Benedict Cumberbatch on The Imitation Game

Actor Benedict Cumberbatch discusses his latest role of playing Alan Turing in The Imitation Game.

Keira Knightley, left and Benedict Cumberbatch in a scene from The Imitation Game. AP

Benedict Cumberbatch has accumulated a filmography littered with high IQs, portraying characters such as Sherlock Holmes, Julian Assange, Stephen Hawking and, most recently, Alan Turing in The Imitation Game, which is screening at the Dubai International Film Festival on December 16 and 17.

Such characters of analytical prowess and fast-deducting intellect have made Cumberbatch something like the ultimate quicksilver mind of the digital age. No actor has made computation sexier.

Cumberbatch, relaxing in a Toronto hotel room, quickly points out that he has – like his spineless plantation owner of 12 Years a Slave or his painfully shy son in August: Osage County – played some "pretty dull, ordinary" people: "Let's say us. I've done us, versions of me and you," he says.

And yet, Cumberbatch is clearly drawn to highly complex, ­real-life characters under extraordinary circumstances – roles that demand technical preparation (an accent, a stammer), considerable biographical research and a precision of approach. Puzzles to be solved.

“Maybe that’s a fair one,” he says, turning over the idea. “Maybe I do. I think for the reasons people are attracted to those characters, as well. You can never fully understand them. There’s always a certain amount of enigma or mystery to them.”

Cumberbatch's latest riddle is Alan Turing, a hugely important figure to Second World War codebreaking and a computer science pioneer. The Imitation Game is about how Turing and others at Britain's Bletchley Park solved the seemingly unbreakable Enigma code used by the Germans throughout the war. Winston Churchill said Turing made the single greatest contribution to the war, but his achievement wasn't widely recognised until recently, when the codebreaker's work was ­declassified.

“Considering all of that, why isn’t he on the front cover of every school history textbook?” says Cumberbatch. “He’s a properly important figure in our ­culture.”

The Imitation Game, directed by the Norwegian filmmaker Morten Tyldum and written by Graham Moore, is a kind of ode to outsiders. Cumberbatch's Turing isn't just different because of his sexuality, he's utterly ­antisocial. Rarely making eye contact, the single-minded Turing was disinterested in etiquette. "I don't care what's normal," he says in the movie.

His Bletchley collaborators also included Joan Clarke (Keira Knightley), a rare female in that world. Knightley says the film “is about trying to celebrate differences because of the tragedies that can occur when you destroy the people who aren’t like you”.

The film’s mix of historical drama with contemporary resonance has won it acclaim on the festival circuit and positioned it as an Oscar contender. Especially lauded has been Cumberbatch’s depiction of a mathematical mind wracked by repression. “He can play so many emotions at the same time. There’s strength and vulnerability. There’s arrogance and there’s this lonely boy,” says Tyldum. “It’s not every actor who can play a genius.”

Knightley, a friend of Cumberbatch's since the two worked together on Atonement, calls him "the sort of actor who never tries to simplify anything". "If it's a complex person, he wants to dive into all the complexities and try to get all the nuances out," Knightley says. "You completely believe him in any of these roles, whether it's Assange, Stephen Hawking; whoever. He's very intelligent, but he's got a curiosity you can see and it sort of burns through his ­performances."

Cumberbatch, however, makes no claim to cleverness. Of Sherlock, he credits its writer: "Steven Moffat is the brain. I just say it fast."

With no footage to draw from for Turing’s manner and speech, Cumberbatch met his relatives. The actor also began many of his days jogging. (Turing was an elite runner.) And he worked at crafting a plausible stutter for the famously awkward mathematician. Still, playing a man of such brainpower was ­challenging.

“I’m not stupid but I’m not that smart. So I can at least lend something of that within the performance, like maybe the alacrity of thought, making fast connections,” says Cumberbatch. “But when you actually start talking about the language he used to get to those stunning conclusions, you might as well ask me to write my name in Mandarin.”

After The Imitation Game, the 38-year-old Briton, who recently announced his engagement to Sophie Hunter, is ready for a simpler equation.

“I’ve done evil. I’ve done good. I’ve done smart,” says Cumberbatch. “I haven’t done much sexy, sexy, really. I know Sherlock’s some people’s cup of tea. I’d like to do a romantic comedy. I really would.”

• The Imitation Game is on Tuesday, December 16, at 6pm at Madinat Arena and on Wednesday, December 17, at 6.15pm at Mall of the Emirates Cinema 11.