Simon McBurney: Ground-breaking theatre director, Hollywood actor and screenwriter

I am in a hotel lobby in Amsterdam, looking at my watch and wondering if I have miscalculated the time when I am meant to meet Simon McBurney, the globe-trotting actor-director who turns 50 this year. It turns out the interview has slipped his mind – which is amusing given that his award-winning show Mnemonic kicked-off with a lecture on the nature of memory. When I finally ring his room, he sounds startled then contrite, like a small-voiced schoolboy with the trace of a stutter.

Three-quarters of an hour later, we are sitting outside a canal-side café. It is 24 years since McBurney graduated from the inspirational Paris mime school of Jacques Lecoq and formed his influential and fabulously inventive theatre company, Complicite. He has since played a key part in bringing expressionistic physical theatre into the British mainstream. Today, though, he is looking fantastically scatty, with his hair sticking up like Ken Dodd's. Sideways on, he has a surprisingly bulbous nose. His striped shirt has odd checked patches and his shoelaces are untied. Is this a dramatic affectation? Possibly, but he certainly isn't playing the fool. His conversation is nervously hesitant yet highbrow and he has beady eyes like a vivacious vole. The effect is curiously charming. Indeed, the actress Kathryn Hunter – an early Complicite star – has remarked that when she first met him he struck her as incredibly ugly, but when she got to know him he became extraordinarily beautiful.

He is talking, right now, about the beauty of mathematics and music which are interconnected in Complicite's new show, A Disappearing Number, which has a specially commissioned score by the British-Asian composer Nitin Sawhney. The show is a high-powered species of biodrama about mathematics and mortality, cut-off points and continuums, cultural divides and the historic friendship between the Cambridge don, GH Hardy, and Srinivasa Ramanujan (1887-1920), the Indian Brahmin and genius who died young but whose work has since fed into string theory. The night before we were due to meet I saw McBurney on-stage in this piece, amidst algebraic equations and spinning projection screens. At that time the work was, characteristically, still in development, but this month it has its London opening at the Barbican, accompanied by a season of films by and about Complicite.

As research for the show, Complicite has been conferring with the media don Professor Marcus du Sautoy. "One of the most beautiful ideas that Marcus exposed us to and which," McBurney underlines, "is very important to Ramanujan's work, is the mathematical concept of infinity, and that is very often expressed as infinite series." He adds that he finds these more and more beautiful because he is interested in music: some infinite series, called harmonic series, correspond directly with instrumental harmonics. (His brother is the musicologist Gerard McBurney).

If you are already suffering an attack of maths anxiety, you may be relieved to know that, in the show itself, Saskia Reeves plays a 21st-century university lecturer whose incomprehensible formulae – demonstrating infinite series – become an entertaining running joke. Yet McBurney is also trying to embrace mathematical ideas in artistic forms. Hardy and Ramanujan's meetings and partings are like a series of cultural convergences and divergences, and their ideas and experiences are echoed, generations on, in the love affair between McBurney's character and Reeves (who, like Ramanujan, is tragically cut off in her prime).

McBurney further explains – pay attention now – that when Ramanujan is formulating his equations, the accompanying tabla music actually corresponds to the numerical patterns in his mind. "Any Indian in the audience would immediately recognize that the mathematics is being transposed into tihis," he says – tihis being overlapping beat cycles that build up intricate interlocking patterns.

Does A Disappearing Number additionally reflect McBurney's own life? It feels as if it does, especially regarding his on-stage persona's acute pain at lost love and bereavement. "I have lost a lot of people in my life," he says, after a long pause. "My friend Katrin Cartlidge [the actor] died in 2002, the same year as my mother. When someone close to you dies there is this gap, nothing tangible, but this huge hole which you feel intensely... And so you look for ways of describing these difficult experiences on stage, whether it's dying or getting older or not having children." (There is a harrowing miscarriage in A Disappearing Number.)

A long time ago, in McBurney's final year as an English undergraduate at Cambridge, the death of his father and his break-up with his then girlfriend, Emma Thompson, propelled him to Paris and Lecoq where he co-founded Complicite. Now, it appears his recent relationship with the Australian actress Jacqueline McKenzie has ended too. "I find it difficult to talk about... I would be very happy to be in a long-term relationship and to have children, but various things have conspired to..." he tails off. He is, palpably, aware of life's clock ticking and a sense of impermanence.

McBurney is fascinated by the strata of time, as was his father – an eccentric, American-born, Cambridge University archaeologist who used to take the family on digs in Iceland. The Complicite show Mnemonic was a chamber piece which overlayed the present and past, a mesmerising contemporary story of lost love and the discovery of a neolithic man deep-frozen in Alpine ice (Mnemonic can be seen in the Barbican cinema season, the original staging having been filmed in 2000, co-starring Katrin Cartlidge and McBurney himself).

Another multilayered production was Complicite's 2003 show An Elephant Vanishes, based on Haruki Murakami's short stories about urban alienation. That project, a collaboration with Japanese actors, was so hair-raising in its creative chaos that McBurney felt his mind "had gone into meltdown". Yet what he forged in the end was dreamlike and electrifying – including a joyride fantastically evoked with projections, a blur of city lights and TV monitors ricocheting in and out like screeching cars.

In fact, artistically speaking, he has done a vanishing act by the time I am writing this article. He is no longer appearing in A Disappearing Number. He has subtracted himself, reworking the creative equation. Maybe theatre fans should further worry that he'll leave them for the film industry or opera. He is currently in talks with the ENO and Simon Rattle. He is working on a film version of his recent Measure for Measure and collaborating on a new screenplay with Jonathan Safran Foer, author of Everything is Illuminated. "I really think my life is moving towards cinema a lot more," he says, and he has been acting in an increasing number of big-screen movies, commenting: "It's fascinating and like a holiday for me... not being responsible for the whole thing!"

In the remake of The Manchurian Candidate, he played the mad scientist, Dr Atticus Noyle. Last year, he was outstanding as Frances McDormand's fastidiously gentle husband in Friends with Money, and as the weasly British diplomat in The Last King of Scotland. Next he is Fra Pavel, alongside Nicole Kidman, in the forthcoming Philip Pullman adaptation, The Golden Compass. He also wrote the storyline for Rowan Atkinson's most recent film, Mr Bean's Holiday, making a connection back to his youth as a comedian in the Cambridge Footlights and at London's Comedy Store.

McBurney's Complicite productions, inevitably, cannot be an infinite series of works. Nonetheless, it's not over yet. He is planning another Japanese collaboration, and his love of theatre is deep-rooted. It goes back to his childhood and to his mother, a thwarted actress who once trained with a doyen of the Comédie Française. "We grew up without a television," McBurney recalls. "But she adored the theatre and used to write little plays for us. We'd make all the props and costumes. As a result," he concludes with a smile, "I can't remember a single year of my life when I haven't made a piece of theatre."

'A Disappearing Number': Barbican Theatre, London EC2 (0845 120 7550), now previewing, 11 September to 6 October