Suppose a young man approaches you in an empty café and asks you to tell him everything you know about numbers in ten minutes. Maybe you’re a mathematician. Maybe you’re an armchair math aficionado with an enthusiastic layperson’s knowledge of the field. Maybe you stopped taking math classes as soon as you could. But this mysterious fellow doesn’t ask you how you know about numbers. He asks you what you know. And no matter who you are, you’re going to have a lot to say. Panic takes over. You have to buy some time, organize your thoughts. You take a swig of your mocha. And then?
This month’s topic was that shadowy gentleman, coming up to all thirty of us in our offices or at our desks or in our dreams, tapping our shoulders, clearing his throat impatiently, demanding to know everything but only giving us ten pages to tell all. “Kingdom of Number,” read the prompt, drawn from a poem by master W.H. Auden. While I enjoy the prompts with deeper grounding (like the passage from Eugene O’Neill’s Long Day’s Journey Into Night in November 2010), “Kingdom of Number” went even deeper than I’d imagined.
Before we were told the prompt, we were treated to three talks at the MSRI by stars in the field of Number Theory: Harvard Professor Barry Mazur, whose many eponymous discoveries include the Mazur Manifold and the Mazur Swindle, Professor Alice Silverberg of UC Irvine, formerly a consultant for the (much-lamented, sadly-concluded) Rob Morrow vehicle Numb3rs, and Professor Manjul Bhargava, one of the youngest-ever mathematicians to be granted tenure and a full professorship at Princeton.
Needless to say, the presentations were stimulating. Professor Mazur spoke to us about the “transcendental truth” of mathematics, about eerie numbers and their biographies. Professor Silverberg led us through the world of Primality. Finally, Professor Bhargava introduced us to Pingala’s Numbers, a mathematical series discovered by a Sanskrit poet in 500 B.C., and then re-named the Fibonacci Sequence some 2000 years later. Of course the sequence itself had existed long before either discovery of it, Professor Bhargava explained, and it is, quite literally, at the heart of everything.
So, in this swirl of information, of inspiration, where to begin? I can only speak for myself. My mind is inclined towards the darker, bleaker side of things (dusty, empty coffee houses, strange men with strange questions, and so on), so I started with G.H. Hardy. On page 14 of The Mathematician’s Apology (1940), a text referenced by Professor Silverberg in her talk, Hardy writes:
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
This is a gorgeous passage, to be sure, but is there not something a bit sinister about it, too? After all, how many political movements of the past century have destroyed people or places using aesthetic justifications? What happens when we value the “harmonious way” above all else – but choose to define “harmonious way” exclusively in our own terms? Hardy was against using mathematics in service of weaponry and violence, Professor Silverberg told us, but I wonder if Hardy realized how oddly similar his rhetoric was to that of some of the less-well-intentioned figures alive in the 1940s.
And so my conversation with the stranger began. He gave me a nod, listened for a few seconds, and then evaporated. The prompt had done its job. Now I had to write a play.
Photo appears courtesy of the LSE Library on Flickr.