Mathematics should be considered not just as a science, but very much as an art. I think that the reason that many of us do mathematics is not for utilitarian reasons but because of the beauty and aesthetics of the subject, and the satisfaction of the stories that we tell and the dramas that we produce within our field.
Professor Marcus du Sautoy
In their keynote addresses at ESOF 2012, Professors Enrico Giusti and Marcus du Sautoy considered the importance of, and the challenges involved in, popularising mathematics. Professor Giusti spoke of his work within the emerging field of mathematics museums, whilst Professor du Sautoy discussed ‘secret mathematicians’ from the fields of art, music, literature, choreography and architecture to demonstrate the all-pervasive nature of his subject.
Whilst the exhibits of science museums have always alluded to mathematical endeavour, the concept of museums dedicated solely to mathematical theories and applications is a fairly new one. Since retiring from academic life, Professor Giusti – who has lectured at the University of Florence, the Australian National University, Stanford University and the University of California, Berkely – has dedicated his efforts to the popularisation of mathematics. As founder and Director of the Giardino di Archimede – one of the first examples of a mathematical museum – Professor Giusti has been instrumental in bringing mathematics to the masses.
In his keynote address, ‘Touching the Abstract: Mathematics at the Museum’, Professor Giusti outlined the merits and difficulties involved in creating public monuments to mathematics. He began by describing a Lorenzian Waterwheel in order to illustrate the power of mathematics as a subject.
"Water flows into containers that hang at the edge of a rotating cycle, and slowly, it passes through holes in the bottom of these containers," he explained. "In the beginning, the movement is fairly regular and predictable, but soon – either because some visitor sneezes, or because the water-flow is not perfectly uniform, or because some butterfly flaps its wings in the Amazon jungle – the movement becomes essentially irregular. Even a powerful computer cannot predict its motion more than a few minutes in advance. Still, modern mathematics is able to treat this phenomenon. The waterwheel is a physical model of the power of mathematics and an example of its success."
It has, however, taken a long time to reach this juncture. As Professor Giusti explained, mathematics exhibits have not always been so inspirational.
"Science museums haven’t always had such spectacular maths sections," he continued. "In particular, one of the oldest ones had portraits of famous mathematicians of the past, displayed on its walls. Three-dimensional models in display cases showed the interests of 19th
Century mathematicians, and all around the room were written tens of thousands of decimals of pi. Rumour has it that the 23,743rd
was wrong, but this belongs to the past."
According to Professor Giusti, mathematics museums need to answer two fundamental questions: ‘Where is the mathematics?’ and ‘What can she answer?’ In order to reveal a living mathematics to their audiences, museums must include displays that show principles in action. In a presentation that spanned Pythagoras, Archimedes and the sewing machine, Professor Giusti outlined the difference between what he called ‘living’ and ‘dead’ mathematics.
Professor du Sautoy uses his new play, X&Y, to illustrate how maths and the arts can sometimes intertwine
"Abstract thinking and mathematics in particular, emerge from the physical reality of the object on show, not by experimenting on isolated phenomena – each of which speaks a different language – but by organising objects and principles along a meaningful path," he said. "In this way, I think that it is possible to involve the visitor in the world of mathematics creatively, thus making
mathematics instead of just evoking
"More than showing objects, one has to tell stories," he continued. "A good museum of mathematics is a place where good stories about mathematics are told. There aren’t recipes that can guarantee that the stories will be good, but there are some tricks that can help us to avoid serious mistakes."
Professor Giusti also emphasised the importance of intriguing one’s public. Without the attention of their audiences, mathematical museums will remain irrelevant to society as a whole.
"We must always remember that communication involves two
agents: the communicator and the listener," he reiterated. "Even if the latter is not always able to command or respond, they can express their dissent simply by interrupting communication. A visitor’s attention is not guaranteed; it must be earned every time. In order for this to happen, the level of communication cannot be too difficult or too easy. If it is too difficult, the visitor will leave – at least mentally – because they don’t understand. If it is too easy, the visitor will become bored and distracted.
"[A visitor’s] attention might be captured by showing them something that is not extraneous to their experience. This information can then be linked with a familiar situation or with new groups of acquired knowledge – even outside of the world of mathematics."
Whilst Professor Giusti spoke about dedicating museums to mathematical endeavour, Professor du Sautoy, Simonyi Professor for the Public Understanding of Science, Professor of Mathematics at the University of Oxford and President of the Mathematical Association, argued that we should be doing more to broaden the public conception of mathematics, and to instil its virtues within the minds of younger generations. Professor du Sautoy began his keynote address, ‘The Secret Mathematicians’, by bemoaning a decision that schoolchildren are often forced to make.
"When I was at school, I got asked to make this choice, and I think that this happens to many people," he said. "I had to choose between Rubens and relativity, Shakespeare and the second law of thermodynamics, Debussy and DNA; [I had to choose between] art and science. I found this very frustrating because when I was about 12 or 13, I suddenly started to fall in love with my subject of mathematics. I was very lucky to have a teacher at my comprehensive school in England who showed me what maths was really about.
"But it was at about that time that I started learning the trumpet, I played in orchestras, I was singing in choirs and my love of theatre started as well. I just found it deeply frustrating that I was pushed into two camps, and I had to make this decision. It turned out that I was better at maths than I was at playing my scales on the trumpet, so that’s the direction I followed. But all the way through my career, I have been interested in keeping a connection with the arts. As I’ve carried on in life, I realise actually that this is a really false dichotomy and that when you start to look at artists, they’re very often drawn to structures that are similar to those that I’m interested in as a mathematician."
In his presentation, Professor du Sautoy selected five secret mathematicians: the musician Olivier Messiaen, the architect Le Corbusier, the artist Salvador Dali, the author Jorge Luis Borges, and the choreographer Rudolph von Laban. As Professor du Sautoy explained, each of these and many of their contemporaries wove mathematics into the fabric of their artistic creations.
In conclusion, Professor du Sautoy called for a broader understanding of mathematics; a mathematics that could be seen as straddling many different scientific and
"Mathematics should be considered not just as a science, but very much as an art," he suggested. "I think that the reason that many of us do mathematics is not for utilitarian reasons but because of the beauty and aesthetics of the subject, and the satisfaction of the stories that we tell and the dramas that we produce within our field.
"For me, an exciting mathematics is one that has a sense of narrative – or maybe of surprise or development – a little bit like listening to a piece of music."
Later this year, the United States’ first mathematics museum will open its doors to the public. The Museum of Mathematics in New York, or MoMath as it will be called, aims to enhance public understanding and perception of mathematics, to stimulate enquiry and spark curiosity, and to allow a diverse audience to understand the creative, human and aesthetic nature of mathematics. A movement appears to be gathering pace. Modern mathematics is alive and well and it wants the public to recognise this fact. Perhaps it is time for this academic pursuit, which has often been taken for granted, to take centre stage.