The following is an excerpt from the forthcoming book Hidden Figures, a movie version of which will be released in January 2017 starring Taraji P. Henson, Octavia Spencer, Janelle Monáe, Kevin Costner, and Kirsten Dunst.

It was on a trip to the post office during the spring of 1943 that Dorothy Vaughan spied the notice for the laundry job at Camp Pickett. But the word on another bulletin also caught her eye: mathematics. A federal agency in Hampton, Virginia, sought women to fill a number of mathematical jobs having to do with airplanes. The bulletin, the handiwork of Melvin Butler and the National Advisory Committee for Aeronautics’ personnel department, was most certainly meant for the eyes of the white, well-to-do students at the all-female State Teachers College there in Farmville. The laboratory had sent application forms, civil-service examination notices, and booklets describing the NACA’s work to the school’s job-placement offices, asking faculty and staff to spread the word about the open positions among potential candidates.

“This organization is considering a plan to visit certain women’s colleges in this area and interview senior students majoring in mathematics,” the laboratory wrote. “It is expected that outstanding students will be offered positions in this laboratory.” Dorothy’s house on South Main sat down the street from the college campus. Every morning as she walked the two blocks to her job at Moton High School, a U-shaped building perched on a triangular block at the south end of town, she saw the State Teachers College coeds with their books, disappearing into classrooms in their leafy sanctuary of a campus. Dorothy walked to school on the other side of the street, toeing the invisible line that separated them.

It would no sooner have occurred to her that a place with so baroque a name as the Langley Memorial Aeronautical Laboratory would solicit an application from Negro women than that the white women at the college across the street would beckon her through the front doors of their manicured enclave. Black newspapers, however, worked indefatigably to spread the word far and wide about available war jobs and exhorted their readers to apply.

As a college graduate and a teacher, Dorothy stood near the top of what most Negro women could hope to achieve. Teachers were considered the “upper level of training and intelligence in the race,” a ground force of educators who would not just impart book learning but live in the Negro community and “direct its thoughts and head its social movements.” She had earned a full-tuition scholarship to Wilberforce University, the country’s old private Negro college, in Xenia, Ohio. At Wilberforce, Dorothy earned “splendid grades” and chose math as her major. When she was an upperclassman, one of Dorothy’s professors at Wilberforce recommended her for graduate study in mathematics at Howard University, in what would be the inaugural class for a master’s degree in the subject. Possessed of an inner confidence that attributed no shortcoming either to her race or her gender, Dorothy welcomed the chance to prove herself in a competitive academic arena. But the economic reality that confronted Dorothy when she came out of college made graduate study seem like an irresponsible extravagance. With the onset of the Great Depression, Dorothy’s parents, like a third of all Americans, found steady work hard to come by. An extra income would help keep the household above water and improve the odds that Dorothy’s sister might be able to follow her path to college. Dorothy, though, only 19 years old, felt it was her responsibility to ensure that the family could make its way through the hard times, even though it meant closing the door on her own ambitions, at least for the moment. She opted to earn a degree in education and pursue teaching, the most stable career for a black woman with a college degree.

In the first week of May 1943, the Norfolk Journal and Guide published an article that would call to Dorothy like a signpost for the road not taken. “Paving the Way for Women Engineers,” read the headline. The accompanying photo showed 11 well-dressed Negro women in front of Hampton Institute’s Bemis Laboratory, graduates of Engineering for Women, a war training class. Founded in 1868, Hampton Institute had grown out of the classes held by the free Negro teacher Mary Peake, in the shade of a majestic tree known as the Emancipation Oak.

On the eve of World War II, Hampton was one of the leading Negro colleges in the country and the focal point of the black community’s participation in the conflict.There were black jobs, and there were good black jobs. Sorting in the laundry, making beds in white folks’ houses, stemming in the tobacco plant — those were black jobs. Owning a barbershop or a funeral home, working in the post office, or riding the rails as a Pullman porter — those were good black jobs. Teacher, preacher, doctor, lawyer — now those were very good black jobs, bringing stability and the esteem that accompanied formal training.

