Benedict Cumberbatch great in 'Imitation Game' (w/video)

It’s clearly the season for Oscar-worthy performances by British actors playing mathematical geniuses facing daunting personal odds.

Sound overly specific? Consider: A few weeks ago we had “The Theory of Everything,” starring Eddie Redmayne as the brilliant physicist Stephen Hawking.

And now we have Benedict Cumberbatch in “The Imitation Game” as Alan Turing, the man chiefly responsible for cracking the vaunted Enigma code used by the Germans in World War II.

But even though Turing literally changed the course of history - Winston Churchill said he’d made the greatest single contribution to the Allied victory - and, by the way, also created one of the first modern computers, you may well have never heard of him.

That would be reason enough to applaud the arrival of “The Imitation Game,” directed by Morten Tyldum and written by Graham Moore based on a 1983 book by Andrew Hodges.

But though it often feels like your basic high-brow British biopic, the film also happens to boast impeccable acting, especially by Cumberbatch, who masterfully captures the jittery, nervy brilliance of a man whose mind could bring down an enemy yet couldn’t process simple human interactions.

Was Turing autistic, or did he have Asperger’s syndrome? Who knows - today we’d probably say he was “on the spectrum.” He’s a man who can’t coherently answer whether he wants a sandwich for lunch.

At the same time, he’s conceiving a machine that will somehow defeat the Germans’ own cipher machine, the Enigma, which uses code that changes every 24 hours, rendering traditional decrypting methods useless.

As we learn about this painful duality in Turing’s life, we also learn he was gay, in an era when homosexual activity was criminalized in Britain. After the war, he was prosecuted for indecency.

Given a choice of “chemical castration” or prison, he chose the former. He committed suicide at 41, a cyanide-laced apple by his bedside.

Oddly, though, the film addresses Turing’s death only with a quick line in the postscript, and no word on the method. It’s a strange omission - particularly given that Turing was said to have been fascinated by the “Snow White” story.

We begin after the war, with the police investigating a mysterious break-in at Turing’s home and wondering what this fellow’s about (they don’t yet know about his role in the war).

Soon we flash back to 1939, and younger Turing’s job interview with the commander running the secret codebreaking program (a nicely crusty Charles Dance). Given Turing’s dreadful personal skills, it doesn’t go well.

But he’s hired, and immediately starts alienating his colleagues, especially the charismatic Hugh Alexander (Matthew Goode, excellent and also perhaps the best-looking mathematician ever portrayed onscreen, at least until Keira Knightley makes her entrance in this film.)

Turing is ridiculed for insisting on building his machine, taking up time and money while soldiers are dying. Denied funding, he makes a direct plea to Churchill, who puts him in charge.

That’s when he hires Joan Clarke (an appealing Knightley), the only woman on the team and his eventual fiancee.

Still, things go badly, until an offhand remark by a woman in a bar makes Turing realize a way to speed up the machine’s activity. Eureka!

The story gets more interesting as the team realizes it must keep its huge breakthrough a secret, lest the Nazis figure it out and change their code.

They enter into a painful calculus: Which information can be used, and hence which lives saved?

There are surely numerous narrative shortcuts taken here.

There’s also one of those slogan-type lines that seems far too tongue-trippingly clunky to be uttered by one character, let alone two: “Sometimes it’s the people no one imagines anything of who do the things that no one can imagine.”

But there’s truth to it. Turing’s story is indeed hard to imagine. Thanks to Cumberbatch’s committed performance, a lot more people will know it.