Eugenia Cheng always wanted to be a mathematician. But not in the way some might think.
Once a tenured professor at the University of Sheffield in England, Dr. Cheng resigned in 2016 and has since taught at the School of the Art Institute of Chicago and written several popular mathematics books. One was an edible exploration of math; another reimagined gender through her mathematical lens as one of few women in the field.
Dr. Cheng’s latest book, “Unequal: The Math of When Things Do and Don’t Add Up,” is all about equations and will be released in the United States on Tuesday. But it is more than a regurgitation of the many formulas you may recall learning in high school. In the book, Dr. Cheng argues that an equation — in its barest sense, a declaration that two things are equal — can be a profound statement on the choices we make about what is or is not the same.
For example, 2 × 3 may equal 3 × 2. But two packs of three cookies each is distinct from three packs of two cookies each. A cube drawn face-on versus from one edge looks different, though we understand the two shapes to be the same.
“Almost everything can be considered equal and unequal at the same time,” Dr. Cheng wrote. “And it’s up to us what we do about it.”
Dr. Cheng spoke with The New York Times about her mission to bring math to a wider audience and the inspiration behind her new book. This conversation has been edited for brevity and clarity.
Tenure is considered by many to be the gold standard in academia. Why leave to teach art students and write books?
When I was a tenured professor, I was helping people who were already quite good at math. But I really wanted to reach people who had been let down by the education system. I tried to propose a liberal arts math class, but the university wouldn’t let me do it. So I thought, well, I guess I’ll write it.
I realized that I could explain practically every mathematical concept using some kind of food metaphor, and that became an entire book. It was a way of showing that math can be fun, accessible, even tasty. I realized that I didn’t have to be a full-time professor anymore.
What is it like teaching math at an art school?
My students didn’t come to art school to do math. Sometimes, they tell me they chose my class because it was the least worst-sounding one.
There are some recurring themes about why my students have been put off by math in the past. They thought they were memorizing pointless things, or rules were thrown at them for no particular reason, or they were humiliated at being labeled “bad at math.”
But math is actually not just black and white, not just right and wrong answers. It’s not rigid, it’s abstract. Those are all things that they haven’t seen before, but to me that’s really what math is.
Students that have been put off by math are often excited to see that. Maybe they weren’t really sure whether 1 + 1 always had to be 2, and they could dream up scenarios where 1 + 1 might be other things. When I tell these students that there are mathematical worlds in which that is true, they get really excited, whereas people who’ve been labeled “good at math” often push back against the idea.
What inspired you to write “Unequal?”
I had a really terrible argument with someone. I like to think that I’m able to have sensible arguments with people by finding a point of commonality. But on this occasion I completely failed.
We were talking about fairness, what it means for people to be treated equally. This person declared that there was only one definition of what it means to treat people equally, and that means treating people exactly the same. And I thought, well, math has quite a subtle treatment of equality.
We don’t talk about this enough. We make choices about what to count as the same and what to count as different, and we should be aware that we’re making them.
What kind of math do you explore in the book?
Category theory is a branch of math with this radical idea that when you study things, you don’t have to know what they are. What you have to know is how they interact with other things. It’s all about relationships rather than intrinsic characteristics. And one of the most important relationships is sameness and equivalence. When is a relationship good enough to count as things being the same?
One of my favorite tongue-in-cheek examples is if you need to temporarily take over someone’s role at work because they’re on leave. It typically doesn’t matter what you look like. Unless the work is being a body double!
Knot theory studies knottiness. If you take string, tie it in a knot and wave it around, it can look quite different from different angles. Mathematicians ask: When is one tangled-up thing not really different from another?
I also threw in some manifold theory, which is when you patch together small, simple shapes to make really complicated ones. There are situations where the shape looks simple close up, but zoomed out can be very complex. I think that relates to a lot of situations in life. The consequences of our actions very close up are one thing, but if we look at the broader consequences, it can get really twisted.
It seems that studying mathematics has shaped your worldview.
Many people think that pure math is up in the clouds, completely removed from daily life. But math is a way of thinking. It’s not about the specific problems that you’re working on. It’s about training your brain.
My first book was all about food. I’ve since realized that I can use mathematical thinking to analyze anything, from disagreements to why the trains are late. It feels kind of like a superpower.
Every mathematical system starts with some basic beliefs, and then you build up from there. But you can also look at the world and unpack everything down to basic beliefs. That’s a discipline I have found very helpful. Everyone’s got their own logic that follows from something. If we can understand that, then I think we have more hope of getting somewhere rather than just shouting past each other.
How is your latest book equal, or unequal, to your prior writings?
I wanted to take people a bit further. I cover some difficult topics. One of the problems with math is the impression that if people can’t do it themselves, then there’s no point in doing it. You can still enjoy music even if you can’t play. You can go into an art gallery even if you can’t make art.
I want people to be able to gaze at math. I want to show them how it goes and what I love about it and what the possibilities are. I’m not expecting everyone to understand all the way to the end, but that’s the whole point. If you only read things you understand, then how do you grow?
Katrina Miller is a science reporter for The Times based in Chicago. She earned a Ph.D. in physics from the University of Chicago.
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