Thinking in Numbers: How Maths Illuminates Our Lives (29 page)

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.