But the job at the aeronautical laboratory was something new, something so unusual it hadn’t yet entered the collective dreams. Not even the long-stalled plan to equalize Negro teachers’ salaries with those of their white counterparts could beat this opportunity. Even if the war ended in six months or a year, a much higher salary even for that brief time would bring Dorothy that much closer to assuring her children’s future.

So that spring, Dorothy Vaughan carefully filled out and mailed two job applications: one to work at Camp Pickett, where the need for labor was so great, so undifferentiated, that there was virtually no possibility that they would not hire her. The other, much longer application reviewed her qualifications in detail. Work history. Personal references. Schools attended: high school and college. Courses taken, grades received. Languages spoken (French). Foreign travels (none). Would you be willing to accept a position abroad? (No.) Would you be willing to accept a position in Washington, D.C.? (Yes.) How soon could you be ready to start work? She knew the answer before her fingers carved it into the blank: Forty-eight hours, she wrote. I can be ready to go within 48 hours.

Melvin Butler, the personnel officer at the Langley Memorial Aeronautical Laboratory, had a problem, the scope and nature of which was made plain in a May 1943 telegram to the civil service’s chief of field operations. “This establishment has urgent need for approximately 100 Junior Physicists and Mathematicians, 100 Assistant Computers, 75 Minor Laboratory Apprentices, 125 Helper Trainees, 50 Stenographers and Typists,” exclaimed the missive. Every morning at 7 a.m., the bow-tied Butler and his staff sprang to life, dispatching the lab’s station wagon to the local rail depot, the bus station, and the ferry terminal to collect the men and women — so many women now, each day more women — who had made their way to the lonely finger of land on the Virginia coast. The shuttle conveyed the recruits to the door of the laboratory’s Service Building, on the campus of Langley Field. Upstairs, Butler’s staff whisked them through the first-day stations: forms, photos, and the oath of office: I will support and defend the Constitution of the United States against all enemies, foreign and domestic … so help me God.

Thus installed, the newly minted civil servants fanned out to take their places in one of the research facility’s expanding inventory of buildings, each already as full as a pod ripe with peas. No sooner had Sherwood Butler, the laboratory’s head of Procurement, set the final stone on a new building than his brother Melvin set about filling it with new employees. Closets and hallways, stockrooms and model shop floors stood in as makeshift offices. Someone came up with the bright idea of putting two desks head to head and jury-rigged the new piece of furniture with a jumpseat, in order to squeeze three workers into space designed for two. In the four years since Hitler’s troops had overrun Poland — since American interest and the European War had converged into an all-consuming one — the laboratory’s complement of 500 odd employees at the close of the decade had was on its way to 1,500. Yet the great groaning war machine swallowed them whole and remained hungry for more.

Just two years prior, with the storm clouds gathering, President Roosevelt had challenged the nation to ramp up its production of airplanes to 50,000 per year. It seemed an impossible task for a country tooled to stamp out just 3,000 of the flying machines in a year. Now, America’s aircraft industry was a production miracle, easily surpassing the mark by more than half. It was the largest industry in the world, the most productive, the most sophisticated, outproducing the Germans by more than three times and the Japanese by nearly five. The facts were clear to all belligerents: The final conquest would come from the sky.

“Victory through Air Power!” Henry Reid, engineer-in-charge of the Langley Laboratory, crooned to his employees, the shibboleth a reminder of the importance of the airplane to the war’s outcome. “Victory through Air Power!” the NACA-ites repeated to each other, minding each decimal point, poring over differential equations and pressure-distribution charts until their eyes fatigued. In the battle of research, victory would be theirs.

