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In an airy office in the Mathematics Institute of the University of Warwick we find Ian Stewart, the prominent maths professor, Fellow of the Royal Society and one of the UK’s most prolific popularisers of mathematics. He has published over 80 books, between 1991 to 2001 took over Martin Gardner’s original Mathematical Games column for the magazine Scientific American, and in 1995 won the Michael Faraday Prize for excellence in communicating science to UK audiences. He greets us with a kind smile, a warm handshake and leads us to his desk.

He begins by telling us how he first became involved in writing about maths for a general audience during his undergraduate days at Cambridge, when he edited Eureka, the Archimedean Society’s magazine. He moved on to the University of Warwick to begin his PhD and, on graduating, was awarded a full time position there; at the time the University’s mathematics department had only recently been founded by Christopher Zeeman. During his early years at Warwick, Stewart began producing a magazine called Manifold, which “although not strictly speaking a mathematical magazine, mostly concentrated on topics that had some kind of mathematical connection”. Over the course of its 12-year lifetime, more than 20 issues were printed and sent to university libraries and mathematics departments around the world, with 600 subscribers at the magazine’s peak. Stewart acknowledges that its success was partly due to the open-mindedness and support provided by the department’s senior researchers. It acted as a good advertisement for the newly founded department, managing to attract good researchers to the annual maths symposium held at the university and convincing mathematicians that Warwick was a “friendly place with amusing people”.

This was one way the American government managed to convince the public that the atomic bomb could possibly work.

Stewart found his home in the Mathematics Institute at Warwick, and barring a few sabbaticals has always been there, gradually becoming one of Britain’s best-loved popular maths authors. When asked about his favourite self-authored book, Stewart pauses to think for a moment, raising his head slightly. But not for very long: he leans in and proclaims “17 Equations!”. With a big smile on his face and not much prompting he tells us that the idea for 17 Equations that Changed the World came about during a book fair in Frankfurt, when a Dutch publishing house asked Stewart’s English publisher if he would be interested in the project. Stewart accepted, and originally designed a book about 30 equations, but then narrowed this down to 20 to make the book more manageable. He finally settled on 17 as he believed that this was a much more interesting number! By focusing on the historical impact and stories behind the equations, Stewart created a fascinating book that was accessible to everybody. In the chapter on relativity, Stewart was proud of debunking one prevalent myth, that the equation $E=mc^2$ was directly responsible for the development of the atomic bomb. In fact this is not the case at all, as nuclear explosions only use a small percentage of the materials’ mass energy, and it was already known experimentally that nuclear reactions could release a lot of energy. But the myth prevailed as this was one of the ways the American government managed to convince the public that the atomic bomb might possibly work.

Another of his favourites is Why Beauty is Truth: a History of Symmetry, which looks at the historical development of group theory explained through the concept of symmetry. The book starts with the Babylonians, where the calculations of ancient scribes reveal the earliest known solutions to quadratic equations. It moves on to the Renaissance period and its attempts to solve quartic equations, follows this up with Galois’ work on quintics (anyone who has studied Galois theory will no doubt be aware of Stewart’s excellent textbook on the subject), before ending with modern developments in group theory. The book was very well received and shortlisted for the Royal Society Winton Science Prize for Science Books. Turning to his competitors in the popular maths market, Stewart likes Marcus du Sautoy’s Music of the Primes, Douglas Hofstadter’s seminal Gödel, Escher, Bach and Zeno’s Paradox by Joseph Mazur. He’s also a fan of Euclid in the Rainforest, again by Joseph Mazur, where each chapter is presented as a personal story taking its readers to the heart of mathematics: logic and proof.

In the late nineties he began collaborating on the science of Discworld with Terry Pratchett, the much loved, best-selling fantasy author, and Jack Cohen. As Stewart begins describing his experiences of collaborating with Pratchett and Cohen he sits up in his chair and his speech quickens. Pratchett’s Discworld books are set in a fictional world consisting of a flat disc balanced on the back of four elephants who in turn are perched on the back of a giant turtle. The Science of Discworld books aimed to explain interesting scientific ideas through the use of fiction, although Pratchett had to be convinced that the books would work as he did not believe that the scientific backdrop to a fictional, magical world could be written about. In the end, the story was adapted to be about the wizards of Unseen University’s accidental creation of Roundworld, a place where magic doesn’t exist. Between the third and final books Pratchett was diagnosed with Alzheimer’s disease but still managed to write new stories until he sadly passed away last year.

In 1995, Stewart received the Michael Faraday Prize for popularising science and he claims this put him in the running to present the Royal Institution Christmas Lectures, which he did in 1997 with a series entitled The Magical Maze. He gave five lectures, the final of which was on symmetry, focusing especially on patterns in the animal kingdom. The lecture began with William Blake’s poem The Tyger, which he eagerly recited to us, ending with the line “Dare frame thy fearful symmetry?”. To help him explain the mathematics of pattern formation in

animals he decided to bring a live tiger onto the stage. Finding a tiger to borrow was harder than first anticipated and the producers almost had to settle on a lion cub, since cubs have rudimentary stripes on parts of their body. Eventually, however, a living tigress, Nikka, was found. She was six months old and two burly men had to hold onto her with chains, with the front two rows of chairs used as a barrier. A live tiger is certainly one way to keep an audience attentive during a maths lecture!

