Hidden Figures, Theodore Melfi’s salute to the black female mathematicians who were the booster rockets of NASA’s early space program, swerves around a conversation-ending refrain: “That’s just the way things are.” It’s what geometry genius Katherine Johnson (Taraji P. Henson) hears when her coworkers won’t let her attend their all-male meetings. It’s what group leader Dorothy Vaughan (Octavia Spencer) hears when denied the title of supervisor, though she’s been doing the work of one for years. And it’s what science whiz Mary Jackson (Janelle Monáe) hears when she’s told that the classes she needs to become NASA’s first black female engineer are restricted to “whites only” schools.

The irony is clear. Even the men trying to do the impossible — put a man on the moon — couldn’t smash barriers on Earth. Their failure of imagination fails their mission. Here, boss Al Harrison (Kevin Costner) can’t figure out why the Soviet Union is winning the space race. It’s simple: The Russians doubled their brainpower by putting women to work. During the early ’60s, Russian women earned almost half of all chemistry PhDs. In America, that number plummeted to 1 in 20. The Russians blasted their first female cosmonaut, Valentina Tereshkova, into orbit in 1963. America wouldn’t green-light Sally Ride for another 20 years.

Melfi sees the big equation: Solving institutional discrimination has proven to be harder than getting John Glenn to circle the globe. But Hidden Figures focuses on people, not numbers or policies or platitudes. He makes his problems human-size. Like Ginger Rogers with calculators, Katherine, Dorothy, and Mary have to sprint their leg of the space race while being held back by dress code–required heels, “whites only” coffee pots, constant condescension, and a work commute that forces them to either ride in the back of the bus or risk getting pulled over by the Virginia cops.

Melfi and the cast keep indignation out of these indignities. Like their coworkers, they accept how Jim Crow’s Virginia is, mostly. They smile more than scowl. After the ladies gripe about being stuck on the side of the road, Dorothy jokes, “You’re welcome to sit in the back of the bus.” They giggle. Katherine feels lucky to join Harrison’s Mercury team as a “computer” — the actual name given to female employees hired only to double-check the male scientists’ math. Separate but equal? They’re barely counted as humans. She’s not intending to revolutionize civil rights. (Last fall, Katherine told the New York Times she was worried she’d be portrayed as “aggressive.”) She’s just trying to do her job while enduring injustices like the half-mile trek to the nearest colored ladies’ room at Langley.

Forcing one of NASA’s sharpest minds to waste 40 minutes a day trekking to pee isn’t just rude — it’s illogical. And at Langley, logic makes a stronger argument than justice or idealism. Costner’s stressed-out supervisor isn’t swayed by emotion. He’s old-school enough that he ends a pep talk with “amen” and orders the team to call their wives when they work late, forgetting that they also could have husbands. When he exasperatedly declares, “Here at NASA, we all pee the same color,” he’s not trying to be science’s Oskar Schindler. He just wants his brainiac to spend more minutes at her desk. Numbers are numbers.

Henson, so ferocious in Empire, plays Katherine with a quiet strength. She raises her voice just once and punctuates her otherwise soft requests by pushing up her glasses with one finger, like a cartoon geek. As the film’s lead, Katherine gets the most screen time — and the only romantic arc, with Moonlight’s Mahershala Ali, a sugar-coated hunk based on her real-life husband of 58 years. I adored an opening shot of 10-year-old Katherine solving an equation at the chalkboard. (Hidden Figures has a lot of not-exactly-thrilling spectator math.) Finally, she circles her answer and nods. She doesn’t need the teacher to assure her she’s right — she’s confident that everything will work out if she follows the steps.

Spencer’s Dorothy is more cynical. Instead of smoothing resistance drop by drop, the way water conquers stone, Dorothy sneaks past the walls, pocketing a computing book from the forbidden white section of the library (“I pay taxes,” she hisses to her sons) and slipping in after hours to master this newfangled IBM contraption. “Good girl,” she coos to the machine, nonchalantly deciding that this mind is female, too.

Monáe’s Mary has the biggest mouth. We barely get enough time with her character to appreciate more than her wardrobe of high-waisted pants. Still, there’s a lovely moment when Mary first spots the Mercury capsule and strokes it reverently, like she knows it’s as close to the sky as she’ll get, and a great early scene when, after convincing a suspicious police officer that the three women are crucial to beating the Commies, she accepts his offer to escort them to Langley, lights ablaze. Katherine and Dorothy would rather be left in peace, but Monáe can’t resist speeding behind his siren, cackling, “Three negro women chasing a police officer down a highway!”

Melfi paints his true-life story in bold colors, contrasting the clean, modern laboratories of Langley’s East campus with the cramped, dark corridors where black employees were stationed on the West — gray rooms that literally look like they’re from antiquity. He costumes his actresses in plaids and jewel-toned blouses that clash against the men’s bone-white button-downs. In a room of 20 nerds, you spot them right away, as out-of-place in the frame as they were in reality. You feel your eyes on them. And then you realize how visible they must have felt.

Hidden Figures is at its best when capturing this unspoken tension. For the sake of drama, Melfi bangs the drum louder by having every other white actor, from Jim Parsons’s researcher to Kirsten Dunst’s office manager, play a sneering villain. Often, their bigotry is plain. “We’ve never had a Negress in here before Katherine,” cautions Dunst’s blonde. “Don’t embarrass me.” Sometimes it’s more disguised, like the way Katherine’s only female officemate shoos her off with, “Go on, get settled,” as though she’s a child. (While Katherine, Dorothy, and Mary are real, all the white characters besides Glen Powell’s charming John Glenn are fictionalized composites.)

It’s exhausting to watch these women try twice as hard for half the credit. Melfi and Allison Schroeder’s script, based on Margot Lee Shetterly’s nonfiction book of the same name, is all dignity and perseverance. (Shetterly’s father was one of NASA’s early black male mathematicians, who are still off-screen waiting for their own biopic.) It’s candied history. The timeline is all wrong, the soundtrack is too cheery, the movie is too eager to please. Yet at the end, I found myself tearing up anyway to learn that last year, Obama awarded 98-year-old Katherine the Presidential Medal of Freedom — and grumbling that I hadn’t been aware of it at the time.

All this syrup might keep Hidden Figures from being an awards contender. We prefer our Oscar-nominated mathematicians to be white men overcoming physical rather than cultural hurdles: schizophrenia (A Beautiful Mind), motor neuron disease (The Theory of Everything), or Asperger’s (The Imitation Game) — bonus points if they’re a jerk. But there’s value in applauding women who do everything: They’re wives, mothers, dancers, whiskey-drinkers, pie-bakers, and, as Katherine was for 50 years, singers in the church choir. They’re well-rounded human beings who refuse to define themselves by their gender or skin color. As Katherine chastises her husband-to-be, she and her friends aren’t special because they wear skirts: “It’s because we wear glasses.”