| ||Special Issue - March 2004|
| The beauty of maths
'Many mathematicians see their discipline as an art. They work according to their specific methods, but also using aesthetic theories that can be applied to artistic creation. Conversely, some artists are attracted and/or stimulated by mathematics and use ideas developed by scientists.' That is the opinion of Michele Emmer, a mathematician and film-maker in whose company – among others – we take a look at the relationship between art and maths, images and visualisation, and aesthetics and education.
Whether it is considered as art or not, mathematics plunges us into a world of balance and harmony – its links with music have long been the subject of study for example - and also of form (don’t understand this sentence). Do we not speak of mathematical objects – and of ‘objets d'art’?
When rendered visible or palpable, equations become less obscure. Felix Klein (German mathematician, 1849-1925) was one of the first to understand this and, back in the 19th century, produced a collection of plaster models of complex functions that form the collection of the University of Göttingen (SE). The campus of Bangor University (UK) is also the site of James Robinson's Symbolic Sculptures, inspired in particular by the famous Borromean Rings – an idea that came from the mathematician Ronnie Brown, founder of the university's Centre for the Popularisation of Mathematics. For Professor Brown 'the major problem of teaching is converting mathematical reality into mathematical objects'. His exhibition on knot theory, based on an exhaustive and fascinating presentation of knots, also proved a resounding success.
But sometimes the initiative comes from artists rather than mathematicians. Max Bill, an artist who worked with plastics and member of the Bauhaus school, spent many years investigating these abstractions – and sculpting, in his way, another life (see Emmer's lens). ‘Is it necessary to say that a mathematical approach to art has nothing to do with any ingenious system of calculation based on ready-made formulas?' he wrote in 1949. 'As regards composition, however, we can affirm that all schools of art have had, more or less, mathematical foundations.'
In Germany, Konrad Polthier, of Berlin's Technische Universität, is an enthusiast of mathematical visualisation. He quickly realised that his research on shapes and surfaces, in three or more dimensions, were too complex to be represented using 'ordinary' tools. That is why he created his own software. Known as Java View, it can run on any PC with an Internet browser – and no copyright is charged for non-commercial use. Java permits on-screen visualisation of the widest range of calculations. A simple ‘mouse click’ is all it takes to 'manipulate' the virtual object – twisting or stretching it, flipping it over to show other surfaces, etc. 'This software is designed to enrich scientific publications through visualisation. I would be happy to see many researchers use it,' comments its creator. We know that multimedia technologies are set to become increasingly important in the world of publishing. In some cases, it may seem like a gadget but, when discussing multidimensional mathematical problems or describing complex processes in science and technology, visualisation will become an essential tool.'
These new shapes are sometimes very surprising and the images fascinating. 'Some of these structures are so harmonious that it is almost impossible not to view them as works of art,' adds Konrad Polthier – who, by the way, denies any pretentions to being a creative artist himself. He sees the beauty of these forms as absolute, comparable to the natural beauty of plants and minerals, rather than a subjective expression or message.
Manuel Arala Chaves has initiated a number of exhibitions, in particular Matematica Viva, in Lisbon in 2000. 'An important point is the target public. This exhibition was aimed at everybody and succeeded in its goals. Schools and individual visitors visited who wanted to investigate their discoveries further.' The modules were designed so that they could be appreciated and understood at various levels, depending on the interests and mathematical background of the individual.
'When I was young I often visited the Deutsches Museum in Germany and the Palais de la Découverte in Paris. They made a big impression on me, but I always felt that they did not pay enough attention to mathematics and that this oversight was not due to the specific nature of mathematics as such,' he explains.
Fun and games
Manuel Arala Chaves also worked on and adapted the exhibition Symmetry and the play of mirrors, designed by the team from Milan University's Department of Mathematics, for exhibition in Portugal. The same team has since launched the particularly original Matemilano exhibition, which investigates four principal themes (topology, massimi e minimi, vision and symmetry) with reference to the city itself. Architecture, sculpture and painting serve as a gateway to geometry, perspective, knot theory, etc. The Roman mosaics, Renaissance painting, the layout of the city, the Gothic rose windows of the Duomo… all the periods in the city's history play a part. 'In these exhibitions we gave a lot of space to images and we are firmly convinced that this beauty plays an important role in communicating mathematics, especially to young people and people of different cultural origin,' believes Maria Dedo, one of the key players in this initiative. In addition to beauty, the exhibition also incorporates the notion of play in connection with mathematics. With its problems and its enigmas, maths can take us on some exciting new journeys. All it takes – as Matemilano shows – is some paper, a length of cord or a few matches to have some fun and games with maths.