What is it that intrigues us about maths? As her latest book is published, category theorist Eugenia Cheng says it’s the smallest yet biggest question of all: why?
I have always loved maths. I want to know why things are happening, and have never stopped being a toddler who keeps asking questions. Maths always gave me satisfying answers to those ‘whys’ – and generated the most interesting new questions.
My mother always talked to me about maths and logical thinking at home – things such as patterns, graphs and logical concepts like converses, false equivalences and the importance of clear definitions. She worked in the City, commuting by train wearing a suit, carrying a briefcase and surrounded by men. I think this helped me not to feel pressured by gender stereotypes. It also helped that I went to a girls’ school and had no brothers, so there were no comparisons with boys. It never occurred to me that girls might not be good at maths. I arrived at school ahead in maths, putting me at an advantage.
It was obvious that I wanted to study the subject at university. There was a moment when I considered doing music, but I was brought up to be financially pragmatic and it seemed more plausible to make a living with maths and play music on the side, rather than the other way around.
When I was young I wanted to be ‘a mathematician’ without knowing what that meant. In any case, this did not count as a career from my school’s perspective. During Sixth Form, when we were applying for university, we had to research three careers we were interested in that could follow from our degree subject. ‘Actuary’ was suggested to me as one of them; I also researched accounting and merchant banking.
I never ended up being clear what a merchant banker does, but actuarial work captured my imagination. However, I didn’t enjoy probability and statistics at school because the data we analysed was fabricated. We never got to analyse real data, let alone set up a study, obtain data and analyse it. The idea of doing this for real situations made me think about statistics differently. However, the lure of the ‘why?’ questions won out so I went into pure maths, and then into arguably its most abstract branch: category theory.
It makes me sad that so many people leave school hating maths, feeling traumatised by it or just being glad that they never have to do it again. Most are put off for the wrong reasons, having only been shown a narrow, rigid and unrepresentative view of the subject. Maths is frequently presented as ‘important’ and ‘useful’, but lessons so often fail to teach important or useful things, or emphasise exactly what the importance of maths is. Often it isn’t the content that’s important (I never use trigonometry in my daily life!) but the way of thinking. However, in the race to cover the curriculum and get students through exams, there is little time for thinking – in particular, for deep and open-ended questions.
I wrote Is Maths Real? to address that. Curious students have deep questions about why things are true in maths, but those questions aren’t often encouraged. I wanted to validate and answer them – and not just in a sentence, because these are questions that spark long journeys of mathematical discovery. I start with simple questions such as ‘Why does 1+1=2?’ and show how this takes us deep into serious mathematical thinking. Not only are these questions profound, but they also show us the true point of maths, which is developing ways of thinking clearly and logically to build rigorous arguments and push forward human understanding while keeping it on secure foundations.
This is part of the broad aim of all my work: reaching people who have been, or are in danger of being, excluded from maths and mainstream education, and giving them a way in. I want to eliminate the concept of ‘maths people’ and ‘non-maths people’. I firmly believe maths can be for everyone, that it can help everyone, and that we need to find ways to make that a reality.
Dr Eugenia Cheng is scientist in residence at the School of the Art Institute of Chicago and an honorary visiting fellow of pure mathematics at City, University of London. Her book "Is Maths Real?" (Profile Books) is out on 1 June