*(Interview by Mireia Martínez i Sellarès)*

Last week we shared with you the first part of our interview with category theorist Emily Riehl. We talked about mathematical competitions, female mathematicians helping each other progress in academia, and the importance of asking questions in class.

This week we are back with the second part of that interview, in which we discuss language and queerness in mathematics. Enjoy the read!

M: I think this thing that you do, proactively making students ask questions… Now in the broader picture of mathematical culture, not just focused on women, I think that’s very important because I think there’s a very (not explicitly, but subconsciously) aggressive environment sometimes when it comes to asking questions…

E: Oh for sure, totally.

M: …where so many people are thinking the same but nobody will ask because you’re like “Wow, if I ask I’m the stupid one in class!”. And this only creates a vicious circle.

E: Well, and I also think that part of it is that there’s an *aggressive *way to ask questions… There is a hostile way to ask questions and in some rooms that’s the norm. Part of the point I make when I show this [xkcd] cartoon, before I even get to the gender thing, is that it’s great that you’re making a comment and you’re pointing out something’s wrong, but you don’t have to be an asshole about it. There is no environment where you should say “You suck at that”, you can say something like “I think there might be a bit of a confusion…”, you know? *(Laughs.)* So yeah, that’s part of the story too.

M: Ah, that’s really cool! Especially because I feel that there’s so much that we learn implicitly: there’s so many rules that nobody taught you but that you learn just by attending lectures, going to workshops… So having people now who stand up and say “this is not okay” or “this needs to change” is very important. Not only for female mathematicians but for mathematical culture in general. You know, I came across Piper Harron’s thesis a bunch of years ago and I was so impressed that someone was being so bold!

*(Note: Piper Harron got her doctoral degree from Princeton University in 2016. Her thesis in number theory is written in a very unconventional style, as she attempted to make the hard mathematical content accessible for any reader. In the thesis, she also gives some critical opinions on mathematical practice in academia, sharing her experience in trying to “do math ‘the right way’”. You can have a look at it **here**.)*

E: Brave enough to do that, yes!

M: The thing is, I was just starting my undergrad when I read some articles about her and her thesis, so I am wondering: did it have some kind of impact? Was it talked about?

E: Oh, yeah, definitely. I mean, it was huge, everybody knows who she is now and nobody did before, so it was definitely talked about. She’s written a number of blog posts since then that have also been talked about, and she’s been on a bunch of panels. We invited her to Johns Hopkins [University] and she came to talk there too.

M: What did you think about her thesis?

E: I thought it was awesome. I think she makes a lot of good points, and frankly it has changed the way I communicate mathematics. You know, I’m lucky in that I knew I wanted to do math [since] high school and so when I was an undergraduate I was learning to speak the language and I’d feel comfortable with it. I mean, part of what she describes is how alienated she felt as a graduate student. She discovered math very late in her undergraduate degree so she wasn’t as well prepared and used to the way people use language –you know, saying “This is trivial”, or “As we all learned in kindergarten…” She pointed out how alienating that was. A lot of speakers answer questions with “This is obvious”, “As you all know…” So now I try to be much more careful in the language I use to suggest that it’s okay if you don’t understand this the first time because it’s too fast and you haven’t had time to absorb it yet. You know, when I say something is “an easy proof”… Sometimes, for example when you are teaching abstract algebra, you want to be able to convey like “This proof of the Sylow Theorems is really, really hard” *(laughs)*, in contrast with this other proof. So I try to phrase that in a way that suggests that right now you might be really confused with this and that proof but later on, in the fullness of time, you’ll see there’s no new ideas involved. I’ll phrase it like that as opposed to saying something that makes people feel dumb if they don’t get it immediately. So I attribute a lot of that to [Piper Harron], this making me think about what it’s like to be a student who’s not a mathematician already.

M: Also, I think this kind of language feeds the myth of the genius, and of the professional mathematician as this gifted person who was born to be working there. Which I wouldn’t deny that you need something in you to end up working as a mathematician, but…

E: There’s an essay you should read if you haven’t yet, it’s also old but it’s still great and so inspiring. It’s by Moon Duchin and it’s called “The sexual politics of genius”. She’s a mathematician, she’s famous now because she’s working on gerrymandering in the US. Her math is awesome too, but this is something she wrote in grad school, I think, but it’s exactly about the genius stereotype and the point you’re making about how “genius” is read in a certain way.

M: Especially in mathematics.

E: Especially in mathematics, yeah.

M: Because I don’t know of any other field where it’s as blatant or strong.

E: That’s right. Well there’s male mathematicians who also don’t fit into that paradigm. Famously, in algebraic topology there’s this guy called Daniel Quillen, who invented model categories and K-theory. I mean, he was a very singular creative mind and apparently he used to say that he was really slow and needed a lot of time to think about things very carefully. So obviously he was very persistent and creative, he is a genius but of a different sort. I think a lot of the perception of “genius” is of speed, really. If you can absorb something quickly and understand quickly then you come off as very smart because that’s what happens in a conversation. But [Quillen’s] contributions are of a different sort. I have no idea what it would’ve been like to talk to him but his papers are beautiful and really visionary.

M: That’s very interesting.

E: Another thing I think about is: you always make comparisons at one point in time, but that’s really unfair. Like, if I compare with myself as an undergraduate, I am so much smarter than I was then! *(Laughs.)* But I’m the same person. And when I think about my collaborators… I have a collaborator who I think is just really, really sharp, but he’s also older than me, and I try to remember that if I could talk to him when I was at his age, I think it would feel more on par.

M: That’s such a good point though! I agree. Can I ask you one last question? I have seen also on your website that you have an interview called “On performing queerness”.

E: With Mike, yeah.

M: Is this an important part of your identity? Because it certainly adds yet another level of “minority” so to speak, and in a very man-populated environment it creates an interesting variable.

E: Right. I think my queerness has been helpful for me personally in a number of ways. I think that there are so many negative stereotypes associated with femininity specifically more than femaleness. I am a cis woman but I don’t present as feminine as some other women do, and for that reason I think I get to sort of slide past a lot of these negative stereotypes. Something very basic, like if I am giving a talk, I am wearing the same kind of clothes that most mathematicians wear, just because those are the clothes I like to wear. And so you don’t notice that about me, whereas some of my friends, if you look at the clothes they like to wear, then that’s a thing you would notice when they’re giving a talk. So I don’t have to face that.

M: One less thing to worry about.

E: You also hear these horror stories about female grad students and postdocs getting hit on at conferences and that never happened to me, I think in part, because it’s kind of obvious if you look at me that this isn’t exactly going to work out. So for the most part, it’s actually been a positive thing. The main downside is that it’s another level of alienation because you’re often the only queer in the room and that’s a thing that you notice and it’s not as fun. But I think it’s largely been protective to me for some of the negative stereotypes. And I think that, as a kid, there’s very well documented research that if you remind students that they are female right before a math test, they do worse because they sort of associate with the stereotype. And I think that’s another thing that’s protected me, because I’ve never associated that strongly with being female so those stereotypes didn’t feel like they applied to me.

All this said, I really do think that things are getting better. For one thing, we have a long and growing list of amazing female mathematicians doing exciting work. Of course Karen Uhlenbeck who just won the Abel prize, but also Moon Duchin, Kathryn Hess, Gigliola Staffilani, Ulrike Tillmann, Claire Voisin, Natalie Wahl, Katrin Wehrheim, Kirsten Wickelgren and I could name many, many more.

*Thank you Emily for your time! You can have a look at Emily’s work on her **website**.*