From left, Mary Jackson (Janelle Monae), Katherine Johnson (Taraji P. Henson) and Dorothy Vaughan (Octavia Spencer) in “Hidden Figures.” (Hopper Stone/SMPSP/Twentieth Century Fox)

This piece discusses the plot of “Hidden Figures.”

It’s the time of year when movies with ambitions for major awards lie thick at the theaters, and when gripes begin about “Oscar bait,” films that supposedly conform to some set expectation of what Academy voters like, while showing little sense of creativity or spark. So one of the many reasons I’m so grateful for “Hidden Figures,” Theodore Melfi’s terrific movie about three African American women who made integral contributions to the U.S. space program, is that the film provides a powerful reminder of just how much it’s possible to do within the confines of a handsome period piece about race. Certain artistic forms persist for a reason.

And in telling a story about a federal agency challenged to make use of the talent it had on hand, no matter the gender or color of the people who possessed it, “Hidden Figures” issues a striking challenge to the entertainment industry itself. The pleasures and arguments of “Hidden Figures” are no less — and maybe even a bit more — for coming in a conventional package.

One of the smartest decisions director Melfi and his co-writer Allison Schroeder make in “Hidden Figures” is to start the story once math prodigy Katherine Johnson (Taraji P. Henson), Dorothy Vaughan (Octavia Spencer), who supervises the black women who work as “computers,” and aspiring engineer Mary Jackson (Janelle Monáe) have already begun working at NASA, dropping us into the flow of their warm banter.

It’s not as if the movie needs to do a lot of work to make us like these three engaging women. But it’s still a delight to watch them make biting jokes about their commuting options — Dorothy’s unreliable car, or the back of the bus — or to see the eagerness with which Mary and Dorothy set up the widowed Katherine with the dashing Col. Jim Johnson (Mahershala Ali) at a church picnic. “Please, have some shame,” Katherine hisses at Mary when she smiles in Jim’s direction. “I will not,” Mary shoots back at her.

And this timing also pays off in the film’s sophisticated treatment of sexism and racism. “Hidden Figures” is too wise to believe that the battle for equality ends when women of color get hired.

Al Harrison (Kevin Costner), Katherine’s boss at the Space Task Group, is quick to accept her work. But he’s blind to the conditions that make her job more difficult: the embarrassment of a “Colored” coffee pot that suddenly appears in the office; a dress code that limits her to a single string of pearls as jewelry; the fact that, as a woman, she doesn’t have a wife to pick up the slack at home when Al arbitrarily increases her hours but not her pay; the way her colleague Paul Stafford (Jim Parsons) constantly denies Katherine information, forcing her to redo complicated calculations.

“I put a lot of faith in you,” Al tells Katherine, grouchily, when she returns to the office one afternoon, soaking wet and late from a dash to the only bathroom she’s allowed to use in the whole complex. “There are no colored bathrooms here, or anywhere except the West campus,” she breaks down, cataloging the insults for him. “I don’t own pearls. You don’t pay coloreds enough to afford pearls. And I work like a dog living off a pot of coffee the rest of you don’t want to touch.”

In a blunter movie, Al’s next moves would seal him as a good, redeemed white person: He takes the “Colored” sticker off the coffee pot and knocks down the “Colored Ladies” sign, saying that at NASA, “we’re all the same color.” But the work continues: Katherine has to push him to admit her to important meetings, and he invites her in to watch John Glenn (Glen Powell) orbit the earth only after a door is slammed in her face. Equality is a process, not a destination.

Gender doesn’t magically erase the divisions of color, either. Ruth (Kimberly Quinn), Al’s assistant, alternately supports Katherine and undermines her. One minute, she reminds Al that Katherine can do the analytic geometry he needs, as well as speak for herself. The next, Ruth is refusing to help Katherine find a ladies room.

Vivian Michael (Kirsten Dunst), the white woman who supervises all of the female computers, relies on fine print and a honeyed tone of voice to undermine the black women she supervises. She rejects Mary from an engineering training program on the grounds that she lacks required classes taught in segregated institutions and feigns uncertainty to deny Dorothy a promotion to supervisor.

