One is familiar with the classic images and stories of the black struggle in America in the ’60s – Martin Luther King, Rosa Parkes and the bus protests, Black Power salutes, riots, Emmet Till – but Hidden Figures reminds us that the black experience in America touched every part of life in ways that still shock.

The film (weak title; the pun tries too hard for effect) intertwines the stories of three black women working for NASA in the early ’60s to illustrate their trials, tribulations and the institutional and ordinary casual racism which affected their lives. They are ‘computers’ – mathematical prodigies hired by NASA to run the maths behind the early space programme. Confined to a back room – ‘Colored Computers’ says the sign on the door – they toil at their numbers with slide rules and blackboards, unrecognised and largely unappreciated.

One, Katherine Johnson (played by Taraji P Henson) is plucked to join the elite team preparing for John Glen’s first flight, under the watchful gaze of Al Harrison, played by Kevin Costner, who turns out (surprise, surprise) to be a sort of good guy; has Costner ever played a baddie?

On her first day Johnson walks into the room and one of the white men shoves some rubbish into her arms, assuming her to be the cleaner. Later, she goes to get a cup of coffee from the communal pot as the other  white male mathematicians watch on silent, open-mouthed and aghast. The next day she finds a coffee pot just for ‘coloureds.’ Harrison is annoyed that she disappears for long periods during the day, eventually demanding why she takes such long breaks. She loses her temper and shouts that she has to go out of the building and walk 2 miles (usually in the rain) to find the toilets for use by the ‘coloureds.’ Later in the film he takes a baseball bat to the ‘coloured’ toilets sign, to the cheers of the assembled multitude and declares that in future all toilets will be mixed. It’s a powerful and moving scene although one wonders whether the institutional racism of NASA was so easily over-turned.

When John Glen and the other potential astronauts arrive at NASA they are introduced to the waiting staff but not the black women who stand separate from the white people – until Glen insists on meeting them and shaking their hands. One can’t help wondering whether this actually happened or whether it is adding a gloss to Glen’s biography.

Dorothy and the others report to their white female boss played with chilling relish by Kirsten Dunst who is as casually racist as the others. Towards the end of the film Dorothy  and Dunst meet by accident in the newly integrated toilets and Dunst says that she was never really racist. Dorothy’s response is wonderfully apt, both moving and funny and one of the defining moments of the film.

Janelle Monae plays Mary Jackson, a feisty young black woman who aspires to be an engineer but finds that she can’t apply for the role because she doesn’t have the correct qualification which can only be obtained by going to an all white school, forcing her to petition the state court for special dispensation to attend. I’ll leave you to decide whether she gets it. The third woman – Dorothy Vaughan, played by Octavia Spencer, is the supervisor of the ‘computers.’ Half way through the film NASA gets its first IBM computer which the white men are unable to operate. She gets a book on Fortran from the library and reads it on the bus until she has taught herself to programme. By the end of the film she and all her girls (no longer required as ‘computers’ now that a proper computer is in use) march upstairs to the computer room where they all become programmers.

Hidden Figures is a fine film, it’s well made and tells an important and hidden (certainly to me) story and there are scenes which are very moving. It is not without some minor faults – the film gives the impression that the only decent mathematicians at NASA were black women – while all the men are portrayed as racist and sexist and not very good at numbers. I can believe the racist and sexist bit, but I suspect they were better mathematicians than they are portrayed.

Katherine meets, falls in love with and finally marries Colonel Jim Johnson played by Mahershala Ali (who is in everything and now an Oscar winner for Moonlight). It provides a back story but adds little to the plot. At the end of the film we see the actresses standing by the real women they portrayed in the film with their potted biographies – all went on to have senior positions in NASA – we learn that the real Katherine Johnson is now 98. Oddly, we learn nothing of the Kevin Costner character – was he perhaps a composite?