My two great passions in life are mathematics and theatre. (And the Arsenal football club, but I regard that as a combination of the two.) In the past I used to think that I did one to escape from the other. When my maths was going badly I would dream of running away and joining a travelling theatre company. Many’s the time I downloaded the application form for Le Coq theatre school in Paris only to realise my French was probably not up to it. And when the irrational world of human interaction got me down I’d withdraw into the safety of the mathematical world where, once you’d proved a theorem, it wouldn’t suddenly turn on you and contradict itself.

But I’ve come to the realisation that the two sides of my character have more in common than I was originally aware of. The reason I love theatre is that it is a place of the imagination, it is space where you can play games – where a piece of bamboo can become a door, a boat, or just a piece of bamboo. The mathematical world is also one of the imagination where things can transform and morph to become something new. The best mathematics is where you set up simple rules, yet the result is a structure of fascinating and surprising complexity. You seem to get more out than you put in.

The best theatre exercises work in a similar way. You set up simple rules of interaction, which, when you let the actors loose, create surprising scenarios. One of my favourites requires each actor in a large group to choose two other actors. When the exercise starts, the original actor has to try to position himself to make an equilateral triangle with his chosen two actors. Of course it’s likely that your chosen two actors have themselves chosen another pair of actors. So every time you attempt to make your triangle equal probably disrupts another triangle. The dynamic of the group is fascinating to watch. Often it appears to reach a stable equilibrium only for one actor to move slightly to correct their triangle, setting off a total descent into wild movement. It is a beautiful example of the mathematics of chaos theory at work. And it also creates an exciting piece of visual theatre.

My revelation about the connections between my two passions was sparked by the theatre company Complicite, whose recent award-winning show A Disappearing Number interwove the worlds of maths and theatre on the same stage. Complicite invited me to come in during very early development of their piece to help them with their maths. The play explores the fascinating collaboration between Cambridge mathematician GH Hardy and the Indian genius Srinivasa Ramanujan. But rather than being a play about two eccentric and extraordinary characters who happened to be mathematicians, the company was keen to embed the mathematics they created at the heart of the play. As the play opens in the middle of a maths lecture about the analytic continuation of the Riemann zeta function, you can feel the audience’s sense of unease when, after five minutes of maths, they begin to worry if that’s all there is. But the play’s success lies in the way mathematics bubbles seductively below the structure of the whole performance.

My job during the early stage of development was to explain something of the mathematics that Hardy and Ramanujan created. One of the mathematical topics that they worked on together was the theory of partitions. If I take four stones how many different ways are there to arrange them into piles? I can have one pile with four stones. Or I can have four piles with one stone. But in between there are other possibilities. 3+1. 2+2. 1+1+2. In total there are five different ways to partition four stones. But how many ways are there to partition five, six, or 100 stones? Hardy and Ramanujan wanted to find a formula that would calculate the number of partitions however many stones there are.

Turn the stones into actors and suddenly you’ve got theatre. Each partition tells a story:

1+1+1+1: the isolation of four actors on their own.

1+3: the exclusion of one from the group.

2+2: allegiances and conflict.

Set the actors off trying to realise the different partitions in a theatrical tableau and you see them attempting to work out a pattern to find them all. This pattern-searching is what mathematics is all about and what Hardy and Ramanujan successfully uncovered.

The more we played with the mathematics, the more we found the theatre a wonderful space to explore the abstract mathematical ideas of infinity, pattern, convergence and divergence. So much so, in fact, that I’ve embarked on a new project that explores the four-dimensional shape of the universe through a piece of theatre inspired by the Borges short story The Library of Babel. It might even give me the chance to strut the boards and finally realise my dream of running away with a travelling theatre troupe – while still keeping up with my mathematics.

Marcus du Sautoy is a professor of mathematics and the Simonyi Professor for the Public Understanding of Science at the University of Oxford. He is author of The Number Mysteries