I told him. ‘Paris,’ he echoed. ‘Why, we love Paris!’
France’s capital has something of a one-sided reputation as the consummate city of artists. We know it as the city of Manet, of Rodin, of Berlioz; as the city of street singers and can-can dancers; as the city of Victor Hugo and of young Hemingway in A Moveable Feast: scribbling in a café corner, turning coffee and rum and the strictures of Gertrude Stein into stories. But Paris is also the city of mathematicians.
Its researchers, a thousand strong, make the Fondation Sciences Mathématiques de Paris (FSMP) the largest group of mathematicians in the world. About one hundred of the city’s streets, squares and boulevards are named after their predecessors. In the twentieth arrondissement, for example, one can walk the length of rue Evariste Galois, named after a nineteenth-century algebraist felled at the age of twenty by a dueller’s bullet. On the opposite side of the Seine, in the fourteenth arrondissement, lies rue Sophie Germain whose namesake introduced important ideas in the fields of prime numbers, acoustics and elasticity before her death in 1831. According to her biographer Louis Bucciarelli, ‘She did not wish to meet others in the streets or houses of the day, but in the purer realm of ideas outside time, where person was indistinguishable from mind and distinctions depended only on qualities of intellect.’ A few minutes’ walk away is Fermat’s little road. There are also streets called Euler, and Leibniz, and Newton.
Among the letters waiting for me on my return to my adopted home was one from the city’s Fondation Cartier. A museum for contemporary art, it had sent me a preview invitation to its upcoming exhibition ‘Mathematics: A Beautiful Elsewhere’: the first in Europe to showcase the work of major living mathematicians in collaboration with world-class artists. The timing seemed doubly auspicious: October 2011 happened to be the two-hundredth anniversary of Galois’s birth.
The museum stands in the fourteenth arrondissement at the lower end of one of the long boulevards that diagram the city. It is an ostentatiously modern building, all shiny glass and geometric steel, bright and spacious, an example of ‘dematerialised’ architecture. Reflected in the glass, scraggly trees denuded of their summer foliage appeared twice. I looked up at the symmetrical branches as I passed and entered.
Mathematics and contemporary art may seem to make an odd pair. Many people think of mathematics as something akin to pure logic, cold reckoning, soulless computation. But as the mathematician and educator Paul Lockhart has put it, ‘There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.’ The chilly analogies win out, Lockhart argues, because mathematics is misrepresented in our schools, with curricula that often favour dry, technical and repetitive tasks over any emphasis on the ‘private, personal experience of being a struggling artist.’
It was the mathematicians’ artistic impulse, and inner struggle, that the exhibition’s organisers intended both to communicate and celebrate. A white interior, zero-shaped, was the work of the American filmmaker David Lynch. Walls usually reserved for frames and canvases lent their space to equations, light effects and number displays. I walked through the rooms, now bare and silent, now colourful and stimulating, stopping here and there to take a closer look. I watched the other guests stand back and point and converse in low voices. Before a bright collage of sunrays and leopard spots, waves and peacock tails, and the underlying equations for each, fingers swayed and eyes widened. Another hall arrested visitors’ feet around a lean aluminium sculpture, its curves reaching toward infinity.
But, for me, the highlight of the exhibition took place in a darkened room downstairs. Here the visitors melted into twilight, rendered homogeneous in the darkness, sitting or standing in silence, all eyes, observing a large screen where a film shot in black and white was playing. A youngish face, screen big, was talking about his life as a mathematician. I pressed my back against the far wall and listened as he spoke of ‘fat triangles’ and ‘lazy gases’. Three or four minutes old, the film suddenly altered: the face gave way to another, wearing glasses. Four minutes after this, the face changed again: this time, a woman’s began to speak about chance. In total, the film lasted thirty-two minutes – eight faces long. The men and women featured came from a wide range of mathematical sub-disciplines – number theory, algebraic geometry, topology, probability – and spoke either in French, or English, or Russian (with subtitles), but their passion and wonder linked each personal testimony into a fascinating and involving whole.
Two of the testimonies, in particular, stood out. They reminded me of my conversations with the mathematicians in Mexico, and with those in other lands, and the feelings of kinship and excitement that these exchanges incited within me. During his four minutes, Alain Connes, a professor at the Institut des Hautes Études Scientifiques, described reality as being far more ‘subtle’ than materialism would suggest. To understand our world we require analogy – the quintessentially human ability to make connections (‘reflections’ he called them, or ‘correspondences’) between disparate things. The mathematician takes ideas that are valid in one area and ‘transplants’ them into another hoping that they will take, and not be rejected by the recipient domain. The creator of ‘noncommutative geometry’, Connes himself has applied geometrical ideas to quantum mechanics. Metaphors, he argued, are the essence of mathematical thought.
Sir Michael Atiyah, a former director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, used his four minutes to speak about mathematical ideas ‘like visions, pictures before the eyes.’ As if painting a picture or dreaming up a scene in a novel, the mathematician creates and explores these visions using intuition and imagination. Atiyah’s voice, soft and earnest, made attentive listeners of everyone in the room. Not a single cough or whisper intervened. Truth, he continued, is a goal of mathematics, though it can only ever be grasped partially, whereas beauty is immediate and personal and certain. ‘Beauty puts us on the right path.’
The faces, old and young, smooth and hairy, square and oval, each had their say. Gradually, the room began to empty. Its intimate ambience slowly dissolved. I followed the last group of visitors up the stairs and out the building and not a word was exchanged. The night absorbed us.
I walked for a while, beside the river, with the night in my hair and in my pockets and on my clothes. The night, I know, is tender to the imagination; at this hour, throughout the city, artists sharpen pencils and dip brushes and tune guitars. Others, with their theorems and equations, revel just as much in the world’s possibilities.
The world needs artists. Into words and pictures, notes and numbers, each transforms their portion of the night. A mathematician at his bureau glimpses something hitherto invisible. He is about to turn darkness into light.
Thinking in Numbers: How Maths Illuminates Our Lives Page 22
