WASHINGTON — When Katherine Johnson began working at the National Advisory Committee for Aeronautics in 1953, she was classified as ‘‘subprofessional,’’ not far outranking a secretary or janitor.
Hers was a labor not of scheduling or cleaning but rather of mathematics: using a slide rule or mechanical calculator in complex equations to check the work of her superiors — engineers who, unlike her, were white and male.
Her title, poached by the technology that would soon make the services of many of her colleagues obsolete, was ‘‘computer.’’
Mrs. Johnson, who died Monday at 101, went on to develop equations that helped the NACA’s successor, NASA, send astronauts into orbit and, later, to the moon. In 26 signed reports for the space agency, and in many more papers that bore others’ signatures on her work, she codified mathematical principles that remain at the core of manned space travel.
She was not the first black woman to work as a NASA mathematician, but Mrs. Johnson was eventually recognized as a pathbreaker for women and Blacks in the newly created field of space flight.
Like most backstage members of the space program, Mrs. Johnson was overshadowed in the popular imagination by the life-risking astronauts whose flights she calculated, and to a lesser extent by the department heads under whom she served.
She did not command mainstream attention until President Obama awarded her the Presidential Medal of Freedom — the country’s highest civilian honor — in 2015. “Katherine G. Johnson refused to be limited by society’s expectations of her gender and race while expanding the boundaries of humanity’s reach,” the president said.
The next year, her research was celebrated in the best-selling book ‘‘Hidden Figures’’ by Margot Lee Shetterly and the Oscar-nominated film adaptation with Taraji Henson, Octavia Spencer, and Janelle Monáe.
Mrs. Johnson was ‘‘critical to the success of the early US space programs,’’ Bill Barry, NASA’s chief historian, said in a 2017 interview for this obituary. ‘‘She had a singular intellect, curiosity, and skill set in mathematics that allowed her to make many contributions, each of which might be considered worthy of a single lifetime.’’
A math prodigy from West Virginia who said she ‘‘counted everything’’ as a child — ‘‘the steps to the road, the steps up to church, the number of dishes and silverware I washed’’ — Mrs. Johnson worked as a teacher before becoming a computer at the NACA’s flight research division, based in Hampton, Va.
The agency was established in 1915 and began hiring white women to work as computers 20 years later. Black computers were first hired during the labor shortage of World War II. Mrs. Johnson was one of about 100 computers, roughly one-third of whom were black.
As Mrs. Johnson herself was fond of saying, her tenure at Langley — from 1953 until her retirement in 1986 — was “a time when computers wore skirts.”
For some years at midcentury, the black women who worked as computers were subjected to a double segregation: Consigned to separate office, dining, and bathroom facilities, they were kept from the larger group of white women who worked as NASA mathematicians. The white women in turn were segregated from the male mathematicians and engineers.
But over time, the work of Mrs. Johnson and her colleagues — myriad calculations done mainly by hand — won them a level of acceptance that for the most part transcended race.
“NASA was a very professional organization,” Mrs. Johnson told The Observer of Fayetteville, N.C., in 2010. “They didn’t have time to be concerned about what color I was.”
Nor, she said, did she.
“I don’t have a feeling of inferiority,” she would say. “Never had. I’m as good as anybody, but no better.”
Mrs. Johnson, who had a bachelor’s degree in mathematics, spent her early career studying data from plane crashes to help devise safety standards, at a time when the agency’s central concern was aviation.
The only black member of the flight research division, she quickly demonstrated that she was armed with an invaluable asset. “The guys all had graduate degrees in mathematics; they had forgotten all the geometry they ever knew,” Mrs. Johnson told the Fayetteville Observer interview. “I still remembered mine.”
She remained in the division for the rest of her career.
Then, in 1957, the launch of the Soviet satellite Sputnik thrust the space race into full tilt. One of rocket science’s most vexing challenges, they soon realized, was calculating flight trajectories to ensure that astronauts returned safely, splashing down in the ocean reasonably close to a Navy vessel.
“As NASA got ready to put someone in space, they needed to know what the launch conditions were,’’ she told the Associated Press. “It was our assignment to develop the launch window and determine where it was going to land.”
Their work was secret — at times even from the mathematicians themselves.