Unless, of course, Melvin Butler failed to feed the three-shift, six-day-a-week operation with fresh minds. The engineers were one thing, but each engineer required the support of a number of others: craftsmen to build airplane models tested in the tunnels, mechanics to maintain the tunnels, and the nimble number crunchers to process the numerical deluge that issued from the research. Lift and drag, friction and flow. What was a plane but a bundle of physics? Physics, of course, meant math, and math meant mathematicians. And since the middle of the last decade, mathematicians had meant women. Langley’s first female computing pool, started in 1935, had caused an uproar among the men of the laboratory. How could a female mind process something so rigorous and precise as math? The very idea, investing $500 on a calculating machine so it could be used by a girl! But the “girls” had been good, very good — better at computing, in fact, than many of the engineers, the men themselves grudgingly admitted. With only a handful of girls winning the title “mathematician” — a professional designation that put them on equal footing with entry-level male employees — the fact that most computers were designated as lower-paid “subprofessionals” provided a boost to the laboratory’s bottom line.

But in 1943, the girls were harder to come by. Virginia Tucker, Langley’s head computer, ran laps up and down the East Coast searching for coeds with even a modicum of analytical or mechanical skill, hoping for matriculating college students to fill the hundreds of open positions for computers, scientific aides, model-makers, laboratory assistants, and, yes, even mathematicians. She conscripted what seemed like entire classes of math graduates from her North Carolina alma mater, the Greenboro College for Women, and hunted at Virginia schools like Sweetbriar in Lynchburg and the State Teachers College in Farmville.

Melvin Butler leaned on the Civil Service and War Manpower Commission as hard as he could so that the laboratory might get top priority on the limited pool of qualified applicants. He penned ads for the local newspaper, the Daily Press: “Reduce your household duties! Women who are not afraid to roll up their sleeves and do jobs previously filled by men should call the Langley Memorial Aeronautical Laboratory,” read one notice. The personnel department published fervent pleas in the employee newsletter Air Scoop. “Are there members of your family or others you know who would like to play a part in gaining supremacy of the air?” they wrote. “Have you friends of either sex who would like to do important work toward winning and shortening the war?” With men being absorbed into the military services, with women already being demanded by eager employers, the labor market was as exhausted as the war workers themselves.

A bright spot presented itself in the form of another man’s problem. History would forever associate the black-freedom movement with Martin Luther King Jr.’s name, but as America oriented every aspect of its society toward war for the second time in 30 years, it was A. Philip Randolph’s long-term vision and the specter of a march that never happened that pried open a door that had been closed like a bank vault since the end of Reconstruction. With two strokes of a pen — Executive Order 8802, ordering the desegregation of the defense industry, and Executive Order 9346, creating the Fair Employment Practices Committee to monitor the national project of economic inclusion — Roosevelt primed the pump for a new source of labor to come into the tight production process.

Nearly two years later, as the laboratory’s personnel needs reached the civil service, applications of qualified Negro female candidates began filtering in to the Service Building, presenting themselves for consideration by the laboratory’s personnel staff. No photo advised as to the applicant’s color — that requirement, instituted by the administration of Woodrow Wilson, had been stricken down the year as the Roosevelt administration tried to dismantle discrimination in hiring practices. But their alma maters tipped the hand — West Virginia State University, Howard, Arkansas A&M, Hampton Institute just across town, all Negro schools. Nothing in the applications indicated anything less than fitness for the job. If anything, they came with more experience than the white girls, with many years of teaching experience on top of math or science degrees.

They would need a separate space for them, Melvin Butler knew. Then they would have to appoint someone to head the new group, an experienced girl — white, obviously — someone whose disposition suited the sensitivity of the assignment. With around-the-clock pressure to test the airplanes queued up in the hangar, engineers would welcome the additional hands. So many of the engineers were Northerners, agnostic on the racial issue but devout when it came to mathematical talent.

There had always been Negro employees in the lab — janitors, cafeteria workers, mechanic’s assistants, groundskeepers. But opening the door to Negroes who would be considered professional peers, that was something new.

