For many people, Marcus du Sautoy might just be the most recognisable face in modern mathematics (although Carol Vorderman fans may disagree with this assertion!). He writes regularly for several national UK newspapers, is a frequent guest on the BBC and is about to release his fifth book. He has also taken mathematics to some more unconventional places, including the Glastonbury festival, the Royal Opera house and the Barbican. His academic work focuses on number theory and group theory, something that he says appeals to him due to its inherent structure, and because once you have the right idea “it kind of runs itself”. This love for big ideas and the story of mathematical discovery will be familiar to anyone who has ever seen him enthusiastically explain one of his favourite subjects, Euclid’s proof that there are infinitely many primes, on radio, television or in print.

However, despite his broad research background and his familiarity with, dare we say it, intimidating-sounding concepts such as ‘zeta functions of infinite-dimensional Lie algebras’, du Sautoy assures us that he is not the sort of person who “gets things really quickly”. This, he says, has helped him become effective at communicating mathematics—you must “get in the head of your audience” and understand why they aren’t comfortable with a concept, or “find the thing that they get, which you can use” to take them on the same journey that you have been through on your own road to understanding. In short, it is empathy.

## Science is for sharing

His passion for science communication is evident in his impressive résumé of creative projects (he is most likely the only person to have discussed prime numbers on TalkSport Radio, explored the mathematics of consciousness through ambient electronic music and held the position of ‘mathematical consultant’ for an award-winning West End play) and in his animated and lively responses to our questions on the subject. “It’s all about good storytelling” he says, as we discuss what makes some parts of mathematics more easy to communicate than others. “That’s at the heart of why we do mathematics: the bits of maths that I want to talk about are those that take you on a really interesting story. We get excited when something weird happens.” It is also important not to underestimate or “think for” your audience. After all, if you are excited enough about something and can communicate what it is that motivated you to learn about, write or create a piece of mathematics—“tell stories about big ideas”, as du Sautoy puts it—then there is a good chance that someone else will be excited by it too.

But why bother? Does anybody really want to hear people talk about mathematics? For du Sautoy, publicly-funded scientists have a “social responsibility” to attempt to explain their work, both to show people what their money is being spent on and also to inspire the next generation. He recalls “cutting out anything about maths” from newspapers and “devouring” it later, grateful that someone had gone to the effort of explaining things to him; and so he sees his time spent in science communication as a way of paying back those who inspired him. This is a belief that he has had reinforced by the Royal Society, who appreciated his passion for communication and allowed him to develop his skillset accordingly while supporting his early career as a researcher. He admits to being “worried that they would be upset that I was doing this thing that clearly wasn’t my research. But they said we really want our research fellows to be doing this, we think this is important”.

In addition to this clear moral desire for public service, du Sautoy also sees an opportunity to challenge himself and develop his own knowledge through communication, quoting David Hilbert: “you cannot truly say you understand something until you can explain it to the person on the street”.

## Too cool for school?

This all sounds like a very noble effort, but personal experience suggests that many people switch off at the very mention of mathematics. Du Sautoy admits that he thinks we have a culture problem today in the UK, where there is a “badge of honour in admitting that you’re bad at maths”. The main issue, he says, is the ‘technical’ nature of the school curriculum, which obscures how wide-ranging mathematics is and leads people to be dismissive of its usefulness.

Maths is about developing a critical, analytic way of thinking, not that you can solve a quadratic equation. That ain’t useful. It’s about producing somebody who can look at a problem in a different way.

Intriguingly, he suggests that such a mentality is especially important in today’s world where we need people who are able to look beyond “short-termist soundbites” and understand the data that permeate into our highly-connected, digital lives. It’s a fascinating thought, the idea that a prescriptive approach to mathematics education could have contributed in such an unexpected way to today’s political norms, and something that du Sautoy fears could get worse as we become more familiar with big data, which he says we mustn’t use as “an excuse for not thinking clearly and analytically” or as a substitute for deeper understanding.

Another problem is that the current focus on specific techniques, rather than the big picture, can easily put people off mathematics. To recapture their attention, du Sautoy loves using the creative arts to show people that maths is everywhere, prompting a response of “oh if *that’s* maths then I get *that*”. He fondly recalls an interactive performance of Mozart’s *The Magic Flute *at the Royal Opera house, in which he managed to introduce a “hardcore” opera audience to mathematics, and (perhaps more impressively) had mathematicians enjoying themselves at the opera.

## A steep learning curve

It’s not all been plain sailing, however. Like many mathematicians, du Sautoy says he was “rubbish” at writing while at school, and there has been a definite learning process that has lead to the confident, polished multimedia operator that we see today. His first attempt at an article for the *Times* was on the awarding of a Fields medal to Efim Zelmanov. It was sent back by the editor, who chastised him for leaving his “best story” (about the death of Évariste Galois, shot in a duel with a mysterious love rival at the age of 20) to the end of the piece.

