3 sections, but I am the target audience for those (a math prof albeit not in number theory or algebraic geometry). When I looked at the .1 sections I though, I wouldn’t be able to pull those off. It would come off as condescending if I tried to do something similar.
i think it’s condescending to “lower” yourself based on your prejudgments of someone else. if you are happy and comfortable to talk at one level, but you determine that baby-wearers would find it too difficult to understand, that would be condescending. but if you always talk informally, you’re not lowering yourself. i don’t know to what extent you can affect other people’s perceptions of who you “usually” are in a single encounter/paper. i think my concerns are usually around not how people present themselves at first, but how they respond to questions. and i wish math papers were more readable. not comedy. just more readable.
About math papers being readable: of course, this would be fantastic! But let me just be slightly contrarian and point out that poorly written papers containing a high concentration of (correct) ideas, typically written by experts that have spent decades of their lives studying the relevant mathematical objects, inadvertently serve an important role in mathematical training: by giving only vague hints for proofs of non-obvious assertions, they force the reader to come up with the proofs themselves, and this kind of “active learning” can be a *very* productive experience for the reader in the long run (though, admittedly, it can also be demoralizing in the short term). In particular, I suspect that this phenomenon is what leads to aphorisms along the lines of “Each sentence of X’s paper led to a PhD thesis!”
Having said that, the line between giving just the right amount of hints and being completely impenetrable is blurry and an impossible target to hit (for one thing, it varies with the reader). So I’m not advocating people *try* to do this!
yeah, so I don’t think it’s so terrible when mathematicians write the way they want and it is hard to read (providing the paper has, as you say, a high concentration of correct ideas).
my real beef is that those who would prefer to write readable math could only do so at their own peril. because readability is not valued there is no place in respected research math world for people who want to publish user friendly research. it is hard to create new math. but it is also hard to learn new math well enough to make it accessible. yet we only value one. I think I would be quite happy if my “only” contribution to mathematics was accessibility. yet if I pursue that goal openly, I would be effectively banning myself from the best jobs. (which is not to presume I’d be up for the best jobs anyway, but just talking about the pressure that exists.) my choices would probably be math writer outside of academia or a teaching job with little time allowed for research.
I just think our criteria for “new” “contributions” are seriously flawed and counterproductive and marginalizing. any mathematician who cares about “diversity” needs to be willing to shatter current paradigms.
There is a ton of freedom associated with doing research in a teaching job, though.
My husband is a mathematician. Just yesterday he had lunch with another mathematician with whom he got into a very heated argument around differing mathematical perspectives.
Apparently, they spent an entire lunch bullying each other about their points of view. They are both from the same country and culture, which is why they decided to have lunch in the first place when they met at a conference. It didn’t stop them from bludgeoning each other when they discovered that they came from different “schools.”
I don’t think it has anything to do with mansplaining or whitesplaining. But I do agree with you the culture in math seems like it can be very confrontational, and I have always wondered exactly who gets to decide what is “important” or “interesting.”
It seems to me that individuals who manage to achieve influence typically maintain it for many, many years. And unfortunately “the game” means being savy to the trends.
Even science is biased. There is no escape 😮
I’m not sure what you mean by not having anything to do with mansplaining or whitesplaining. Given your example, are you saying that it’s not an oppressive “~splaining” situation because they do it to themselves? It’s important to look at actual impact, not intent or mitigating factors. It doesn’t matter how rude or dismissive a man is to other men, it is still mansplaining when he does it to a woman. And in fact a man who learned to curb his mansplanations would probably be a better person to be around in general, not just for women. If a confrontational culture disproportionately pushes out certain groups of people, it’s important to look at that.
I don’t think that a culture as confrontational as what we have in mathematics can ever be gender-neutral or race-neutral. The problem is that while everyone else is being confrontational, women are not welcome to respond in kind, even when they’re willing and capable. There’s always a penalty to pay. And from what I seen, women of colour have to watch themselves even more. It’s a gun fight where we’re only allowed to bring a knife, or not even that.
This is also why I’ve closed comments on my blog. I was getting comments from mathematicians, some of whom I actually know professionally, that were aggressive and confrontational in a way that would not be acceptable if I were to adapt it. In the end, figuring out polite responses to that sort of stuff was just too much work and not really worth it. There was one time when I did respond in kind; the commenter in question toned it down a bit in his follow-up, but that exchange seemed to shut down the discussion. Presumably, people did not want to be talked back to in that manner. Eventually I deleted that exchange, and lo and behold, people started commenting again. I think the same happens in mathematical interactions, more often than we like to think.
