Growing up in Hampton, Virginia, Margot Lee Shetterly was surrounded by brilliant female scientists and mathematicians who, like her father, worked for Nasa. “I would see them in the context of community organisations or church, or you’d run into them at the grocery store – they were my parents’ friends,” she says. It didn’t seem unusual to her that, within her community, so many women had enjoyed long careers at Langley, Nasa’s research centre – and so many of them were black women. It was her husband, on a trip back to visit Lee Shetterly’s parents, who pointed out how remarkable it was.

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In 1940, she points out in her book, Hidden Figures, just 2% of black women got a university degree and more than half became teachers. But a few defied all expectations and obstacles and joined Naca (the National Advisory Committee for Aeronautics, which would become Nasa). Their work underpinned some of the biggest advances in aeronautics, during some of the most defining moments of the 20th century – the second world war, the cold war, the space race, the civil rights movement, and the adoption of electronic computing.

While some of this generation of female black scientists were recognised – in 2015, Katherine Johnson was awarded the US’s highest civilian honour, the Presidential medal of freedom for her work, which included calculations that helped the moon landing – the fact that there was a crack team of all-female, all-black maths whizzes is largely unknown. “For a long time, African Americans were not allowed to read and write,” says Lee Shetterly. “We forget but it was not that long ago. Women were barred from studying at many colleges. If you are not able to read and write, then you are not going to be able to tell your own story. There haven’t been critical masses of women, minorities, whatever, and I think that’s something that is changing now.”

Facebook Twitter Pinterest Margot Lee Shetterly was surrounded by brilliant female scientists and mathematicians who, like her father, worked for Nasa. Photograph: Hopper Stone, SMPSP/2016 Twentieth Century Fox Film Corporation

Lee Shetterly’s book, and the story of how a group of African American women – transcending racism and sexism to embark on some of the most important scientific work in the world at the time – has been turned into a film, starring Octavia Spencer, Taraji P Henson and Janelle Monae. Henson plays the brilliant mathematician Johnson. It was the real Johnson, now in her nineties and whom Lee Shetterly knew, who first told her about Dorothy Vaughan (played by Spencer).

Hidden Figures trailer: Nasa's overlooked black female mathematicians Read more

In 1943, sitting in the “coloured” section, Vaughan caught the bus for her first day of work at Langley as a “computer” – someone who made calculations and crunched numbers for the engineers developing aerospace technology. She had been a talented maths student, and became a teacher. By the time she applied to Langley, she was married with four children. Vaughan joined a small group of other black female mathematicians, who would become known as the West Computers, segregated from their white counterparts. It was the same elsewhere – black employees were barred from the white employees’ bathroom, and in the canteen a sign on one of the tables read “coloured computers”.

“Today it seems absolutely unthinkable and yet back then it was very normal,” says Lee Shetterly. “In every aspect of their lives, these women had to face the segregation that pervaded their lives. It made total sense in that context that it also governed their lives at work, and yet obviously people never stopped trying to find a way to break those chains.” The women kept removing the sign on the table, but it was always replaced. Until one day it wasn’t.

Facebook Twitter Pinterest Nasa research mathematician Katherine Johnson at her desk at the Langley Research Center in 1966. Photograph: NASA

It proved difficult for the West Computers to move beyond their roles and get promotions to other areas of the institution, such as working directly for an engineering team, unlike the white mathematicians. As for a management role, the highest a black woman could reach at that time was heading the West Computers’ office – in 1951 Vaughan was made head of the unit, becoming Langley’s first black manager.

Like Vaughan, Mary Jackson became a teacher first – she had a degree in maths and physics – but, returning to her home town of Hampton, she worked as a secretary. She left when she became a mother. A few years later, she became a military secretary but, in 1951, Langley offered her a job as a computer. Two years later, Jackson was working with the engineering team working on the supersonic pressure tunnel, where they tested models. Soon after that, she was training to become an engineer – after humiliatingly having to apply for special permission, she started taking classes at a whites-only school.

Around the same time, Johnson started at Langley. Another former teacher, she started as a computer but soon joined the thrusting flight research division. She was brilliant and confident – she refused to use the “coloured” bathrooms, through sheer force of will she got into meetings she was barred from, and put herself forward for work. Her first research report, on orbital flight, was also the first flight research division report written by a woman. She calculated the trajectories of Nasa’s first human space flights, and her work was crucial to the Apollo moon landing. Now 98, Johnson spent decades after her retirement visiting schools and giving talks.

Facebook Twitter Pinterest The West Computers, in Hidden Figures. Photograph: 2016 Twentieth Century Fox Film Corporation

“They never stopped trying to find ways, large and small, to expand the space for themselves and the people who came after them,” says Lee Shetterly. “I think all of these women had a great sense that if they were to succeed in these jobs, they would increase the chance that another black woman would be hired and would be perceived as being capable of that work. That was a responsibility they felt.”

Christine Darden had fallen in love with geometry at high school, but her father insisted she train as a teacher after her masters in applied mathematics. “Jobs for black women – I finished high school in 1958 – were not plentiful at that time. Most of the time, it was [becoming] a teacher, or nurse, or a secretary.” But she took extra courses in advanced calculus and number theory.

Facebook Twitter Pinterest Christine Darden in the control room of Nasa Langley’s Unitary Plan Wind Tunnel in 1975. Photograph: NASA

She joined Langley as a computer, and worked in that role for several years, even though she found it unfulfilling. She wanted to become an engineer but watched as men were promoted ahead of her. Darden confronted the division chief and asked why men who had the same education and experience as her – and often less – were promoted while she was not. “His answer was that the women had never complained about it before,” remembers Darden. There was the belief that women would give up work as soon as they had children. “You would find that, for the most part, that was not true for a lot of black women who, once they went to work, had to continue to work.”

Darden argued her case, and was almost instantly promoted to an engineering team where she started her career in sonic boom research. She would later complete a doctorate in mechanical engineering, but her early work provided some of the fundamentals in sonic boom reduction technology. During the course of her 40-year career at Nasa, Darden became one of the world’s leading experts in this area.

She had started her Nasa career in the computer pool in 1967 (it had been desegregated by then), and she knew several women who had been in that first cohort of West Computers. “I knew that I stood on their shoulders and was able to do some things because of what they had done,” says Darden. “And I like to think that some of the younger ones might have stood on my shoulders, too.”