Eugenia Cheng defies convention with her approach to teaching.
The Chicago-based British mathematician tells Matthew Reisz why similar
out-of-the-box thinking is required to improve gender equality
July 23, 2020
Twitter: @MatthewReiszTHE
·
Source: Getty/iStock montage
“Pure maths is a place of dreams,” writes Eugenia Cheng in her
new book, x + y:
A Mathematician’s Manifesto for Rethinking Gender. “It’s
about dreaming up new concepts and new structures.”
Such dreams, as her subtitle suggests, are not just intellectual
games but can help us address complex and intractable real-world issues. And
she draws on the story of her own career to illustrate how.
Scientist-in-residence at the School of the
Art Institute of Chicago since 2013, Cheng was previously
senior lecturer in pure mathematics at the University of
Sheffield. Her first two books – How to Bake Pi: Easy Recipes for
Understanding Complex Maths and Beyond Infinity: An
Expedition to the Outer Limits of Mathematics – provided
wonderfully accessible introductions to some pretty challenging ideas.
The first, which includes recipes for custard, chocolate
brownies and fruit crumble, was strongly influenced by her teaching experience.
“When I was in
When she moved to
“I’m now teaching more advanced maths in a slightly less
rigorous way,” she says, “whereas at
Such an approach challenges the conventional idea that maths is
basically “cumulative” and consists of “increasingly high hurdles, where you
are tested to see if you can pass this hurdle and then are allowed to progress
to the next”. Unfortunately, this only serves to “keep people out”. As someone
committed to overcoming “maths phobia”, she is always looking to break down
such barriers.
What Cheng has also discovered at the Art Institute is that
discussions of food “didn’t make [students there] perk up in the same way”.
Instead, “it was questions of social justice and political issues which really
motivated them…I had been very wary of talking about politics out loud up
until then because, like most mathematicians, I had thought maths was
supposed to be very neutral – and then [with the 2016 US presidential election]
it became too important…If I ask my students to stop thinking about
politics when they walk into the classroom, they are not going to be interested
in anything I’m saying.”
Cheng’s third book, The Art of Logic: How to Make
Sense in a World that Doesn’t, published in 2018, already drew
on her new, more politically engaged style of teaching, illustrating logical
points with examples about white privilege, sexual harassment and fat shaming.
She has now taken this several steps further. x + y is a
book very much designed to change the world.
So where does gender come in?
In parallel with her teaching, research and public engagement
work, Cheng – as a prominent female mathematician – is often asked to take part
in discussions about getting more women into maths and science. Yet she often
finds herself at odds with the consensus view.
“The other women on those panels”, she reports, “typically
exhort everyone: ‘You have to step out of your comfort zone! You have to take
risks! You have to be OK with failure!’ But I know there are many young
women, and men as well, who don’t feel they want to do those things, and so
they will be put off and decide they are just not cut out for [certain
disciplines].” A more productive approach, she suggests, relies on “building
safety nets, having a network of supporters around you and defining failure out
of existence by saying everything is a learning process. It is just a shift in
psychology.”
Similarly, x + y cites a study from the
1990s into why men did better than women in Oxbridge exams. In subjects such as
history, it turned out, one important factor was that “men tended to write
essays that took a strong position and argued it fiercely, and that this was
highly valued. A balanced position argued from all points of view was valued
less.”
One possible response, of course, is to “train women to make
more one-sided arguments”. But this is an example of what x + y describes
as “pseudo-feminism…in which women are exhorted to become more like men in
order to be successful”.
A central problem, Cheng writes, is that debates about gender
often turn into “an argument about what we should be arguing about”. It is easy
to get lost in endless, dizzying disputes about whether a particular piece of
research really demonstrates that men are statistically “better at
systematising than empathising” and, if so, whether this is innate and whether
it is a reliable proxy for “better at maths”.
What this fails to address is that certain characteristics –
such as taking a strong but perhaps simplistic position in an essay – may be
associated with men (for whatever reason) and favoured by society, which then
leads to men being more successful. Yet we also need to ask whether such attributes
are actually desirable. In the case of the Oxbridge exams, as Cheng points out,
we might consider the impact on our political culture: should “politicians be
judged by how well they make a speech” or “how well they listen to other
people’s concerns and respond to them”?
If we decide such characteristics are not desirable
and we therefore work to promote other values, that will not only benefit
society in itself but also help alter the gender balance of power without the
need for quotas, “leaning in”, assertiveness training for women or many other
familiar forms of intervention.
It is here that Cheng adopts the mathematician’s privilege of
inventing “a new dimension” and terminology. She uses the word “congressive” to
refer to forms of education, research, discussion and behaviour that “focus on
society and community over self”, “tak[e] others into account more than
impos[e] on them” and “emphasis[e] interdependence and interconnectedness”.
“Ingressiveness”, by contrast, means “focusing on oneself over society and
community”, and, among other things, involves a “tendency towards selective or
single-track thought processes”.
Having this bold new conceptual framework, in Cheng’s view, has
helped her analyse everything from teaching methods to voting systems without
bringing in the baggage (and gendered assumptions) of words such as
“competitive” and “cooperative”. In teaching maths the way she now does in
Although ranging widely across many aspects of our lives, the
book also slaughters a number of specifically academic sacred cows, including
journal publishing and peer review. Cheng believes she has experienced “being
held to a different standard than my male peers in refereed reports”. And while
she “just quietly lament[s] in a corner” when she feels her work should have
been cited in a paper, she often receives communications from male
mathematicians who are “angry because I didn’t cite them. It’s quite
unpleasant, so I think about who might get angry [when deciding who to
cite], which means I’m skewing my own citations.”
Further distortions arise from the fact that “people who are
principled decline to read papers written by their friends, whereas
unprincipled people are willing to review their friends”. It was also
depressing when famous authors seemed to have little difficulty in getting
substandard work published, “exactly like what happens in the pop music world,
which shouldn’t happen in academia because we are supposed to be rational”.
But despite the biases they can introduce, don’t editors and
reviewers also perform an important function in excluding really bad papers?
“The usefulness of gatekeepers could be preserved while removing
the problems,” Cheng replies, “by making it less of a gate and more of a slope.
The all-or-nothing aspect makes it really problematic: the idea that keeping
people out makes things better. It’s a bit like false positives and false negatives.
We may be keeping something out that was worth letting in – and I think
that’s much more problematic than the other way round, the fear of letting
something in that wasn’t worth it.
“I don’t object to experts evaluating other people’s papers, but
peer review is based on something completely anachronistic…The cut-offs are
based on how much space there is in a journal, even though now everyone reads
everything digitally.”
These are not easy times to be optimistic, particularly for
those seeking more congressive forms of politics. Yet Cheng finds a sliver of
hope in the way that “people have had to start really thinking about what is
happening with exams and entry into universities”. For instance, in the
Looking further forward, does Cheng foresee a utopian world
dominated by congressive behaviour and institutions – or will congressive and
ingressive forces always have to battle it out against each other?
“I personally don’t feel any need to be ingressive any
more,” she reflects. “I can’t think of any reasons why ingressive
behaviour is important. It’s inevitable that there will always be some, just as
there will always be morons. But we can try to get people to be less moronic
and more congressive.”
Eugenia Cheng’s x + y: A
Mathematician’s Manifesto for Rethinking Gender has
just been published by Profile Books.