I have mixed feelings about this point: “It doesn’t matter how rude or dismissive a man is to other men, it is still mansplaining when he does it to a woman.”
Maybe it’s better just to call it rude and dismissive then?
And does it push out certain groups disproportionately? Many white men also get pushed out of math. Percentage wise do more women and minorities get pushed out than white men? I’m not convinced that’s true.
I have been closely following the Math Jobs Wiki for the past several years, and each of the past several years the handful of “star” applicants (on several short lists) were women. And they each ended up getting very nice positions.
In any case, it seems like you have an issue with dogmatic, dismissive, cliquish behavior in math. And there I completely agree with you. What is the solution?
I can say this – talking about things being wrong or unfair rarely changes anything, no matter how real and true the complaints. For better or worse, strategy is required to enact change.
my response is a little rushed, but:
white supremacy is a fact of life. patriarchy, all the other systems of oppression, they are indisputable. i will not pretend they are debatable or require proof.
math academia is disproportionately white and ridiculously overwhelmingly male. these are facts.
there is only one possible explanation for why there are so few women and people of color in math, and that is that it stems from white supremacy and patriarchy. (any other explanation is racist/sexist/etc.) now one can debate the mechanisms and ways to mitigate symptoms and such. but to suppose that the known systems of oppression we live in aren’t to blame for lack of representation is either silly or a sign of belief in the oppressive systems.
it takes a lot of work to unpack privilege and to liberate oneself from internalized oppression. but it’s worth doing.
your comment about female stars is erasure. it’s the “obama one b/c he’s black” argument that totally ignores that as a black man in the united states he was never supposed to get anywhere near a position to even pretend to benefit from his blackness in a presidential race. most of the women who should’ve gone into math were pushed out. it’s obvious from the data.
men would agree with you it’s better not to call it mansplaining. white people would agree it’s better not to call it whitesplaining. the status quo agrees it’s better not to talk about it.
i’m fine with you implementing strategies to dismantle any privileges you benefit from. but silencing the marginalized is not fighting for justice.
Edited to add: it’s my opinion that the culture I’m complaining about is pushing women and people of color out. but there are so many obstacles, I’m not making any claims about which obstacles have how large of an effect.
I am 62 I was trained in Applied Mathematics + Phys and Chem I have not worked in those fields so I don’t have professional experiences that may match up with yours Always understood [since undergrad] that there are pressures to appear like one’s peers Luckily I went to a lower-ranked school where all my co-students got over themselves early and we could get together and talk Math without fear Grad school was in a higher-ranked school and the anxiety was palpable Luckily I have worked in professions where i have never felt inferior Anyone who had pretensions could be disregarded without penalty Now I am being penalized just by disagreeing with the paradigms current in the industry All industries/organizations/academies have norms of behaviour and accepted information that can be highly restrictive and seem more so within those sectors where creative envelope-pushing is nominally promoted I have found that one can only be themselves You seem to be off to a good start I wish you the best
Thanks for your honest feedback on the nature of mathematical conversations. I believe you have spoken the “unspoken truth” in this blog post.
My question is how did you manage to overcome the unpleasant experiences? Any tips that you can share that enabled you to finish your PhD at Princeton, which I can imagine was a long and hard journey?
All the best for your future endeavours!
I’m not sure I overcame anything while I was at Princeton. I left a long time ago.
Part of why I’m speaking out about all this is because I think it would have helped me to be able to recognize these outside pressures for what they were. I lost a lot of time/energy on the question of whether I should even continue. If I had realized how offensive it was for me to be receiving so many indicators that I did not belong, I think it would have been easier. I was never offended. I never felt I deserved better. And given my particular situation of not having a complete background, I took it all as being my fault.
Also, the amazing amount of positive feedback I’m getting tells me that things are not quite as dire as I felt. Mathematics may be dominated by a certain way of being, but there is a thriving counter-culture. Being able to connect with other likeminded mathematicians would have been really helpful too.
So all I’m really saying is that I believe emotional isolation creates inefficiency, as does mathematical isolation. Therefore trying to either be less isolated, at the very least not internalize the isolation so much, could have helped me. Beyond that, I don’t know.
