Based on Margot Lee Shetterly's book, Hidden Figureshas a triple-meaning title. It is about the mathematics that served as a rationale and a backstop for manned space capsules launched into space and brought back safely to earth. It is about the African-American women who carried out these vital functions in Langley, VA, without the public acknowledgement granted astronauts like Alan Shepard or John Glenn, or even the buzzcut white men at Mission Control. And it is about these human "colored computers" literally being hidden from view, tucked away in a segregated building on NASA's campus, a florescent-lit purgatory from which there was no path to deliverance.

In broad but mostly satisfying terms, Hidden Figures celebrates the few African-American women who broke out of the West Area Computers building because their talent was no longer worth suppressing. This wasn't a moral calculation so much as a practical one: America was losing the space race to the Russians, and NASA needed the best possible people to catch up, regardless of the color of their skin. When Katherine Johnson, an expert in analytic geometry, gets promoted to a position in the Space Task Group, co-writer/director Theodore Melfi (St. Vincent) makes a running joke out of Johnson having to dash a quarter-mile across campus in high heels just to use the "colored bathroom." It takes her boss a while to put an end to this unsustainable folly, and her colleagues' respect comes even slower still.

Now 98, Johnson has lived long enough to receive the Presidential Medal of Freedom from President Obama and have a computational facility named after her at Langley. Taraji P. Henson plays Johnson as a quietly insistent woman who made herself so indispensable that her presence in otherwise all-white offices and high-level meetings could not be denied. In the early '60s, she and her colleagues Dorothy Vaughan (Octavia Spencer), a mathematician who would later take over early IBM processing computers, and Mary Jackson (Janelle Monáe), a trailblazer in engineering, are shown carpooling to NASA together in broken-down Chevy Impala. When they flash their credentials to a white cop who pulls them over, they're greeted with the first in a series of double takes.

So begins a rinse-repeat pattern of slow-clap moments where the women are disrespected or underestimated at work, only to show up a parade of crew-cut dolts in dress shirts and thin black ties. One of these men is Al Harrison (Kevin Costner), the gum-chomping head of the Space Task Group, whose single-minded quest to get the numbers right leads naturally to an egalitarian leadership style. The best scenes in Hidden Figures show Johnson and Harrison hard at work on hammering out the data for entry and re-entry that will support Glenn's Friendship 7 capsule as it orbits the earth and splash-lands in the Caribbean. In these moments, Melfi doesn't have to elbow the audience to get them to pick up on the significance. It's touching simply to see them as colleagues, on equal footing, applying their passion and brilliance toward keeping the astronaut safe and advancing the space program. Harrison doesn't advance Johnson out of a deep-seated belief in racial justice; he does it because her gifts are self-evident and essential, and any obstacles to her are obstacles to him, too.

Much like Johnson in the film, Hidden Figures isn't nearly as certain of itself when it's away from the chalkboard. Vaughn and especially Jackson are not allotted nearly enough time to develop as discrete characters, so the best the film can manage is to run them up against the cardboard nemeses holding them back, like Kirsten Dunst as the condescending functionary who denies Vaughn a supervisory role. Johnson's relationship to her second husband, played by the estimable Mahershala Ali, also gets short shrift, if only because the stakes of their courtship and marriage are not nearly as high as winning the space race. He's just another skeptic for her to turn around.

The generic feel-good vibe of Hidden Figures does feel good, however, particularly once the Friendship 7 vessel approaches liftoff and all the characters coalesce around the event. In light of Glenn's death earlier this month, the film's treatment of him as a gregarious, forward-thinking man who was personally invested in Johnson's calculations counts as a lovely incidental tribute. He doesn't want to step inside the machine without knowing she's calculated his trajectory down to the last decimal point. As he rattles around on re-entry, Johnson's numbers are the invisible hand that hold him aloft, out of sight and on the page.

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