“You know, despite what you think, I don’t have anything against y’all,” Vivian tells Dorothy after Dorothy gets assigned to program the new IBM machine. “I know. I know you probably believe that,” Dorothy tells her, kind and devastating all at once. When Vivian finally delivers Dorothy’s long-delayed promotion, she also grants Dorothy the dignity of addressing her as Mrs. Vaughan, a courtesy she had previously denied her. The gesture doesn’t redeem Vivian; it merely means she’s behaving as she ought to have all along.

That potent intersection of sexism and racism plays out beyond NASA’s walls, too, of course.

“I had no idea they hired — ” a white cop (Ron Clinton Smith), who stops by Dorothy’s broken-down car, remarks when he learns where the women work. “There are quite a few women working in the space program,” Dorothy tells him, letting him off the hook — sort of. Later in the movie, when Dorothy tries to find a textbook on the programming language Fortran, a white librarian has her and her son ejected for daring to browse in the white section. Later, her son realizes Dorothy stole the book she was looking for. “I pay taxes,” she tells him tartly. And when Mary wins admission to the classes she needs to start her engineering program, she’s both the only black person and the only woman in the section. “The curriculum isn’t designed for teaching a woman,” the professor (Michael Hartson) tells her, disconcerted. “I imagine it’s the same as teaching a man,” Mary reassures him, taking her seat in the front of the class.

White people and men aren’t the only people who hinder the women. Mary’s husband, Levi (Aldis Hodge), disparages her attempts to rise in the system, and Jim initially underestimates Katherine’s fierce intelligence. Refreshingly, there’s never a moment when Dorothy, Mary or Katherine have to compromise; it’s Levi and Jim who prove themselves by coming around to support Mary and Katherine’s ambitions, and to pick up the slack at home.

Any one of those scenes (or the one where Mary goes to court to desegregate the engineering class) might have been the climax of another movie about racism and civil rights. “Hidden Figures” treats them like the incremental steps that they are, which doesn’t sap any of the power from these moments.

Spencer, Monáe and Henson’s command of their craft saves these moments from tipping over into cliche. After Mary makes a saccharine appeal to the judge, she jumps up and down outside the courthouse, celebrating her victory with more dignity than joy. As Katherine continues to push Al to live up to his stated ideals, she puts on the thinnest veneer of deference, Henson’s line readings as precise as the tap of her heels or the way Katherine offers Jim her hand but only after a carefully calibrated delay. Dorothy is the rare role that allows Spencer to exercise her wicked streak, rather than immobilizing her in a cloak of rigid dignity.

Melfi brings a smart visual sense to these ideas. After repeated scenes of Katherine running back and forth across the NASA campus to use the bathroom, it’s a delight near the end of the movie to watch a man from the Space Task Group make a mad dash to retrieve her from the West building so that she can check the math on Glenn’s flight. For all the discussions of pearl necklaces, the most valuable neckwear Al gives Katherine isn’t jewelry but the pass that gives her access to the control room.

Costume designer Renee Ehrlich Kalfus dresses Henson, Spencer, Monáe and the other black women in the computing group in jewel tones so that they stand out not merely because of their skin color. In one scene, Katherine stands between two waves of white men, glowing in a jade dress. In another, after Dorothy insists that she won’t continue to work on the IBM computer that has stumped the white engineers unless her black colleagues get jobs there, too, she leads the other women across the NASA campus, their dresses and hair gleaming like a rainbow cutting across a sea of white men in white, short-sleeved dress shirts.

Ultimately, “Hidden Figures” makes a case for inclusion that’s not rooted in aesthetics or niceness. Instead, the movie argues that NASA needed Katherine Johnson, Dorothy Vaughan and Mary Jackson because, in the words of that cop, “We got to get a man up there before those Commies do,” and NASA couldn’t have done it without their singular talents and determination. Equality isn’t a matter of corporate branding or self-righteousness: It’s the only way to make sure that organizations and countries don’t miss out on genius. If Hollywood looks at the work that Henson, Spencer, Monáe, Ali and Hodge do in “Hidden Figures” and gets that message, too, that would be awfully nice and embarrassingly overdue.