It took me years after I’d physically left Princeton to finish. And I can’t recommend my path to anyone. 🙂 But I do think that letting go of all the internalized oppression was key. For me. Getting angry at mathematics and academia instead of worrying about whether or how to fit in was key. For me.
I like your observation that “emotional isolation creates inefficiency”. To me, that seems the kernel of oppression.
We can spend a lifetime naming the multiple facets on the abuse spectrum, but I feel progress demands that we actively address that ineffciency and find ways to alleviate that emotional isolation. Whichever side of advantage we may be on, we can make continual steps to make communication more healthy.
I never knew how to answer the question “why have all the other women dropped out of mathematics, what are we doing wrong?” because I was the one who stayed, while also being isolated from those other women, and information about their choices.
The internet has quite recently given us the opportunity to build alternative networks to support our professional and personal growth. It is a joy to see more different kinds of women coming to play at the same professional table (in my case software). It is also a pleasure to find the professions starting to cross-fertilize.
The openness of the internet can be a 2-edge sword, when those who have an advantage are so bound in competition (and ritual), that they can’t tolerate alternative perspective. Somehow we need to learn better etiquette around that, listening, sharing. We don’t have it yet. Like we haven’t fully got there on the comfortable constructive technical and professional discussion. It is indeed a problem for us to work together on.
Best wishes (from an average MSc.).
Come be a cryptographer! I’ve found it to be a far more emotionally healthy field than pure mathematics.
First, there is a strong need for clear dialog between theory and practice, so anyone who lives in jargon lala land misses out. Really, there are thousands of developers, system administrators, interface designers, etc. who know nothing about pure mathematics, but need to understand how the math impacts what they’re doing. And conversely their issues can translate into cryptographic questions too.
Second, there is far less advantage to rushing through an “impressionistic” proof that few people really understand because the “fixable mistakes” that doing so glosses over could lead to real security holes, or at least waste months of time for other less mathematically included people trying to implement it or learn to trust your work.
Third, there is a greater appreciation for ethics in research, applications, life, etc.
Hello just wanted to give you a quick heads up.
The text in your post seem to be running off the screen in Opera.
I’m not sure if this is a format issue or something to do with internet browser compatibility but I thought I’d post to let you know.
The design and style look great though! Hope you get the issue resolved soon. Many thanks
i just put words into a box and it magically goes on the interwebs! maybe a future update of the theme will fix it?
I am also a PoC and while my field of study wasn’t math, So many times I have encountered people who expect a common basis of knowledge and deem such questions trivial. Other things I’ve encountered are people asking me obscure trivia that I don’t know the answer too. Constantly trying to prove me wrong. Constantly trying to correct me. Leading me to false conclusions then explaining why I was wrong. Talking about things in ways I don’t understand.
How ever I am also not neurotypical, and these behaviors are the way many neurodirvgent people engage with each other.
Constantly trying to prove me wrong? That shows they value what I think and what I am saying. That they find my ideas interesting enough to think about. If they just sat there and I agreed with me I would used to think that they didn’t care.
Testing me by asking “trick questions” (a math version might be, “Is every smooth function analytic”)? That shows they value me enough to want to teach me. That they care about me.
A hierarchical basis of knowledge that deems some questions trivial? Is Gandalf human? That Gandalf is not human would be considered pretty trivial knowledge amongst Tolkien fans. I don’t think how ever we would ever call such a question stupid. We would love to answer such a question because it lets us talk about interesting things. For example did you know that Sauron and Gandalf are in fact, the same type of being?
Asking me an obscure question? We do so to reflect our interest in the topic at hand, and figure that as you too like the topic, you will like said obscure question. Further more, we ask the question rather than tell you the answer first, because we want you to think about it, because we would want to think about the question first, rather than the have the interesting answer handed to us.
Talking about things in ways I don’t understand? That just reflects what the other person thinks of my intelligence. He thinks I know enough to understand him. And if I don’t I’ll tell him, and no one will be upset because that just leaves more room to learn, and learning is fun.
On the other hand a “laysplanation” ? That would be condescending and insulting as it shows you don’t think very much my intellect. Better to overshoot than undershoot and insult me.
The fact that neurotypical people find such behavior rude, and that I felt many people (who I later realized did not think like me), did not seem to care about me, or my ideas (because they engaged in neurotypical behavior, such as “building a shared dialogue”), was a large part of my struggle through my life.
