Benedict Cumberbatch is cornering the market on playing exceptionally brilliant problem solvers, first on television with his dazzling portrayal of a modern Sherlock Holmes and now on the big screen in a superb performance as Alan Turing, who cracked the German Enigma code and helped win World War II.

Engrossing, nicely textured and sadly tragic, The Imitation Game is overly reluctant to dive into the nitty gritty of how the man who’s often called the father of artificial intelligence accomplished what he did, while the matter of his eventual arrest for homosexuality provides a potent and topical framing device. After significant festival exposure, The Weinstein Co. has several angles it can play to build this prestige production into a considerable commercial success.

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Young screenwriter Graham Moore has cogently streamlined and simplified the story of a man who was recognized very early in life as a rare prodigy and whose rudeness and insulting manner is so condescendingly superior that it plays as amusing; “That’s actually not an entirely terrible idea” is his notion of the highest praise. An eccentric in a country famous for them, Turing (like Holmes) sees things that others do not, which in wartime is a talent to be prized, even if tolerating the genius on a day-to-day basis is something his colleagues can scarcely endure.

With the blitz battering London and the Nazis taking control of Europe, the British government engages six math and chess whizzes to try to crack the Germans’ code — perceived as unbreakable — by which the enemy’s naval forces receive new instructions on a daily basis. As analyzed by the experts, Enigma has 159 million million million possible configurations, meaning it would take decades to decipher it by conventional methods.

Overseen by old-school Commander Denniston (a very good Charles Dance) and led by two-time chess champion Hugh Alexander (a smooth Matthew Goode), the group is hardly welcoming to Turing, who lets the others know in no uncertain terms that he considers them so useless that he’d be better off working on his own. In one fine scene, after an exasperated Denniston fires Turing, the latter trumps him by writing to Winston Churchill directly to win support and further financing.

Although the film is filled with scenes of these bright young men putting their noses to the grindstone in Hut 8 at Bletchley Park (the top secret facility bearing the public name of Bletchley Radio Manufacturing), it’s never made clear how they’re planning to crack the code and what they’re concretely doing to achieve it. No doubt all the arcane details would sail right over the heads of nearly all of us, but some shop talk would have been welcome, as well as some clarification of what disagreements are putting the eggheads at loggerheads.

For his part, Turing puts together a large device with dozens of moving discs and nobs, something that’s easily recognizable as an early computer. Although one can deduce that this gizmo is going through innumerable combinations of letters and numbers in the hopes of eventually hitting on what the Nazis use to convey instructions about their next targets, some basic explanations about what Turing has brought to the table would have honored the man’s mind and accomplishments as well as respected the audience’s intelligence and curiosity about what set him so decisively apart.

“He’s different,” remarks one character, stating the obvious, but the difference the film seizes upon is his sexuality. Structured around a 1951 police investigation stemming from a break-in at Turing’s flat that eventually leads to his arrest for “indecency,” the film advances a contemporary “It’s OK to be different” perspective that will probably speak strongly to younger audiences and is very much in line with then-Prime Minister Gordon Brown‘s 2009 official public apology for “the appalling way he was treated,” and with Queen Elizabeth‘s posthumous pardon issued last year. But it’s also possible that a more true-to-period, reserved approach might have proven an even more moving way to deal with the love that, even then, dared not speak its name.

The arrival of the only woman admitted to the inner circle of code breakers, Joan Clarke (Keira Knightley), adds further layers of interest, both emotional and sociological. A brilliant puzzle solver, Joan quickly becomes the only person Turing likes to talk to, their confidential relationship eventually leading to his odd and, in the end, insincere and half-hearted proposal of marriage.

At the same time, their professional relationship has to be hidden, as regulations dictate that women are only permitted lower-level clerical and communications jobs at the site and are required to live together in communal housing. Knightley’s turn here is alive, alert and altogether sympathetic.

After two years go by without concrete results, the pressure for some breakthrough becomes extreme. But when it does come (anachronistically accompanied by the entirely modern “Yes!” exclamation on the part of one character), it’s a success leavened by the insistence of MI6 head Stewart Menzies (an authoritative and reserved Mark Strong) that the solving of the code must remain a tightly guarded secret; if the Allies tip their hand by thwarting too many German attacks, the enemy will certainly cease using it. So the artificial brain puts its creators in the position of playing God, deciding who will live and who will die.

Norwegian director Morten Tyldum, whose lively and provocative 2012 feature Headhunters is the most successful Norwegian production on home turf of all time, moves things along nicely and achieves some rich visual texture, but doesn’t seem all that interested in the finer points of period flavor, especially in regard to personal behavior; if you watch English films about WWII made either during or after the war, the sense of tightly coiled courage, behavioral reserve and resilience under pressure is unmistakable. There’s little of that here, as the characters are allowed a far greater and, one might argue, more modern range of emotional expression, which could be all to the good in terms of audience acceptance.

But dominating it all is Cumberbatch, whose charisma — tellingly modulated — and naturalistic array of eccentricities, Sherlockian talent at indicating a mind never at rest, and knack for simultaneously portraying physical oddness and attractiveness combine to create an entirely credible portrait of genius at work. In addition to everything else, Alan Turing was a highly accomplished long-distance runner, and occasional glimpses of the man putting his all into the sport lend physical punctuation to a largely indoor story.

The subject of numerous books, Turing was the central character in Hugh Whitemore‘s successful play Breaking the Code, which opened in London in 1986 and moved to Broadway the following year. With Derek Jacobi again playing the leading role, it was made into a BBC television production in 1996.

Production: Black Bear Pictures, Bristol Automotive Productions
Cast: Benedict Cumberbatch, Keira Knightley, Matthew Goode, Mark Strong, Rory Kinnear, Charles Dance, Allen Leech, Mattew Beard, Alex Lawther
Director: Morten Tyldum
Screenwriter: Graham Moore, based on the book Alan Turing: The Enigma by Andrew Hodges
Producers: Nora Grossman, Ido Ostrowsky, Teddy Schwartzman
Executive producer: Graham Moore
Director of photography: Oscar Faura
Production designer: Maria Djurkovic
Costume designer: Sammy Sheldon Differ
Editor: William Goldenberg
Music: Alexandre Desplat

No rating, 114 minutes