Butler proceeded with discretion: no big announcement in the Daily Press, no fanfare in Air Scoop. But he also proceeded with direction: nothing to herald the arrival of the Negro women to the laboratory, but nothing to derail their arrival either. Maybe Melvin Butler was progressive for his time and place, or maybe he was just a functionary carrying out his duty. Maybe he was both. State law — and Virginia custom — kept him from truly progressive action, but perhaps the promise of a segregated office was just the cover he needed to get the black women in the door, a Trojan horse of segregation opening the door to integration.

The shuttle bus made the West Side rounds, stopping to deposit Dorothy at the front door of an outpost called the Warehouse Building.

There was nothing to distinguish the building or its offices from any of the other unremarkable spaces on the laboratory’s register: same narrow windows with a view of the fevered construction taking place outside, same office-bright ceiling lights, same government-issue desks arranged classroom style. Even before she walked through the door that would be her workaday home for the duration, she could hear the music of the calculating machines inside the room: a click every time its minder hit a key to enter a number, a drumbeat in response to an operations key, a full drumroll as the machine ran through a complex calculation; the cumulative effect sounded like the practice room of a military band’s percussion unit. The arrangement played in all the rooms where women were engaged in aeronautical research at its most granular level, from the central computing pool over on the East Side to the smaller groups of computers attached to specific wind tunnels or engineering groups. The only difference between the other rooms at Langley and the one that Dorothy walked into was that the women sitting at the desks, plying the machines for answers to the question “What makes things fly?,” were black.

Dorothy took a seat as the women greeted her over the din of the calculating machines; she knew without needing to ask that they were all part of the same confederation of black colleges, alumni associations, civic organizations, and churches. Many of them belonged to Greek letter organizations like Delta Sigma Theta or Alpha Kappa Alpha, which Dorothy had joined at Wilberforce. By securing jobs in Langley’s West Computing section, they now had pledged one of the world’s most exclusive sororities. In 1940, just 2 percent of all black women earned college degrees, and 60 percent of those women became teachers, mostly in public elementary and high schools. Exactly zero percent of those 1940 college graduates became engineers. And yet, in an era when just 10 percent of white women and not even a full third of white men had earned college degrees, the West Computers had found jobs and each other at the “single best and biggest aeronautical research complex in the world.

After 12 years at the head of the classroom, the tables had turned, and for the first time since graduating from Wilberforce University, Dorothy Vaughan gave herself fully to the discipline that had most engaged her youthful mind. She had come full circle and then some, as she tried to attune her ear to the argot that flew back and forth between the inhabitants of the laboratory, all seeking to answer the fundamental question “What makes things fly?” Dorothy herself had never flown on a plane — something she shared with more than 98 percent of all Americans — and in all likelihood, before landing at Langley, she had never given the question more than a passing consideration.

For seven months Dorothy Vaughan apprenticed as a mathematician, growing more confident with the concepts, the numbers and the people at Langley. Her work was making a difference in the outcome of the war. And the devastation … she had a part in that as well. Honed to a razor’s edge by the women and men at the laboratory — flying farther, faster, and with a heavier bomb load than any plane in history — B-29s dropped precision bombs over the country of Japan from high in sky. They brought destruction at close range with incendiary bombs, and they released annihilation — and a new, modern fear — with the atomic bombs that they delivered. War, technology, and social progress — it seemed that the second two always came with the first. The NACA’s work — work intense and interesting as she never would have imagined — would remain her work for the duration.

When the war ended three years later, nearly to a woman, the West Computers had decided they were going to hold on to their seats, whatever it took. Black or white, East or West, single or married, mothers or childless, women were now a fundamental part of the aeronautical-research process.

Not a year after the end of the war, the familiar announcements of vacancies at the laboratory, including openings for computers, began to appear in the newsletter again. As the United States downshifted from a flat-out sprint to victory to a more measured pace of economic activity, and as the laboratory began to forget that it had ever operated without the female computers, Dorothy had time to pause and give consideration to what a long-term career as a mathematician might look like.