Of course now I know that the lack of such behavior isn’t coming from an intention to harm. That when some one “laysplains” she’s not doing it because she thinks I’m dumb. Or that when a teacher simply tells me the answer, rather than lead me to it an sort of Socratic Method, that doesn’t mean they don’t value me. But I didn’t understand that at first.
In fact, I would say that I found the way neurotypicals engaged with me to be… oppressive. I’m sorry you found the way we engage with each other to be oppressive, but as we all know as people not, of power, neurodirvergents can’t be oppressive along those lines. While a neurodirvgernt person can certainly be oppressive if he is white, or straight and such, “Mathsplaining” comes not from whiteness, or maleness, or heteronormativity, but from neuro-atypical minds and so thus isn’t oppressive.
Finally, I find it ironic that you rail against:
“hierarchy of knowledge that says some information is trivial, some ideas are “stupid”; that declares what is basic knowledge, and presents open incredulity in the face of dissent”
When in later posts in this discussion you say things like:
“white supremacy is a fact of life. patriarchy, all the other systems of oppression, they are indisputable. i will not pretend they are debatable or require proof.”
How is that not doing the very same? By saying some knowledge is not debatable or requiring of proof, you are both displaying incredulity to the face of dissent, and declaring what knowledge is basic/trivial. I would not be surprised if you also said that ideas contrary white supremacy or patriarchy, are stupid.
I mean, I don’t disagree with you when it comes to racism or patriarchy or any form of the kyriarchy, but do you not see you are engaging in the very behavior you condemn? In many neurodirvergent circles no belief is beyond debate or absolved from a lack of proof, and that we experiene oppression due to this is a fact of life.
Thank you for sharing your experience with me. If the needs of neurodivergent people and neurotypical marginalized people conflict, the answer would be to allow for both (all) ways of communicating instead of picking one over the other. Do you think that’s possible?
As for the irony, I understand your point, however there is no neutral option. When one group of people puts another group’s humanity up for debate, there is no neutral. The existence of the debate is dehumanizing. The only way to humanize the marginalized group is to ban the debate. So, given that we live in a hierarchy, it is unavoidable that there will be a hierarchy to this blog. The hierarchy I choose is the one that affirms the humanity of all marginalized people. (And it’s not to say that I deny the humanity of dominant people, but that if a system puts the two in conflict, I will always choose against the dominant group; they can find their support in all other places.)
For instance, you stated that all the things I think I stand for go against your needs, but I did not allow this to trigger any of my disagreement buttons. I recognize your right to define your experience and I have to accept it as truth and I have to find a way to work your experience into my future thoughts. It will be difficult and I will make mistakes (I might be making mistakes in this response!), but I will keep thinking about it. If I did not fully believe in my hierarchical choice, I would probably spend time telling you how my beliefs are just really important and the inclusion I fight for is really important and I’d attempt to get you to stop trying to take that away from me. And maybe you’d be okay with that, but I’m not. I don’t think my feelings are more important than your lived experience.
follow-up questions:
1. do you find it oppressive when neurotypical people talk to you the way i complain about? or are you finding neurotypical people who talk to you in the way i would like? or is there some other aspect of neurotypical communication that is the problem?
2. my problem with the communications i’ve had is not so much how people initiate conversation, or first respond to a question. it’s more how the conversation goes on, ignoring my explicit attempts to influence what’s happening. would it be neurodivergence inclusive (if those are the right words) to ask someone to explain things at a different level?
3. would you find it condescending if i spoke to you in the way i speak to all people which is how i think about things myself if it turns out to be at a lower level and far less formal than standard?
Great post. Thanks for the read.
I do not know if my experiences are comparable, but I am a scientist working interdisciplinary and thus experienced in discussions with members of quite diverse scientific communities, including mathematicians, and of course also from another perspective with layman. The first thing to note is that many scientists get quickly annoyed if they think someone steals their time, i.e. discussing about “well-known” things, even if the other person possibly cannot well-know them. Me too! This is because one has struggled so long to aquire some knowledge for oneself, and there comes the newbie talking nonsense straight away. This can be circumvented, of course, by checking the mutual level of understanding first. Another thing you learn is that there are arrogant people out there. As simple as that. People who think they are the greatest but yet are weak indeed, since they need to show off their “talents” by marginalizing other people. Especially many scientists, contrary to common belief, are not open people. Quite restricted in their minds. It does not make sense to discuss with them at all, because they “know” the “right” answers and they will never change their mind on that. But then, this is no discussion. But then, you also do not have to feel bad about it. There are idiots everywhere. Mathematical or scientific abilities do not tell anything at all about character. It is important to build his own opinion on his own judgement, or the judgement of close friends, and get independent in thought from these people, however powerful or influential they might be. This is a third experience, if you managed to be an independent person. Many people cannot cope with that. You are aggressive on them, because you are independent from their views and you show this by your presence alone. Nothing intended. But felt by the weaklings of academia. Forget it simply and go your way.