From this, he learned the need to grab and hold the reader’s attention, to convince them to continue reading your article. Later, he came to understand the power of graphics when he wrote an article in the *Times* on the Riemann Hypothesis, the first of many of du Sautoy’s explorations into this longstanding mathematical problem. Despite the fact that he feels mathematics isn’t “naturally visual”, his article, a conversation with Andrew Wiles about great unsolved problems in mathematics, was not published by the newspaper until he added in a Mathematica-generated image of the Fermat curve $z^4 = x^4 + y^4$. The resulting picture was even put on the front of the paper, so convinced was the editor that it would draw people in.

Standing in front of a camera also took some getting used to. Although he believes that most academics are performers (“You have to stand up in front of 200 undergraduates… and you’ve got to inspire them for an hour!”) there is more subtlety required to appearing on television—you have to “tone it down” and give “a much smaller performance”.

Just think that there’s one person sitting on the sofa, and think about telling them stories.

Again, du Sautoy summarises his philosophy succinctly, this time with a quote from Beckett: “fail, fail again, fail better.”

## How to keep things balanced

At this point, we were about to down tools, abandon our respective degrees and embark on fulfilling and glamorous lives spreading the joys of mathematics at festivals and in theatres around the world to anyone who would listen. Not so fast! Du Sautoy advises a more balanced approach. His career as a science communicator could have begun earlier than it did, were it not for a hesitance about “sticking his head above the parapet”. As a post-doc at Oxford, he recalled sitting next to the *Times’* features editor at dinner (as you do) and, aided by some wine, explaining his work and concepts of symmetry in group theory in some detail. “Wow!” was the unexpected response. “That sounds so *sexy*!” And so he was asked to write an article for the paper explaining the subject. At the time, du Sautoy was cautious, and decided the next morning to let the request lie. “I grew up on the idea that you do maths for the mathematicians, and it’s not for the public.”

Three years passed, when again he found himself seated next to the same editor at another dinner. This time, the journalist persuaded him that it was his responsibility to at least try and explain his work to the public. “OK”, he remembers thinking, “maybe I am being a bit arrogant saying that you won’t understand this”. So he accepted the offer, and a few weeks later the article on Zelmanov was published. This first foray into the public sphere brought immediate response: two readers letters arrived the very next day! Since then, there has been a delicate balancing act in maintaining his research profile and public engagement commitments, but du Sautoy believes that mathematics is well-suited to the sort of double life that he leads—“I can do my research from anywhere in the world, and I don’t have to rush back to the lab before my cultures go off”.

## Delay… delay… win!

The story of writing his first book, the excellent *Music of the primes*, also involves a strategic delay. Having written newspaper articles for a few years, he was approached by an agent about writing a book. But, reasoning that if he wanted to continue his career as an academic he needed time to establish himself, he turned the publishers away and concentrated on putting papers into leading mathematical journals. After all, du Sautoy says, he got into communication because of his love for maths, and he keeps being given opportunities to do it because he is a professional researcher, so it’s important to “keep a balanced head”. The writing of *Music of the primes* was a difficult task, but he sees many parallels between this process and the proving of theorems. Both work on long timescales and require one to bear in mind a “massive long narrative” while focusing on the details from day to day. The book was partly inspired by the proof of Fermat’s last theorem and seeks to illustrate that even basic concepts like prime numbers are not fully understood through discussion of the Riemann Hypothesis.

This is a remarkable thing to attempt to explain in a popular science book, and a challenge that his head of department described as “utterly mad”. His first draft followed a strong scientific arc, which seems very natural to a professional mathematician. But this book was not intended to be for scientists, and when du Sautoy realised that his editor was confused by how the story was “jumping about all over the place” he settled on a historical narrative instead, one which sits easier with the general public. Again, we see that the key to successful communication of complicated ideas is empathy, and a willingness to go against what might seem natural to you on the basis that there is another method that is more natural for your audience.

Today, du Sautoy holds the impressive title of ‘Charles Simonyi professor for the public understanding of science’ at Oxford, a role which has enabled him to look beyond mathematics and start to communicate deep problems from other areas of science. His latest book, *What we cannot know*, probes the boundaries of knowledge in different fields, in an attempt to discover whether other sciences can have an equivalent of Gödel’s incompleteness theorem, that describes the limits of what it is possible to prove in a mathematical framework. Through his research for the book, he probed profound and complex ideas including quantum physics and human consciousness. Wrestling with these ideas has been a challenge, but du Sautoy has found that mathematics often emerges as the best language for describing them: “I love that. It all comes down to maths.” If there is one thing that we learned while talking to Marcus du Sautoy, it is that everything certainly does.