Given his vast experience we asked Stewart to share his thoughts about how best to popularise maths to the masses. He believes that there are two messages that need to be conveyed to the general public. The first and most important is that maths is not stuck in the Dark Ages, that there is still lots of new research still taking place. The second is to then explain to the public what this new stuff actually is, and applications of mathematics are not necessarily the best way to get people interested. Esoteric subjects such as 17-dimensional manifolds, the Big Bang, quantum theory, catastrophe theory, fractals, the Riemann hypothesis and Fermat’s Last Theorem are all examples of complicated abstract mathematics that have captured the public’s attention without needing to be reduced to everyday applications.

Esoteric subjects such as 17-dimensional manifolds, fractals and the Riemann hypothesis have all captured the public’s attention.

On the other hand there are areas of maths that he tries to avoid popularising. Despite this, he was asked to write a book about the famous Millennium Prize Problems, a collection of seven unsolved maths conjectures with a correct solution to one of them worth \$1m. Only one, the Poincaré conjecture, has been solved so far (although the winner, Grigori Perelman, did not claim his prize). One of the problems is the Hodge conjecture, a major unsolved problem in the field of algebraic topology, which asks “which cohomology classes in $H^{k, k}(X)$ come from complex subvarieties $Z$?”. This is a very technical piece of pure mathematics that is hard enough to explain to your average maths professor, let alone the general public! He believes that some areas of maths are easier to popularise than others and different techniques can be used to capture different types of audiences. History interests a certain class of people and telling stories about the mathematicians involved often works: who did what and what sort of person were they (think of the recent films about Alan Turing and Stephen Hawking). And, of course, another good way to interest people is by using links to physics, biology, economics and financial markets (although in the latter case Stewart points out that the global financial crisis shows that these links are not always good advertisements for mathematics).

Perhaps unusually for a modern day mathematician, Stewart’s own mathematical research has been broad, crossing the infamous pure/applied dividing line. He started out his career as a pure mathematician, working in abstract algebra and group theory. However he later began to work increasingly in applied maths, often in the field of dynamical systems, and produced influential work in animal locomotion and pattern formation. Does he think working in many different areas of maths is something more mathematicians should do? “Well there are some deep thinkers who stay in one area for seven years, such as Andrew Wiles when he was proving Fermat’s Last Theorem, and they think about close and related mathematical ideas to keep it alive. Whereas some people, such as Terence Tao, constantly do fifty pieces of work simultaneously in what appear to be totally unrelated areas of mathematics and so often put them together.” He thinks it is good for mathematicians to move out of their comfort zones, as in doing so you often find spin-offs back into your own area, and it helps you avoid getting stuck in a rut. Although he concedes that for some people this doesn’t work: “you may end up getting distracted by several things but end up doing nothing!”.

What does Stewart think of the relationship between research and popularisation? He believes mathematical research does help with popularising science and maths, and gives authority to his writing. Most people who write about pop science usually work in the field and have developed a skill of being able to write in a way others would understand. But there are exceptions, and there are some excellent journalists who spend a lot of time talking to scientists and trying to understand what is going on; Stewart believes both approaches work. The relationship between popularisation and research can work both ways however; in fact, he has often found that popularising something has helped his research. “Writing for a different audience makes you rethink everything—often you find that as you try to explain things to an audience who do not understand things perfectly well, you realise you don’t understand it as well as you thought. And so you get feedback in both directions.” Popularisers also get exposed to different areas of maths that can inspire new research ideas. It was having to review a book on robot locomotion for New Scientist, for example, that got Stewart thinking about how animals walked, spawning a whole new area of mathematical inquiry in which he has subsequently published many papers.

Writing for a different audience makes you rethink everything.

Stewart’s next book, due out at some point in 2016, is called Calculating the Cosmos, and will look at cosmology and astronomy through the window of maths. He sounds particularly excited about this book, and believes it potentially is his best yet. In 17 Equations that Changed the World he was quite outspoken about cosmologists’ current ideas about dark matter, dark energy and inflation. We asked him what his thoughts were now. “I still am outspoken!”, he exclaims. There is a large amount of energy missing from the universe, and the dynamics of objects such as galaxies don’t seem to agree with our theoretical predictions. To account for this, physicists have to add extra energy components to the universe: dark matter, dark energy and the inflaton. This certainly works: the maths can now accurately describe the dynamics of the universe we observe, although these extra components have never been directly detected. There are alternatives: one could, for example, modify the laws of gravity on large scales, an approach that Stewart believes shouldn’t be neglected. “I think modified gravity is the way forward. I don’t think the impetus of dark matter is that strong.” Physicists would lead you to believe that “it is dark matter; we know it’s there”, but Stewart doesn’t find the evidence convincing: “there are a lot of neglected alternatives: that’s bad.”

From his airy office, it was to a more visible sign of the wonders of our universe that Stewart went with his family for Christmas: the northern lights. A well-deserved break for one of mathematics’ most famous and best communicators.

Matthew Wright Matt is a PhD student at UCL, working in the fields of general relativity and cosmology.

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