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Math movies have become a dependable genre. There is a shot of a genius staring rapturously at mind-bending numbers. He is an insufferable person. There will be much drama about whether he can learn to value human emotion over cold fact.

The premiere last week of “The Imitation Game,” the film about Alan Turing, the tragic father of the computer era, is the latest example. The acting is excellent, the drama real, and the story line illustrative of our ambivalence about our age of smart machines and typical of how the math or programming wizard is portrayed in cinema.

In the Turing movie, the numbers and diagrams are tacked to a wall. In “The Social Network,” the insufferable Mark Zuckerberg character writes formulas on windows. John Nash, in “A Beautiful Mind,” starts with the windows, but switches to walls as he goes mad.

The fictional “Good Will Hunting” likes its math mostly on blackboards, but the equations also end up on mirrors – hanging in midair, as it were, the way they do for Mr. Zuckerberg and Mr. Nash.

In each case, the genius protagonist sees numbers as an almost religious truth, in a way we never can, but only at a price to himself and those around him.

Mr. Turing, as played by Benedict Cumberbatch, is a cold man and a necessary one. This narrative is partly drawn from real life: Mr. Turing was a British math prodigy who during World War II broke a supposedly unbreakable Nazi code. He made a programmable machine, which took the information from one task to execute the next, reaching powerful conclusions.

That makes him the father of our world of computers, communications and elusive codes. But biography is always a matter of selection.

“The Imitation Game,” whose title comes from Mr. Turing’s paper musing on artificial intelligence, is also a tale of Mr. Turing’s aloof, analytic heart, pressed between the arrogance of genius and the suffering of a man unable to connect in life.

Mr. Cumberbatch’s Mr. Turing is isolated for many reasons, including the cruelty of ordinary British schoolboys. He nearly connects to another boy, but tragedy intervenes. By adulthood, he has become detached.

A few spoilers: Mr. Turing’s battle against the Nazis is driven by the desire to crack a very hard puzzle. When he does, he must analytically suppress information warning of an attack, lest Germany figure out that he’s on to them.

Mr. Turing is too smart for his bosses, and dismisses everyone around him as a lesser mortal. The heartlessness of war is met by the absolute dispassion of pure number. Later, Mr. Turing is barely affected when informed that his work has saved millions of lives.

Hollywood: message decrypted. What Mr. Turing represented was something we can’t quite bring ourselves to trust. His computers have a strength and purity of execution we love, even as we worry whether their relentless analytic power might also doom us to heartlessness, becoming closer to HAL, the homicidal computer in “2001: A Space Odyssey.”

This kind of cold relentlessness marks Hollywood’s arrogant (and largely fictional) Mr. Zuckerberg, its obsessive Mr. Nash, and its broken Will Hunting — even homicidal HAL. Computer-type intelligence makes them all a little nonhuman.

We lesser mortals, we tell ourselves, feel more authentically, with something essential that they lack. In each of these movies, there is an emotional climax when the hero discovers the limitation of his analytic approach. He is saved, or ruined, in relation to his ability to learn how to feel. Even HAL realizes fear as his machine intelligence is disassembled, and it seems as if he is learning by becoming more simple.

Love secretly steers much of “The Imitation Game.” A Nazi code transmitter keeps signaling his girlfriend’s name, enabling Mr. Turing to start figuring out a flaw in the German code. In his later life and flashbacks to an earlier loss, Mr. Turing mourns what might have been had he found a way to requited love. Loss of that love is memorialized in his passion for hidden messages.

The real life of these characters is different. Mr. Zuckerberg, whom “The Social Network” portrayed as hapless and more than a little rude around women, was dating the woman who is now his wife the whole time he was building Facebook. Mr. Nash may have been arrogant, but he also had a number of relationships with people of both sexes.

Mr. Turing (who was hounded by authorities in later years because he was gay) was a cold guy, but he also had what Alan Hodges, his biographer and author of an excellent website on Mr. Turing, called “lasting friendships” with like-minded people.

The depiction of all these people, essentially diminishing inner lives almost certainly as rich as our own, signals our ambivalence toward living around computers: The machines do so much, and with such quick and quiet precision, that they seem like a threat.

Of course, movies often use professional shorthand. Businessmen are ruthless. Doctors are good, with big egos. Writers drink. At some point in almost every math movie, the hero stares at formulas in the air, bewitched by a world the rest of us can’t see. Then he talks to regular people, and becomes an enchanted, but disconnected, visitor.

“The Imitation Game” is, among other things, a film about code-breaking. It also contains a skeleton key to the way popular entertainment likes to explain our computer-driven, number-enchanted world.

Related Coverage:

Broken Codes, Both Strategic and Social In “The Imitation Game” Benedict Cumberbatch plays Alan Turing, whose code-breaking work helped win World War II yet whose homosexuality led him to face indecency charges in Britain.