Eugenia Cheng is a Caian, a mathematician, a concert pianist, a teacher, a cake enthusiast… and a demolisher of boundaries.
Studying for both her undergraduate degree and PhD at Caius, she became an academic specialising in higher dimensional category theory, before recognising that her talents as an educator and populariser could be put to broader use outside universities. She created mathematics videos on YouTube (developing a distinctive explanatory style often involving cake), then published her first book, How to Bake Pi, to wide acclaim. Now Scientist in Residence at the School of the Art Institute of Chicago, she lectures and campaigns in the US and worldwide to bring mathematics to a wide audience (fitting in piano recitals in her spare time). With her latest book, Beyond Infinity, published this week, she visited Cambridge on Friday 17 March to deliver the Newnham College Gillian Vaisey Memorial Lecture.
Here, Eugenia recalls sleeping on the back of the sofa at Caius, explains how sprouts and yogurt can shed light on polynomials, and reveals why she can’t bear watching Sherlock.
You studied at Caius from 1994 until moving to Newnham to take up a Research Fellowship in 2001. What are your strongest memories of Caius?
I was always really involved in College life: I really believed in it. I believe in the idea of a liberal arts general education, but not in the way it’s too often implemented in America where it’s all about ticking this box and that box. I just threw myself into the idea of this kind of immersive education in a college, surrounded by so many amazing people doing all these different things. All the maths I learned was from the mathematics degree, but everything else I learned was from just talking to people about their studies.
I had a monumental room in my third year: I2, looking out over Caius Court and with a side window on to Senate House Passage. Because it was really in the centre of College, it became a focal point for everybody. I was President of the College Music Society so it became a kind of hub for that, and friends and I would roll in there after dinner in Hall.
There was this fantastic sofa in my room. It had a very bulky back and wasn’t long enough to lie down on, but I used to lie on the top of it anyway – if I was working really late or just to think. You have to go into a state of semi-consciousness to solve a mathematics problem, and if you lose your grip on the consciousness part you go to sleep.
How did the teaching here influence you?
It was the absolute central core of what I was able to do later, because while I had a good school education that got me ready for Cambridge, Caius gave me the confidence to do the things I wanted to do and gave me a really fantastic environment to try things out, figure out what I wanted to contribute and how I wanted to do it.
Professor Jan Saxl and Dr Jonathan Evans were very important to me. At my interview Jan Saxl took the time to see I was interested in music and tailored his mathematics questions to link them to that, and I was just so impressed – I gave up a choral scholarship at a different college and came to Caius. He used to come to my concerts and gave me leeway if I was preparing for a concert and not quite keeping up with work because he knew I would catch up. That flexibility means people can throw themselves into other things besides their academic work.
You’ve made your name using unlikely metaphors – including many culinary ones – to explain complex mathematical concepts to lay audiences. How did you develop that love of imagery?
I trace it back to when I was at Caius. I had a strong group of friends who were mathematicians but also many studying music or other subjects, and we would all talk to each other about what we were studying. I guess I wanted to join in, but I couldn’t say it to them in technical terms so I had to use stories and analogies, and I started to develop ways of doing that. It was even more true when I was in the MCR, when there were all these people doing PhDs and I had even more chance to try and explain what my research was about. I remember having arguments where I tried to convince people that maths was an art really, and I feel it has come full circle now I’m teaching in an art school. I am now the intersection between art and science.
You’re famous for using cooking to explore maths in your videos and talks. How did the focus on food come about?
Well, I do love food! Part of it came from my piano teacher, my great mentor from five to 18, who taught by telling stories about unrelated things such as dog training or ironing. So I would tell stories, and because food looms large in my consciousness at all times, some would be food-related. I noticed that at those times, students perked up, so I repeat the stories that make people perk up the most.
The first one I did involved me stirring blueberry jam and then Brussels sprouts into a bowl of yogurt. I was actually demonstrating an important and quite complex point in number theory about polynomials. I was trying to explain that what you do with polynomials is take ordinary whole numbers, throw in some x’s and – like sprouts – the x’s won’t go back to being a whole number and won’t be absorbed. However, in mathematics you can also take whole numbers and throw in the square root of 2. This is like stirring blueberry jam into yogurt, because some of the square roots form whole numbers and dissolve, like the jam, and the whole yogurt goes purple.
I projected this giant bowl of yogurt on to a screen and the students loved it.
Why does this approach work?