This is a very sad story. I’m sorry to hear of your trouble. One of the thngis I’m very interested in is talking to careers advisors about the advice they give. For careers advice for a post-PhD… hmm. There is a which might be helpful to you. There might be some relevant information on the and there are lists of companies that employ mathematicians on the IMA website under and that might be worth a look.I think that careers advice for mathematicians is a difficult game and there are some careers advisors who do it well. The trick is to help the rest to become better informed. I am having my biannual meeting with the IMA’s liaison to the Association of Graduate Careers Advisory Services next week and we will be talking about this.
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Thank you, both for the post and the opportunity it provided for the comments that followed. I have alternatively passionately agreed with some views and found common ground with your experience (for example, the endemic misogyny, the pretence that what is ‘clear’ or ‘obvious’ is universal) as well as passionately disapproved of some views – sometimes the same ones I had previously agreed with.
I think mathematics, being a historically situated cultural enterprise, is naturally hierarchal – in the sense that some theorems have more value than others and dually some mathematicians are better than others – and that this hierarchy of taste arises together with the mathematical class structure. But, if you remove this (present, given) hierarchy, you will also end mathematics. The existing structure may have been produced and be maintained by a certain group of people to whom it is historically bound (by which I mean something like: the value we place on existence proof is connected to the schoolmen influence on medieval universities), but it was never theirs and instead reflect a general tendency of *human* understanding.
I never comment on blogs. But this blog motivated me – so as a mathematician I have to correct my universal quantifier in the first sentence: I almost never comment on blogs. Being from the privileged group, it is helpful to me to read this blog and comments – it took me decades to get to a point where I could even begin to attempt to understand where you are coming from. On another note, although I can justify that they have too many more important things to do, I have a 0% return rate for emails sent to math professors and graduate students of Princeton over the years. So I have experienced some trivial reverse elitism/discrimination. Anyway, thanks again, your words are helping to change the status quo – things are changing rapidly (relative to human history) in the right direction.
I came across your blog just now, but I still want to leave a comment, as this post resonates with my experience.
I am a white male graduate student, so my perspective might be different. I still have met many arrogant mathematicians that made me feel disappointed about the whole community and even deeply depressed at some point. Maybe the worst accident was with a professor who after discovering that I was somewhat interested in his field, advised me to “find something easier for me” (technically, he was supervising me at the time, but he was so busy that he never got to know me to make any assumptions and judgments). Things like that have made me question whether I should do mathematics at all, but at the end I decided to finish my studies, proceed calmly with some research and teaching, and promote a more respectful, kind, positive, and adequate approach (just from the general human perspective!) through my humble work at some faculty, possibly staying away from the aggressive competitive “alpha male” colleagues. Because the more people leave math because of personal traumas, the more arrogant people will have control over research and education.
Your post caught my attention by its title “Why I Do Not Talk About Math”. “How can a mathematician dislike talking about math?”, I thought. But then it’s true that many “conversations” about math, especially among graduate students, don’t even aim at communicating any knowledge. People just show off how many fancy words they know, without trying to explain anything, or without understanding things themselves. Some even teach this way.
Talking about math is great and important for research and learning things, but only when you talk to friendly people who are on the same wavelength with you and really want to exchange some ideas.
Personally, I feel disappointed when my students, or colleagues I talk to, don’t get my point and don’t feel like asking for clarifications. It seems like many people are so intimidated by their mean teachers and colleagues (I know how it feels!) that they feel ashamed of not understanding or not knowing something. So maybe one of the first things one has to teach their students is that nobody knows everything, everyone makes mistakes and learns a lot from them, asking questions is very important, math is not a competition, and so on.
It’s only been in the past year that I’ve had positive conversations about math, and these conversations have been almost exclusively with women. It’s been really great and it makes me sad about how much I missed out on while in graduate school.