Mrs. Johnson and dozens of colleagues wrote a 600-page technical report titled ‘‘Notes on Space Technology’’ outlining the mathematical underpinnings of space flight, from rocket propulsion to orbital mechanics and heat protection.
For astronauts such as Alan B. Shepard Jr., who became the first American in space when Freedom 7 launched on May 5, 1961, the math was relatively straightforward. Shepard’s craft rose and fell, like a champagne cork, without entering orbit.
Calculating the trajectory for an orbital flight, such as the one to be undertaken by Marine pilot John Glenn in 1962, was ‘‘orders of magnitude more complicated,’’ Shetterly said in an interview.
‘‘I said, ‘Let me do it,’” Mrs. Johnson recalled in a NASA interview. ‘‘You tell me when you want it and where you want it to land, and I’ll do it backwards and tell you when to take off.’’
Mrs. Johnson’s findings, outlined in a 1960 paper she wrote with engineer Ted Skopinski, enabled NASA to determine exactly when to launch a spacecraft and when to begin its reentry. The paper, ‘‘Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position,’’ marked the first time a woman wrote a technical report in the research division.
‘‘You could work your teeth out, but you didn’t get your name on the report,’’ she said in the 1992 oral history, crediting her breakthrough to what she described as an assertive personality. When a superior said that she could not accompany male colleagues to a briefing related to her work, Mrs. Johnson asked, ‘‘Is there a law that says I can’t go?’’ Her boss relented.
Mrs. Johnson’s handwritten calculations were said to have been more trusted than those performed by microprocessors. A short time before Glenn launched into space, he asked engineers to ‘‘get the girl to check the numbers.’’
‘‘All the women were called ‘the girls,’’’ said Barry, ‘‘and everyone knew exactly which girl he was talking about.’’ Mrs. Johnson spent a day and a half checking the trajectory calculations made by the IBM computer before giving the go-ahead to Glenn, who became the first American astronaut to orbit the Earth.
In a subsequent report, Mrs. Johnson took her calculations one step further, working with several colleagues to determine how a spacecraft could move in and out of a planetary body’s orbit. Her formulas were crucial to the success of the Apollo lunar program and are still in use today, Barry said. ‘‘If we go back to the moon, or to Mars, we’ll be using her math.’’
She routinely logged 16-hour days, once falling asleep at the wheel of her car and waking up at the side of the road.
But the work engaged her deeply.
“I loved every single day of it,” she told Shetterly. “There wasn’t one day when I didn’t wake up excited to go to work.”
Katherine Coleman was born in White Sulphur Springs, W.Va. Her mother was a former teacher. She credited her proclivity for numbers to her father, a farmer who had worked in the lumber industry and could quickly calculate the number of boards a tree could yield.
By 10, Katherine had finished all the course work offered at her town’s two-room schoolhouse. Joined by her mother and her three older siblings, she moved to Institute to attend the laboratory school of West Virginia State College while her father remained at home to support the family.
Mrs. Johnson went on to study at West Virginia State, a historically black college, with plans to major in French and English and become a teacher. A mathematics professor — W.W. Schiefflin Claytor, widely reported to be the third Black to receive a doctorate in math — persuaded her to change fields.
Mrs. Johnson recalled his saying: ‘‘You’d make a good research mathematician, and I’m going to see that you’re prepared.’’ She had never heard of the position. ‘‘I said, ‘Where will I get a job?’ And he said, ‘That will be your problem.’’’
After graduating in 1937, at 18, she taught at a segregated elementary school in Marion, Va., near North Carolina.
Three years later, she was one of three black students selected to integrate West Virginia University’s graduate programs. She dropped out of her master’s in mathematics program after one semester to start a family with her husband, James Goble, a chemistry teacher.
Goble died of cancer in 1956. She married James Johnson, an Army officer, three years later. She leaves two daughters, Joylette Hylick and Katherine Moore; six grandchildren; and 11 great-grandchildren. Another daughter, Connie Garcia, died in 2010; her second husband died last year.
After the release of ‘‘Hidden Figures,’’ Mrs. Johnson played down the importance of her role in the early years of the space program. ‘‘There’s nothing to it — I was just doing my job,’’ she told The Washington Post in 2017.
‘‘They needed information, and I had it, and it didn’t matter that I found it,’’ she added. ‘‘At the time, it was just a question and an answer.’’
Material from The New York Times was used in this obituary