Britain’s most famous mathematician, professor **Marcus du Sautoy**, was just twelve when a schoolteacher gave him “a key to the secret garden of mathematics.” Seeing something special in the young schoolboy, the teacher recommended a book, The Language of Mathematics, by Frank Land. For du Sautoy, Land’s book was a revelation — he discovered that mathematics was “the really universal language that we can all take part in.” It launched him — he said in a conversation with Speak Up — on a journey to want to be able to make his own stories in this language.

## EXPERT IN EXPLAINING

Du Sautoy is one of the English-speaking world’s leading experts in explaining science to the general public. Since 2008 he has held Oxford University’s prestigious Charles Simonyi chair for the public understanding of science. Du Sautoy is a prolific explainer! He sees maths everywhere, from music to sports. He participated in three classical music concerts in Sweden exploring the connections between maths and music, and he uses the chaotic turbulence theory to explain the almost miraculous free kick of Brazilian Roberto Carlos in the football match against France in 1997. He also plays football for a local club, with the prime number 17, his favourite number, on his back.

## MAKING MATHS FUN

Speak Up asked du Sautoy to explain what was behind his passion to explain the world of mathematics to the general public.

**Marcus du Sautoy (English accent)**: I don’t really think that people understand what mathematics is about. I think again that’s a fault of our education system, which tends to teach mathematics a bit like learning a musical instrument, where you’re only allowed to play scales and arpeggios, and you never get to hear any real music. So, I think, a lot of people learn the technical side of mathematics, but never encounter the really exciting big stories. And that in a sense is what I try to do in my work, trying to give the public some access to mathematics. Is to tell them some of these big stories, like the stories of prime numbers, the story of symmetry. And this I think generally relaxes people, and they say, “Well, I think that sounds fun.” And so I think the thing that is missing is that we’re giving them the technical side of the subject but not giving them the grand music and stories.

## TWO PASSIONS

Prime numbers and symmetry are du Sautoy’s twin passions. Primes are also, in his opinion, the very basis of the science of mathematics.

**Marcus du Sautoy**: Prime numbers are the building blocks of the whole of mathematics. They’re what build all other numbers. If I take a number like 105, that isn’t prime but it’s made out of the primes three times five times seven. So for me the primes are the atoms of arithmetic, they’re the hydrogen and oxygen of the world of mathematics. But although the chemists have understood patterns in their atoms and have produced a table, the periodic table, which lists the things that you can build matter out of in our universe, mathematicians have not been able to do the same for our building blocks. One of the problems is that there are infinitely many primes, whilst the chemists only have a finite number of atoms to list, so we can’t produce a big table that we can put on the wall. The second problem is that although I call mathematics the science of patterns — I think that’s what a mathematician does, the mathematician is a pattern searcher — yet these fundamental numbers from which our subject is built seem to have no patterns to them at all. And that’s why I call them ‘wild numbers’. So they’re the ultimate tease: nature has given us a subject of patterns built out of a set of numbers which seem to have no pattern to them at all!

## CELEBRATING SYMMETRY

Symmetry is Marcus du Sautoy’s principal area of research. He thinks human brains are evolutionarily programmed to be very sensitive to symmetry. Some years ago, a trip to the Alhambra in Granada became, for the mathematician, an extraordinary celebration of symmetry.

**Marcus du Sautoy**: I’m interested in going beyond our three-dimensional universe and trying to understand the symmetries in higher dimensions. And I would say one of my favourite places in the world is the Alhambra Palace in Granada. It is a palace celebrating symmetry — the way all those tiles dance across the walls is extraordinary —, and you really see the artists trying out different possibilities, and there are [is] an exploration of the many different symmetrical games you can play on a wall. It took until the end of the 19th century, when we came up with a language called ‘group theory’, first created by a very romantic figure in the history of mathematics, Évariste Galois, who started to create a language to help us navigate this world.

And this language enables us to see that, although the Alhambra has many different designs in it, there are actually only seventeen different possibilities for the different sort of symmetries that can occur. So it’s interesting, when I went to the Alhambra, and I described this in my book, Finding Moonshine, we tried to see whether the artists had discovered all seventeen. And they very nearly did. I think there’s one that was missing. And I think this is very interesting, the way that artists can first discover these shapes and then the mathematicians and scientists come in later and perhaps show the limits of creativity in this realm. So I would say my own research is dedicated to trying to create Alhambras but in very high dimensional spaces, and to tile the walls, and see what different ways you can make different symmetries in these high-dimensional spaces.

## OUR MODERN WORLD

Ever since he was a young schoolboy, Du Sautoy has been on a journey through life, using the universal language of mathematics. Now, he firmly believes, this science of numbers is playing a

fundamental role in the making of our modern world.

**Marcus du Sautoy**: People depend on so much technology and they just don’t realise that it’s got mathematics at its heart. I think one of the most extraordinary is the Google algorithm, because this almost feels like magic; that it manages to pull up the website that you’re interested in. But it’s not magic, it’s mathematics. And Larry Page and Sergey Brin understood that something that they had learnt at university, called the ‘eigenvalues of a matrix’, can actually be used to shortcut navigating this incredibly complex network of the internet. So I think that’s a very striking example of mathematics being used to help us navigate this complex world.