Mathematics and Photography

This is a photograph of the ruins of the Arab Baths in Ronda, Spain. Mathematics and black and white photographs (at least the ones that appeal to me) share much in common: form, abstraction, beauty. To be successful they depend on a felicitous mixture of imagination and technique. In both one responds sometimes to the beauty of the detail and local texture and at other times to the overall sweep of form that comprises the canvas.

I like the Arab Baths because they are built of simple materials of completely natural origin which have been shaped by architects and craftsmen of long ago into something which is both a triumph of functionality and of aesthetic beauty. The star-shaped holes in the domed roof allow the outside light to filter through to form a lovely pattern of patches that remind me of the mathematics that I am studying - the mathematics that attempts to uncover some of the fascinating world that lies between total order and total disorder.

Photography for me always represents an emotional response to what I see, whether that be the natural world or the handiwork of some craftsmen or artists. It is easy to let the world grow stale in one's eyes. But in the framing of images and in the pleasurable task of bringing them into printable form, one is drawn to appreciate anew the intimacy of things: the materials of which they are composed, the detail and structure of their composition, and the momentary shared understanding between artist and viewer.

Mathematics also elicits emotional responses - I would not continue to spend so much time on it were it not so - but the underlying energy of my research is directed by the desire to follow, as far as I can, a path that leads from order to disorder. It is a path that like everything else in life is only evident after one has walked it, and will miraculously be seen to have formed its own order. Likewise the photographs here, after the fact, show the way that I have travelled and those of parts of the scenery that have caught my imagination.

Wayfarer, the only way
is your footsteps, there is no other.
Wayfarer, there is no way
you make the way as you go.
As you go, you make the way and stopping to look behind,
you see the path that your feet
will travel again.
Wayfarer, there is no way -
only foam trails in the sea.

Antonio Machado