​Benedict Cumberbatch, Alan Turing and Enigma

Cumberbatch said, "That moment in the film actually gave me goosebumps. To think what it must have been like the first time it worked and stopped to give the settings for the day. I mean, just literally the hairs stood on the back of my neck, as it must have been for them. I mean, this is a 'Eureka!' moment."

Cracking the cypher allowed British intelligence to decode messages to German U-boats that had preyed on Allied shipping. It's estimated Turing's work shortened the war by two years, saving millions of lives.

Jim Hendler, professor of Computer Science at Rensselaer Polytechnic Institute in New York, has taught a course on Turing. He called Turing's work in the 1940s "stunning."

"He revolutionized cryptography, the modern field of computer science, [and] the subfield of artificial intelligence," Hendler said. "A lot of the math with those things goes right back to Turing."

"And he did it all essentially in anonymity," said Mason.

"He did it very much in anonymity, because during wartime he was working under secrecy."

Even his family's wasn't fully aware of what he was doing. Sir Dermot Turing, Alan Turing's nephew, told Mason, "For the first part of the war, the family didn't even know where he was based. All those things were completely unknown until the mid-'70s."

"Even you didn't know what he'd been doing?"

"No, no. We crowded 'round this small black-and-white TV set that we had at home in the '70s to find out, when the BBC put out a little program on it. That's how we found out!"

But by then the man who created the blueprint for the modern computer had already taken his own life.

After the war, Turing had become a world-class marathon runner. He moved to the University of Manchester to do research. But in January 1952, he was arrested and charged with "gross indecency" for having sexual relations with another man.

"When he was prosecuted, he was not in denial about it," said Dermot Turing.

"He didn't try to hide it?"

"He didn't try to hide it at all."

Turing was sentenced to probation, and required to undergo estrogen treatments, then believed to suppress homosexual desires.

"I say it could have been worse," said Dermot. "But I still think what happened to him was pretty awful."

In 1954, Turing died after eating an apple dipped in cyanide. He was 41.

It would take nearly 60 years for his reputation to be fully rehabilitated. Only last year he was finally pardoned by Queen Elizabeth.

Today at Bletchley Park -- now a museum -- Alan Turing is celebrated for what he was: a war hero, with a story like something out of a movie.

His was, said Cumberbatch, "a really epic life. A too-short epic life. Forty-one years of it. We owed him at least double that, I'd say."

To watch a trailer for "The Imitation Game," click on the video player below.

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