The idea is to draw people in and make them curious about when the maths starts. I want the metaphor to connect with someone viscerally first. I have an image that there is a space that is a curious space in the brain, and you have to open the doors to it before you can let ideas in. If those doors are closed you’ll have a big problem getting anything else in. Maths phobic people have closed and locked those doors because they are so afraid of maths, so you have to open them gently, or even bypass them so that instead of going through the suspicious brain it just connects with your emotion straight away. That’s where the sprouts come in: there’s always a point to the ridiculous things I’m doing.
You volunteered in primary school maths classes while researching and teaching in Cambridge and Sheffield. Why do you think so many people seem to be put off maths at school?
I think early experiences do contribute to maths fear. Most Year One children [age 5-6] love maths – they will cheer when it’s time for numeracy – but by 19 they feel miserable about it, and you have to ask what happens in between. One issue is when primary teachers are required to teach all subjects. If maths wasn’t their subject and higher up the school they are teaching at the limit of what they are comfortable with, they can convey that fear. Children can ask really profound questions about maths – if an adult doesn’t know the answer they can discourage the child from asking questions. If a child is discouraged from curiosity, they will see maths as a place of arbitrary rules, an oppressive place.
Plus, maths is the first place children get told they’re wrong. There is a big myth that maths is all about right and wrong. It’s about discovery, about building structures and exploring reasons and saying what if you put these rules together, what sorts of patterns can we create? That is so much more exploratory and creative. If we did that kind of maths early we would put people off less.
There is a perception that there is a maths personality type – and it’s often seen as male. What’s your view?
I think we should talk less about gender and more about character traits, as we can only have a conversation if we use different words. I’ve invented some new words: ingressive and congressive, for things you might usually associate with male and female. Ingressive people like problem-solving, competitions, mathematics Olympiads.
I on the other hand am a very congressive mathematician: category theory is about illuminating things more so other people can make progress, shedding light on the roots so other people can make a big leap. Congressive people are put off maths if it’s all about right and wrong and getting the right answer.
Similarly, I hate maths games, but I love Lego: making something that’s exciting to look at fascinates me. Olympiads are good for some people, but I thought there was a gap and wanted to try and reach people who might be interested by another kind of thing: hence my book talked about category theory, which is the mathematics of mathematics.
So often mathematics is celebrated with Fields Medals, which is about one person’s glory and capitalising on media attention, or the idea of a theory being solved after 200 years, usually by some man working alone in a room. I think the great accomplishment of [French mathematician] Evariste Galois was seeing a relationship between solutions to equations, and algebra. But his story is told because he was killed in a duel. Without that I don't know if his insight into the relationship between two parts of mathematics would have been so famous.
One of my favourite mathematicians is Emmy Noether, who is exceptionally important, but you may not have hard of her because although her work was an important contribution to Einstein's Theory of Relativity, her contribution was about making a connection between maths and physics, rather than solving a huge old problem. Winning prizes and breaking records is more obviously sensational, and it is easier to make it into a story.
You’ve taken what some people would see as a brave decision to leave academia and promote maths to a wider audience. What drove you?
I really think I am helping people, and in the end that is what I value most about human beings.
I know I'll never be the greatest mathematician on earth, but maybe I can try to be one of the best people at helping others understand mathematics. I’m quite good at maths and research, but we tell people to find the thing you could be the best in the world at, and for me that could be bringing mathematics to a wider audience.
I do want maths to look different, and that’s why I decided it was important to put myself out there – I was fed up of all the mathematicians in the media being older white men, or Hollywood portrayals of socially inept white men who may be slightly insane: a Beautiful Mind, Türing. I had to stop watching Sherlock after three episodes: I couldn’t bear the image of what came along with intelligence. It all gives the idea that to be a mathematician you have to be really strange, and that puts people off. But you can’t make a movie out of a mathematician who’s normal and has friends.
What are you working on now?
I’m based in Chicago, although I travel a lot, and I’ve been commissioned to make art installations for Hotel EMC2 in the city. There are two large blackboard installations, and one references the work of Emmy Noether. The idea was to draw people in and make them curious about what the maths was. It as really fun: I felt like it was a very similar process to doing maths research.
My new book, Beyond Infinity, has just been published. Infinity is fascinating: it’s one of those things that everyone can think about without being able to understand it. The meta-message is this is what is fantastic about mathematics: it is the not understanding things. Make them be questions: in exploring the answer you can explore things you otherwise would not have seen.
For more information, contact Caius Communications Officer Lucy Ward: firstname.lastname@example.org
Read more about Eugenia on her website.