Starring Taraji P. Henson. Rated G

This overeager, if oddly satisfying film details what it took for the U.S. to put a man in space at the height of the Cold War with Russia. Hidden Figures doesn’t explain how 30-plus black women—or “coloured computers”, as some called them—came to be crunching numbers on a dingy campus near NASA’s Virginia headquarters. But it does depict the daily indignities heaped upon even the most talented minorities in the Jim Crow South of 1961.

The standout figures here, based on real-life counterparts, are math savant Katherine Johnson (Taraji P. Henson), mechanically minded Dorothy Vaughan (Octavia Spencer), and engineering wiz Mary Jackson (Janelle Monáe, following up on Moonlight). All three directly support John F. Kennedy’s space program. But only Katherine gets invited into the room with the all-white, all-male crew in charge of running data. These crew-cut dudes are quietly freaked out by her using “their” coffee table, and she faces open hostility from an immediate superior (The Big Bang Theory’s Jim Parsons). But her almost magical way with numbers deeply impresses mission leader Al Harrison, played with gruff precision by Kevin Costner.

De facto supervisor Dorothy faces the steel-magnolia resistance of her boss (Kirsten Dunst), although D’s tech prescience with that massive new piece of IBM gear proves a turning point. And Mary must overcome institutional and family resistance to attend a whites-only school to finish her engineering degree.

Happily, our unsung heroines lived to see their dreams realized; in fact, NASA recently named a new research building after Johnson, now 98. This helps explain the two-hour tale’s feel-good ambiance, emphasized by Pharrell Williams’s well-chosen period music and Wynn Thomas’s gorgeous production design. (Check out the countless ways Thomas, who also designed A Beautiful Mind, finds to combine orange and turquoise.)

Neophyte director and cowriter Theodore Melfi (St. Vincent) sets up serious scenes for laughs, and gives the leads far too many Big Breakthroughs, ultimately reinforcing the notion that people of colour must perform 100 times better than white folks just to be allowed to use the same bathroom. But the fact that the smartest president in 50 years is being replaced by the dumbest man on Earth renders these concerns meaningless. The movie keeps overplaying its hand, but when it comes to American audiences, no message can be too broad—and this message truly needs to be heard.