If you were creating an Identikit theatre guru, he might be a little bit like Simon McBurney. He’d probably wear a tatty old T-shirt with more holes than cloth. His hair would be everywhere. He would be rearranging croissant crumbs into very precise, neat lines on the café table. And his conversation would be just this scattily brilliant, ranging improbably across cosmology, “the functional equation of the Riemann zeta function” (nope, I don’t know either), and our inextinguishable need for theatre, for “live experiences that tell us about our place in the world”.

If anyone’s earned the right to play the boho genius, it’s McBurney. His company Complicite are Britain’s pre-eminent stage artists of the past two decades, with a prize-winning comedy pedigree and a string of life-affirming total-theatre classics (The Street of Crocodiles, The Three Lives of Lucie Cabrol, Mnemonic) to their name.

The part-time actor is now a globetrotting auteur, meeting me in Vienna the morning after opening A Disappearing Number, his new play about Ramanujan, the Indian mathematician, soon to come to the Barbican in London.

Other forthcoming engagements include working with Charlie (Being John Malkovich) Kaufman on a movie and directing a Broadway revival of All My Sons with James Gandolfini – which could be explosive: The Wall Street Journal called for his deportation the last time he worked in New York, when his Brecht revival, The Resistible Rise of Arturo Ui (starring Al Pacino) compared George Bush to Hitler.

It might not have helped that McBurney calls Complicite “a terrorist organisation”. But, in person, there’s nothing insurrectionist about the director, who would rather talk cosmic philosophy than politics. McBurney’s father was an archaeologist and, growing up in 1960s Cambridge, the boy Simon inherited a deep curiosity about where we come from and who we really are. He launched Complicite after studying under Jacques Lecoq, the legendary physical theatre sage, in Paris, where he met his co-founders Marcello Magni and Annabel Arden. Within two years of the company’s inception, they won the prestigious Perrier prize for comedy at the Edinburgh Festival, in 1985. Now he runs the company himself.

I saw the Ramanujan show the previous evening; it’s a rich disquisition on maths and identity, on love and loss. The show begins with a comically complicated maths lecture on an upstage blackboard, and is soon spinning infinite sequences of numbers into resonant metaphors for the journey of life.

Did you know that 1 + 2 + 3 to infinity equals minus / ther – but that’s the kind of mind-bending mathematical nugget to emerge from Ramanujan’s correspondence with the Cambridge don G. H. Hardy.

The relationship between the two, which culminated in Ramanujan transgressing his religious rules to travel to England in 1913, forms the basis of this dreamlike play. The show interweaves the story of Ramanujan and Hardy with the present-day story of a man (McBurney) and his maths lecturer partner.

She travels to India in Ramanujan’s footsteps and eventually dies. He follows, to get closer to her ghost. Meanwhile, 100 years previously, Ramanujan is travelling in the opposite direction, making the trip to England that eventually kills him. Partition (as a maths concept) is paralelled appositely with the partition of India and Pakistan, and diverging and converging series in mathematics become a metaphor for the Indian diaspora.

McBurney is wrapped up in the new show’s strengths and failures, devising improvements (between Vienna and London he has dropped out of the cast) and chewing over the mathematical conundrums at its heart. He flatly denies that maths is a tricky subject for theatre; that it’s hard to make formulae and algorithms seem intelligible.

“I always felt maths was incredibly logical and certain, and I had a real problem with it at school,” he says. “Then suddenly I discovered that, at its sharp end, everything is uncertain and people are guessing all the time.” McBurney’s current obsession is with “the imaginary number”, a conceptual leap of faith within mathematics that enabled (among other things) the discovery of electromagnetic waves, says McBurney – and therefore computers and mobile phones. A Disappearing Number posits maths as a creative act like poetry or painting, whose practitioners map the infinite aspects of our universe.

What maths isn’t, says McBurney, is dry or abstract; it’s in the warp and weft of Indian culture. “It’s written into the Vedas, it’s in the music. In India, mathematics feels much more part of life.” But, wherever mathematicians practise, says McBurney, “if they dig ever deeper into mathematical reality, there will be something in there that brings them suddenly back to earth”.

Ramanujan was a poor, untutored Brahmin whose work on number theory caught the attention of Hardy at the turn of the 20th century. “He had no idea,” says McBurney, “that his work would eventually be instrumental in devising a set of physical laws to define everything.” That’s string theory, the holy grail of maths.

This is very much Complicite territory: echoes through time, connections across worlds. In McBurney’s hands, mathematical sequences become journeys through life, and numerology a means of giving substance to the unknowable. “Everybody lives with an idea of infinity and with the notion of death. These two things dance around each other.”

He adds that the show partly confronts his sense of loss after the death in 2002 of the actress Katrin Cartlidge, star of Mnemonic and McBurney’s close friend. “Sometimes I see her so clearly, and feel her so clearly. I’m constantly asking myself: Where is she? How can someone simply not be there? My work is about the wonder of those mysteries, from falling in love with somebody to the void you feel when someone dies.”

Curiosity is the hallmark of great artists and McBurney has it in spades, yet running Complicite, he says, “feels like a struggle”. Shows on this scale cost too much money (“I long to make a show with just five chairs again”). The pressure to live up to the company’s reputation is intense. He hates to feel chained to the wheel of international theatre-making. “Somebody rang me and asked, would I do an opera in the spring of 2012?” he grimaces. “I’m not sure I’ll even be alive then.”

He also dreads criticism, especially of his vanity for appearing in his own shows. “You do have to have a belief, akin to arrogance, in order to do this,” he concedes. The safeguard against an overwhelming ego is that “I have an in-built sense of doubt about what I’m doing. My confidence goes easily. It’s a battle.”

The chat in theatre circles in recent years is that McBurney, like Peter Brook, his fellow auteur, before him, is a frustrated filmmaker. He doesn’t deny it: “I am drifting in that direction. I love acting in movies. It’s like a kind of holiday. I’m not responsible for anything except what I do on screen.”

He recently starred as a weaselly Foreign Office functionary in Kevin Macdonald’s The Last King of Scotland. He was script doctor, improbably enough, on the recent Mr Bean movie. And now, he says, “if somebody tomorrow said, ‘You’ve got five years of film work’, I’d go and do it, just like that.” I don’t believe him: he’s a theatre man through and through, as he himself presently admits. “Theatre is my family,” he says. “In my work, I feel constantly that I’m looking for my home. But in fact, being with all of the people who work with Complicite, that’s my home.”

There is a spiritual hankering to McBurney’s conversation and to his work. He was never a sucker for conventional religion: “I remember as a child trying to pray and wondering, ‘Why isn’t anything happening?’ I thought something should happen. But I was once a bell-boy, carrying the incense. For me it felt like going onstage.” That confusion – between the realm of the spirit and of the stage – has never left him.

McBurney is fascinated by Ramanujan because his notes may lead to a theory “that binds the very small and the very large together”. You could say he aims to achieve the same in his work at Complicite.

A Disappearing Number will be at the Barbican from September 5 (020-7638 8891; www.barbican.org.uk)

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