How could she entertain the idea of returning to Farmville and giving up a job she was good at, that she enjoyed, that paid two or three times more than teaching? Working as a research mathematician at Langley was a very, very good black job — and it was also a very, very good female job. The state of the aeronautics industry was strong, and the engineers were just as interested in retaining the services of the women who did the calculations as the aircraft manufacturers had been in keeping the laundry workers who supported their factory workers on the job.

A new future stretched out before them, but Dorothy Vaughan and the others found themselves at the beginning of a career, with few role models to follow to its end. Just as they had learned the techniques of aeronautical research on the job, the ambitious among them would have to figure out for themselves what it would take to advance as a woman in a profession that was built by men.

Dorothy Vaughan might have eventually lobbied for a job working directly for an engineering section. As a supervisor she came into contact with engineers from a variety of groups, some of whom came to the office insisting that she personally handle their jobs. In 1949, however, the death of her white supervisor would bind Dorothy to the West Area computing office for the next decade.

A June 3, 1949, note in Air Scoop was brusque: “Blanche Sponsler Fitchett, Head of West Computing Section, died last Sunday after a six-month illness.” The cause of her death, not revealed in the note or in her obituary in the Daily Press, was entered on her death certificate as “dementia praecox.” Whether Blanche died as a result of treatments designed to cure an illness that would eventually become known as schizophrenia or from suicide or another cause altogether was known only to her doctors and family.

Blanche’s absence left West Computing with an empty desk, but not a vacuum. It wasn’t the way Dorothy would have wanted to take the next step in her career, but Blanche’s tragedy pushed her up the ladder nonetheless. In April 1949, six weeks after Blanche left the office for the last time, the laboratory appointed Dorothy Vaughan acting head of West Computing.

There were limited ways for a white computer to break into management at Langley. Finding a way to move from being one of the girls to one of the Head Girls took time and persistence, pluck and luck, and there were only so many slots available: while even lower-level male managers might supervise the work of female computers, it was simply unthinkable for a man to report to a woman. Women with an eye on a management job were limited to heading a section in one of the now-decentralized computing pools or in another division with many female employees, such as personnel.

For a black woman, there was exactly one track: It began at the back of the West Area computing office and ended at the front, where Dorothy Vaughan now sat. The view from the supervisor’s desk, with the rows of brown faces looking back at their new boss, wasn’t that different from being at the head of the classroom at Moton: The segregation laws of the state applied just as vigorously to the roomful of highly educated college graduates as they did to the rural black students of Prince Edward County. Yet with its bright lights, government-issue desks, late-model calculating machines, and proximity to tens of millions of dollars’ worth of aeronautical research tools, West Computing was a world away from Moton High School’s deficient building, rundown chairs, worn-out textbooks, and general sense of powerlessness.

It would take Dorothy Vaughan two years to earn the full title of section head. The men she now worked for — Rufus House was her new supervisor — held her in limbo, waiting either until a more acceptable candidate presented herself or until they were confident she was fit to execute the job on a permanent basis. Or maybe the idea of installing the first black manager in all of the NACA’s expanding national empire caused them to demur, lest they stoke the racial anxieties among members of the laboratory and in the town.

Whatever skepticism might have existed among the powers that be about Dorothy’s qualifications, whatever lobbying and advocacy may have been required on Dorothy’s part, the outstanding issue was resolved by a memo that circulated in January 1951. “Effective this date, Dorothy J. Vaughan, who has been acting head of the West Area Computers unit, is hereby appointed head of that unit.” Dorothy must have known it. Her girls and her peers knew it. Many of the engineers knew it, and her bosses eventually came to the same conclusion. History would prove them all right: There was no one better qualified for the job than Dorothy Vaughan.

From the forthcoming book HIDDEN FIGURES: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race, by Margot Lee Shetterly. Copyright ©2016 by Margot Lee Shetterly. To be published on September 6, 2016, by William Morrow, an imprint of HarperCollins Publishers. Excerpted by permission.