Duelling with the Monster By Marcus du Sautoy 1 DUELLING WITH THE MONSTER Marcus du Sautoy DUELLING WITH THE MONSTER will combine a personal insight into the mind of a working mathematician together with the story of one of the biggest adventures in mathematics: the search for symmetry. 1. some background My intention with this second book is to build on the strengths of THE MUSIC OF THE PRIMES – where a meaty mathematical story was told through the lives of a fascinating dramatis personae of mathematicians. In commercial (and publicity) terms, THE MUSIC OF THE PRIMES had the advantage over its competition because it was written by a working mathematician. I now want to extend this advantage and to create something unique within the genre of popular science books, through a book that still has a strong mathematical story at its heart, but which goes one step further. I am constantly striving to push my own boundaries in finding ways to share the excitement of mathematics with a broader audience. THE MUSIC OF THE PRIMES was a first step for me – beyond my journalism – into the world of popular science writing. I want to work on a project that will be as stimulating for me to write as that first book. But I have a strong sense that the market is looking for a fresh approach to telling a scientific story. I was a judge of the Aventis Science Book Prize last year, and I read 94 popular science books from the year’s crop. That experience certainly made me realise that the market is flooded by sound- alike books. But where to go? The reception of THE MUSIC OF THE PRIMES both in the media and through the huge amount of correspondence I have received suggests to me that the reading public has a huge appetite to find out about the world of the mathematician as much as about the subject of mathematics. Readers are keen to get under the skin of the mathematician and to get some inkling into the sensation of doing mathematics. This was 2 particularly reinforced by the surprising response to a small academic writing project I undertook for the Gulbenkian Foundation at the time that THE MUSIC OF THE PRIMES was being put to bed. The idea was to collect into one volume the diaries of scientists over a short period in their academic lives. The book is called SCIENCE, NOT ART. Since publication, there has been fantastic media interest in the record I kept. The level of interest is especially striking given the academic origins and resources of the project. The Guardian chose my diary alone as a serialisation. Radio 4 also featured my diary on “Front Row” in the form of an interview and reading. My diary was also read as Radio 4’s “Book of the Week” in February 2004. I was flattered and initially amazed that my diary won out over the diaries of scientists in such obviously glamorous subjects as the ecologist studying the Amazon, the physiologist investigating medicine in space or the marine biologist in his submarine. But the mysteries of the mathematical world hold a great fascination for readers. They yearn to be transported into this alien world that seems far removed from the physical space around them yet seems to be filled with such universal truth and beauty. Given the success of both THE MUSIC OF THE PRIMES and my diary, I have begun to explore the exciting possibility of combining the two approaches. The central thrust of DUELLING WITH THE MONSTER will be to tell the story of how humankind has come to its understanding of the bizarre world of symmetry – a subject of fundamental significance to the way we interpret the world around us. Our eyes and minds are drawn to symmetrical objects, from the sphere to the swastika, from the pyramid to the pentagon. “Symmetry” indicates a dynamic relationship or connection between objects, and it is all-pervasive: in chemistry and physics the concept of symmetry explains the structure of crystals or the theory of fundamental particles; in evolutionary biology, the natural world exploits symmetry in the fight for survival; symmetry and the breaking of symmetry are central to ideas in art, architecture and music; the mathematics of symmetry is even exploited in industry, for example to find efficient ways to store more music on a CD or to keep your mobile phone conversation from cracking up through interference. Mathematics has provided us with the language to master and to articulate this rich world. It is only through mathematics that we could have discovered some of the extraordinary symmetrical objects that Nature has concocted. And the most fearful and exciting of all the symmetries discovered by mathematicians is the Monster: a huge snowflake that lives in 196,883-dimensional space with more symmetries than there are atoms in the sun. The discovery of the Monster represents the summit of mathematicians’ mastery of symmetry, and it will also be the pinnacle in DUELLING WITH THE MONSTER. 3 The mathematical/historical threads in this story are rich enough, but what will make this book unique is the personal story that will be woven through it. It is here that I hope to explain what it is really like to be a mathematician. DUELLING WITH THE MONSTER will balance the grand historical exploration with my own personal battles – one with a particular deep conjecture about symmetry (my day job, as it were), and one relating specifically to the Monster mentioned in the above paragraph. The stories will interweave very naturally and will illustrate the sense of transformation and discovery in both the personal and historical narratives. The aim in the personal narrative will be to capture the dynamic tension that made the diary for the Gulbenkian Foundation so successful. There are moments of deep frustration, flashes of revelation, fears of competition, tales of friendship and collaboration. These personal episodes in my own battle will echo, and be echoed by, similar themes that run through the historical account. The format of the book will attempt to create a direct dialogue with the reader. In all my work, both academically and through the media, I try to make people understand the way my mind creates, and at the same time to lead them on the path that I have cleared. It is too bold a claim that I can give the non- mathematician an access-all-areas back-stage pass to the mathematical mind, but the personal journey in this new book offers the tantalizing possibility of bringing people extremely close to it. There are no other mathematicians out there who would contemplate such exposure. Even the short diary I did the Gulbenkian Foundation has drawn comments from the mathematical community. Although they recognized in the diary all the emotions that rage in their own mathematical lives, exposing their souls just isn’t what mathematicians do. 4 2. structure of the book There are three distinct threads: The first is the broad mathematical story, a classic “narrative non-fiction” recounting the history of man’s understanding of symmetry, and culminating in the uncovering of the Monster, and what we have learned from it. The second and third threads are personal challenges: One relates specifically to the Monster, and it is simple: can I understand it, and how much of my understanding can I communicate to my reader? The other relates to my ongoing efforts to crack the PORC conjecture, one of the outstanding mysteries about symmetry. My intention is to divide the historical narrative into four distinct sections -- or “seasons”. Each section will contain three chapters -- or “months”. The personal narrative will frame each chapter of the historical story. The sense of time built into the historical narrative will be mirrored in the development of the personal story. 5 3. brief outline of the historical narrative. Spring: The symmetry we can see. The ancient Greeks are the fathers of our mathematical world. It was the likes of Plato and Aristotle who identified the importance of shapes with many symmetries. The five Platonic solids are the beginning of the science of shape and symmetry. Similarly, the iconoclastic belief of Islam meant that the Arabs were particularly fond of expressing their religious belief through designs that included much symmetry. The beginning of the story explores the tangible first shoots of a theory of symmetry. Summer: From pictures to language. The French revolution represented a key turning point in the story of symmetry. The French revolutionary and mathematician Galois single-handedly forged a new language that allowed mathematicians to articulate the symmetry of the unseen. The importance of language will be a big theme in the book, representing a similar strand to the “music” that ran through The Music of the Primes. The power of this language reveals that there is symmetry at work in an unexpected variety of mathematical and scientific settings. Not only does the 3-dimensional physical world like symmetry, but the theory underpins the behaviour of other mathematical objects. Although killed in a duel aged 21, Galois’ mathematical language immortalized the young mathematician. For the first time it allowed us to see symmetries beyond the physical world around us. Autumn: Mapping the world of symmetry. Following Galois’s breakthrough, mathematicians embarked on an epic journey of discovery. Their aim was to produce a complete list of building blocks from which all symmetries could be constructed. In the same way that numbers are built by multiplying together primes, the symmetry seekers wanted a Periodic Table containing a list of all the different basic atomic symmetries.