Mathematical thinking for a new approach to gender

Dr Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist, composer and artist. She is Scientist In Residence at the School of the Art Institute of Chicago. Recently, Dr Cheng came to London where PPM heard her speak at the London School of Economics about her book “X+Y: A Mathematician’s Manifesto for Rethinking Gender”. Following her talk, Dr Cheng allowed PPM to publish this write up to mark International Women’s Day 2023.

“I’ve been asked about my experience as a female person in mathematics for my whole career, precisely because there are so few women in maths. When I was younger I didn’t want to talk about it, because I didn’t want to draw attention to myself as a woman in maths.

But now I feel it’s my responsibility to speak up and speak out about these things.

And, to try and explain the imbalance in maths I reach for the tools and methods I know best – those of abstract mathematics.

I’m a higher dimensional category theorist and this is what we do, we add dimensions to things to gain insight. I’ve done this and it has helped me see things more clearly and that for me is what pure mathematics is all about – it’s not about numbers, it’s not about solving problems, it’s about finding slight shifts in point of view to help us see things differently and think more clearly about a whole wide range array of things. For example, you can look out over Chicago, where I’m now based, and see a vast sprawl stretching to the horizon, but if you alter your viewpoint just a little the apparently impenetrable urban jungle becomes a grid system in near perfect alignment.

My aim is to use abstract mathematics to see things differently and do something about inclusivity not just in mathematics but in society more widely and perhaps in the entire world. No-one can say I don’t set my sights high!

In my previous life I had a normal maths career teaching normal maths in a normal university to normal maths students – those that had done well at maths at school and who intended to purse a maths-y career in a field like finance or science or teaching. And it was a very male dominated environment.

And then I moved to teach at an art school where the pupils are majoring in painting, drawing, photography, film making and design and things like that – and who often had not done well in maths at school and did not consider themselves to be good at maths. And they were overwhelmingly non-male.

We associate personality types with gender in a way that is not only unnecessary it is actively destructive. And when we do so we fall into a one-dimensional trap that places these traits on a straight line that runs between masculinity at one end and femininity at the other. Yet where research has been carried out into gender differences most find that in the resulting bell curves men and women come out just 0.1 standard deviation apart. That means that on almost any measure – including maths computation and problem solving – it’s all but impossible to tell men and women apart.

So the one-dimensional trap creates a false dichotomy.

Better to identify the traits and character types that are valuable and not assign a gender to them. We need a new dimension, and a new vocabulary, to separate out traits and gender. Which is why I coined the words ‘ingressive’ and ‘congressive’. They bring a new dimension, moving us on from dichotomy, to a two-dimensional plane, with an ingressive axis and a congressive axis. People can exist at different points on anywhere on the plane and indeed move around it. You can be ingressive and congressive in different amounts at different points in your life and career and even day to day in different situations.

But I created this new dimension and terminology not to get more girls into maths. I did it because we’ve been presenting maths wrong.

For too long maths has been rewarding ingressive behaviour, even though congressive behaviour is better for us.

Let me explain. Ingressive behaviour traits including focussing on oneself, valuing individualism and taking an aggressive or combative approach to tasks. Congressive behaviour is concerned with community and connectedness and taking a collaborative and cooperative approach to tasks.

In maths that means that ingressive teaching is focussed on outcomes, rules, solving problems, calculating answers and a clear right/wrong binary. Usually taught by someone speaking by a blackboard at the front of the class and assessed via exams.

But at research level, maths much more congressive. It is about processes, investigation, discovery, uncovering relationships and building structures.

So much of school maths is about who can complete the learning the fastest. I prefer projects that have a low barrier to entry but that have essentially no limit on what and how much everyone can learn rather than a defined finishing line. For example, one of my favourite classes is to talk to my students about symmetry and give them cardboard to cut into shapes and make things. Some end up with the platonic solids – without realising they are called platonic solids – and some build dinosaurs. But when we come back together we talk about how triangles are a very effective shape out of which to build things, then we talk about triangulation, then we talk about higher dimensions and before long these students who don’t consider themselves good at maths are talking about higher dimensional simplices. They get to see what was previously denied to them just because they didn’t get the ‘right’ answers in an exam.

We need to change our thinking around what success looks like too, and how to achieve it. Too often at International Women’s Day events and panels girls who want to get into STEM are encouraged to believe in themselves more, develop a thick skin, be ambitious and take risks. Congressive people don’t like those instructions, which is precisely why I think congressive people make better mathematicians. Congressive success involves building a supportive network, being flexible and sensitive, working to improve yourself and the world and achieving all that via collaboration.

So my call to action this International Women’s Day is to teach more congressive maths – including pure maths – and teach it in a congressive way.

I truly believe we can work together to make a more congressive world in maths, education and beyond. And if we do that then it will be better for everyone of all genders.”