**Eugenia Cheng is the author of the new book**

*Beyond Infinity: An Expedition to the Outer Limits of Mathematics*. She also has written*How to Bake Pi*. She is the Scientist in Residence at the School of the Art Institute of Chicago, and an honorary fellow of the University of Sheffield.*Q: Why did you decide to focus on infinity in your new book?*

A: Infinity is something small children can think about and
be intrigued by, but it took mathematicians thousands of years to understand
how to deal with it logically.

I love that big gap between the idea and the explanation.
For me it means there's an interesting journey there and lots to see along the
way. More concretely, people often tell me that their children have asked them
something about infinity and they don't know how to answer: this book is my
answer!

*Q: You begin the book with a comparison of airports and boat travel. Why did you start there, and what do you see linking your feelings toward math and travel by boat?*

A: I think one of the misconceptions about math is that it's
all about getting the right answer. But this is like thinking that all journeys
are just about getting to a destination.

I started the book by talking about different types of
journey to remind us that some journeys are about getting there, but others are
about the experience of travelling, and what you see along the way.

In the same way, some parts of math are more about the
process than the endpoint, and are about the exhilaration of travelling, and
the things you see along the way.

Those are my favourite parts of math, actually, but rarely
the ones you get to see in school. That's why I'm on a mission to share them
widely.

*Q: In the book, you write, "Mathematics suffers a strange burden of being required to be useful. This is not a burden placed on poetry or music or football." Can you say more about that?*

A: Math is thought of as being useful, and too often we
encourage young people to keep studying it because of career prospects. It's
true that math is useful, and being good at math does make you very employable
in a wide range of careers, not just obviously mathematical ones like finance.

The trouble with this, in my view, is that saying something
is useful does not make it sound interesting. Also, it means that anyone can
then dismiss it by saying they don't want to do any of the things it's useful
for.

I think this is further backed up by the fact that most
people really don't use much math in their daily lives: maybe some basic
arithmetic and percentages at most, but we can all get our phone calculators to
do that.

I would rather get people interested in math by showing how
it can be fun and fascinating. We don't seem to get children to play
sport by telling them it's good for them - it's more likely that parents simply
share their enjoyment of it naturally with their children.

I saw a meme this week complaining about being having to
learn parallelograms at school, which are not useful for anything, instead of
something really useful like How To Do Taxes.

It makes me sad that math is seen as something pointless
unless directly useful. Would anyone suggest a How To Do Taxes class
instead of poetry, or sport, or music?

*Q: What are some of the most common perceptions and misperceptions about the concept of infinity?*

A: One of the common perceptions is that there's nothing
much to say about it: it's "just" the biggest possible thing. But
there is a vast amount to say about it - one might say...an infinite amount. [Sorry!] It's
a good example of an apparently simple idea that seems to make sense until you
really scrutinise it logically, at which point it falls apart.

Unfortunately there are plenty of ideas like that floating
around. One response is to simply avoid scrutinising things logically, but
as a mathematician I am not satisfied with that approach.

One of my aims is to persuade people that it's rewarding to
explore why something falls apart under logical examination, and enlightening
to work out how to fix it.

*Q: What are you working on now?*

A: I have many different projects on the go at the same
time. I am doing a series of workshops for New York public school
teachers, sharing creative math projects that I have developed while teaching
art students at the School of the Art Institute of Chicago.

I am also teaching a minicourse on my research subject,
Category Theory, to high school teachers at Math for American in New
York.

I have a new monthly column in the Wall Street Journal
called "Everyday Math", in which I talk about the ways in which I see
the world around me mathematically, but not just in terms of numbers.

The most unusual project is that I am just finishing my
first art commission, some large mathematical chalkboard installations for
Hotel EMC2, a new hotel in Chicago that celebrates the intersection between Art
and Science.

I also continue to run the Liederstube, my art song salon in
Chicago, and have several concerts coming up with some wonderful singers.

And I am always working on my technique for making French
macarons.

**--Interview with Deborah Kalb. For a previous Q&A with Eugenia Cheng, please click here.**

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