Eugenia Cheng combines home baking with higher-dimensional category theory. She talks about pudding, infinity, and why geeks are the new alphas
Eugenia Cheng is a British mathematician who is senior lecturer at the School of the Art Institute of Chicago. Her main interest is higher-dimensional category theory but she has also written a book about the maths of baking entitled How To Bake Pi. Her latest book is Beyond Infinity: An Expedition into the Outer Limits of Mathematics.
What is higher-dimensional category theory? Can you describe it in a sentence?
It is the mathematics of mathematics. It does for mathematics the same thing that mathematics does for the world it makes connections between things and it highlights patterns between things, so that we can be more efficient about how we use our brain power.
Youve declared your vision is to rid the world of mathematics phobia. How do you erode it once it has taken hold?
Unfortunately, the kind of maths we teach in school is often not in any way useful for most peoples lives people say When am I ever going to need to solve a quadratic equation in my life? The kind of maths I teach is about logical thinking, thinking your way through situations, understanding what is causing something to happen and working out how things fit together.
Youve said mathematicians are a bunch of rebels are you an anarchist?
Yes, definitely! Mathematicians really like making up their own rules that make sense for particular situations, and we hate having rules imposed on us.
How to Bake Pi was quite a hit. Why did you use cooking to explore maths?
It started because I always tell an anecdote when I am teaching, because I want everyone to be able to relate it to something in normal life. I realised that whenever an anecdote involved food, my students perked up. One day, one of my students called out Explain some maths using Oreo cookies, and I realised they represented something we were going to do in the lecture that day. It was this thing called conjugation, where you multiply A by B and A inverse you sandwich B between two As, one of which is the other way around. The cookie demonstrated that perfectly, because you have the cream filling between two cookies, but one of them is the other way around from the other. Suddenly they all got it, and I realised I could explain anything using a food analogy.
Whats your favourite maths-based recipe?
The one about millefeuille, because it was the one I did with [US talk show host] Stephen Colbert, and we had a rolling-pin fight. Puff pastry is one of those thingswhich is notoriously difficult to make. It also demonstrates the principle of exponentials.
Are you worried that by turning to cookery, you send the message that maths can only be exciting through analogies?
Mathematics is actually all analogies. What I am trying to do is provide the ideas and the way into something. Unfortunately, a lot of people derive their feeling of self-worth from the fact that they can understand things other people cant. I dont believe in that.
Presumably, your favourite idiom is the proof of the pudding is in the eating?
One of my students at the University of Chicago brought some pudding a bit like Angel Delight and we ate the chocolate pudding and at the bottom was a mathematical proof. It was hilarious!
Your latest book, Beyond Infinity, tackles one of the most mind-boggling concepts in maths. What is the weirdest thing about infinity?
It is one of those things, like optical illusions, where I enjoy not being comfortable with it: you can sort of swim in the weirdness of it. I dont like understanding it too much because then the illusion goes away. There is the thing about some infinities being bigger than others, but one of my favourite things is that one plus infinity is different from infinity plus one. It is like that Shakespeare thing of forever and a day that for ever and a day is longer than for ever.
Theres been a lot of discussion about the best way to teach maths, with the east Asian approach taking off in the UK. What did the west get wrong?
There is that stereotype that east Asian people are really good at maths, and because I am Chinese by origin I get this a lot. It is a bit frustrating and a bit racistthanks for removing all my agency in the things I have done in my life! But I now teach arts students, and many of them are from China and Korea, and many of them say I was put off maths because of the Asian system.
Youve said that people often tell you that you dont look like a mathematician. Are you optimistic that societal stereotypes will fade?
The stereotype is based on some reality, but I think the reality is an accident, and it is self-perpetuating. You dont have to reject looking nice in photos just because you are intelligent, and it is not a proof of intelligence if you reject wearing nice clothes and looking nice in photos. It does frustrate me when the depictions of intelligent people, especially mathematically intelligent people, in things like films are all socially weird white guys. Also, in a very pedantic way it doesnt make sense. I am a mathematician, so I look like one I am me. It is like saying That is not very feminine, but everything I do is feminine because I am female.
Theres only been one female winner of the Fields medal since it was first awarded in 1936 Maryam Mirzakhani. Does maths suffer from an old boys club mentality?
I am happy to say I have not experienced that. On the other hand, maths cares about solving big problems and proving big theorems rather than making a theory that connects things together. There is a great female mathematician, Emmy Noether, who is very neglected. She suffered for many reasons: she was Jewish in Germany in the 1930s, and she couldnt get a position because she was female, but she just carried on anyway. One of her great theorems brought together maths and physics [but] it didnt solve a particular problem, it wasnt relativity. I think it is going to be a very long time before anyone gets a Fields medal for category theory, because it brings things together rather than solving a particular problem. It is not an old boys club, it is more of an old theorems club.
Is the era of big data, coding, and the inherent reliance on numbers changing the reputation of maths? Will it ever be considered as glamorous and powerful as, say, genetics?
I have said for a while that the day of the geek is coming. I dont like the word geek particularly, because I dont think I am one. But I like thinking about the fact that when we were cave people, the important thing was to be able to defend ourselves from woolly mammoths. So we evolved to think that was a thing we needed to be attracted to; and I like to think that now we depend on computers all the time, the most important thing is to be able to fix your computer or code and therefore that is the new beating off a woolly mammoth.
You are an accomplished concert pianist does that come back to a love of maths, or is it a very different discipline?
Its partly that it is quite abstract, playing the piano. Singing is very visceral and, because you are using words, very direct. There is also so much structure in pianos and piano music. It is a mental shortcut, so you can produce more things using less brain power. It is also about a balance. Music balances out the sheer mathematical thinking that I do because it is abstract. The things it is expressing and exploring are emotions. Mathematics is doing the opposite.
Does logic have its limits?
Definitely, but the limits move. I have this image that logic is a sphere at the centre of our thoughts, and all the time we understand more mathematics we are putting more things into that central part, and it is growing. For me, the most beautiful part is the boundary between what we understand logically and what we dont. The more we understand, the more of that boundary we have, because the surface of the sphere grows. So as we go, we get more access to beauty.
Beyond Infinity by Eugenia Cheng is published by Profile (12.99). To order a copy for 11.04 go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over 10, online orders only. Phone orders min p&p of 1.99