Lowdown
What: Eugenia Cheng at Auckland Writers Festival
Where & When: Aotea Centre, Friday, May 17 (with Simon O'Neill); Heartland Festival Room, Aotea Square, Sunday, May 19

Eugenia Cheng once called Schubert's Piano Sonata D960 "a perfectly crafted place to fall in love", then, illustrating her point, gave a lovely performance of the work to an audience of Schubert fanatics.

A couple of years earlier, using similarly evocative words, she explained to a TEDx crowd how she spends her days working in a "beautiful dream world".

That dream world is not music but maths.

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Although Eugenia Cheng plays piano to concert standard, her main gig is lecturing about pure mathematics. Maybe that goes some way to explaining why she uses the same poetic, metaphorical language to describe things that to most of us are polar opposites.

"I feel very similarly about [maths and music]," she says on the line from Illinois, where she teaches at the School of the Art Institute of Chicago. "The joy and elation of doing mathematics to me, at its best, feels very similar to the joy and elation of music."

Cheng combines the two at the Auckland Writers Festival, where she makes a pair of appearances. One is in support of her latest book, The Art of Logic; the other as a pianist, accompanying tenor Simon O'Neill in music by Bach, Wagner and Schumann. Cheng and O'Neill will perform some of their favourite songs, then she will talk about mathematical elements she observes in the music.

New Zealand opera star Simon O'Neill joins Eugenia Cheng for performances at the Auckland Writers Festival.
New Zealand opera star Simon O'Neill joins Eugenia Cheng for performances at the Auckland Writers Festival.

"I do see maths everywhere," Cheng says. "Even if you don't know it's there, it's there. So we're aiming to share the music and show that you can respond to it in an entirely visceral way without understanding anything about it and then explain things to see if we can experience it in a deeper way, or with new insights."

Much has been written about the links between maths and music but Cheng resisted doing so for many years saying when people asked her about the connection, she rolled her eyes because she didn't think it was interesting. Having matured as a mathematician specialising in higher-dimensional category theory ("I think of it as the mathematics of mathematics"), she now finds the subject fascinating.

"Maths to me is about the relationships between things, relationships between ideas. That, I think, is deeply related to classical music and the way I love it, because what I love about classical music is its structure and harmony and the way it fits together."

And Cheng is passionate about using maths to help people see the world anew. Her earlier books, How to Bake Pi and Beyond Infinity, sought to popularise maths by making it accessible even to the numerically illiterate.

The Art of Logic, however, has political intent, and is her mathematically informed attempt to make sense of world events, notably the 2016 election of Donald Trump.

"Like many people, I got very depressed, but I don't like sitting around being depressed, I always want to do something," she says. "I thought, 'What can a pure mathematician possibly do?' One thing I find is that as a pure mathematician I have ways of understanding arguments that seem completely polarised and divisive and I felt that the techniques of abstract mathematics helped me understand these things from many points of view."

Using the mathematical principle of axioms, she looks for the logic underlying people's actions no matter how illogical they may seem.

"Accusing people of being illogical never persuaded anyone of anything. A much more unifying thing to do is understand why people think the things they do and there is always some kind of logic to it. So I talk about the fact that logic and empathy need to go together."

Empathy and logic? Has Cheng seen social media lately?

"There are reasons people think things," she reiterates. She's equally adamant that understanding does not mean endorsement. "Finding those reasons doesn't mean you're endorsing them, and that's important, because in this day and age if you show justification for what people think it sounds like you're supporting them but that's not the case."

What she does endorse, naturally, are the myriad uses and possibilities of mathematics to decode a complicated world. In doing so, she rejects the widely held belief that maths lacks creativity and can't be understood unless you've passed lots of exams.

"Maths has a bit of a bad reputation and that makes me really sad," she says. "It's like having a really misunderstood friend. I want to show what is really loveable about maths, that maths can be appreciated like music, where you don't have to be able to do it in order to appreciate it."