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They asked Katherine Johnson for the moon, and she gave it to them.

Wielding little more than a pencil, a slide rule and one of the finest mathematical minds in the country, Johnson — who died at 101 on Monday at a retirement home in Newport News, Va. — calculated the precise trajectories to let Apollo 11 land on the moon in 1969 and, after Neil Armstrong's history-making moonwalk, let it return to Earth.

A single error, she knew, could have dire consequences. Her impeccable calculations had already helped plot the successful flight of Alan Shepard, who became the first American in space in 1961. The next year, she likewise helped make it possible for John Glenn to become the first American to orbit the Earth.

Yet throughout Johnson's 33 years in NASA's Flight Research Division — the office from which the U.S. space program sprang — and for decades afterward, almost no one knew her name.

She was one of several hundred rigorously educated, supremely capable yet largely unheralded women who worked as NASA mathematicians. But it was not only her sex that kept her long marginalized and long unsung: Katherine Coleman Goble Johnson, a West Virginia native who began her scientific career in the age of Jim Crow.

Johnson became the most celebrated of the small cadre of black women — perhaps three dozen — who at midcentury served as mathematicians for the space agency and its predecessor, the National Advisory Committee for Aeronautics.

Their story was told in the 2016 Hollywood film "Hidden Figures," based on Margot Lee Shetterly's nonfiction book of the same title, published that year. The movie starred Taraji P. Henson as Johnson, the film's central figure. It also starred Octavia Spencer and Janelle Monáe as her real-life colleagues Dorothy Vaughan and Mary Jackson.

In January 2017, "Hidden Figures" received the Screen Actors Guild Award for outstanding performance by a cast in a motion picture.

The film was nominated for three Oscars, including best picture. Though it won none, the 98-year-old Johnson received a sustained standing ovation when she appeared onstage with the cast at the Oscars ceremony that February.

Of the black women at the center of the film, Johnson was the only one still living at the time of its release. By then, she had become the best-known member of her formerly unknown cohort.

Medal of Freedom

In 2015, President Barack Obama awarded her the Presidential Medal of Freedom, proclaiming, "Katherine G. Johnson refused to be limited by society's expectations of her gender and race while expanding the boundaries of humanity's reach."

In 2017, NASA dedicated a building in her honor, the Katherine G. Johnson Computational Research Facility, at its Langley Research Center in Hampton, Va.

She "helped our nation enlarge the frontiers of space," NASA Administrator Jim Bridenstine said Monday, "even as she made huge strides that also opened doors for women and people of color in the universal human quest to explore space."

As Johnson herself was fond of saying, her tenure at Langley — from 1953 until her retirement in 1986 — was "a time when computers wore skirts."

At one point, the black women who worked as "computers" were subjected to a double segregation: Consigned to separate office, dining and bathroom facilities, they were kept separate from the much larger group of white women who also worked as NASA mathematicians. The white women, in turn, were segregated from the agency's male mathematicians and engineers.

But over time, the work of Johnson and her colleagues — myriad calculations done mainly by hand, using slide rules, graph paper and clattering desktop calculating machines — won them a level of acceptance that for the most part transcended race.

"NASA was a very professional organization," 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," Johnson said on at least one occasion. "Never had. I'm as good as anybody, but no better."

Creola Katherine Coleman was born Aug. 26, 1918, in White Sulphur Springs, W. Va. From her earliest childhood Katherine counted things: the number of dishes in the cupboard, the number of steps on the way to church and, as insurmountable a task as it might pose for one old enough to be daunted, the number of stars in the sky.

"I couldn't wait to get to high school to take algebra and geometry," Johnson told the Associated Press in 1999.

She is survived by two daughters; six grandchildren; and 11 great-grandchildren. Her second husband, James Johnson, died in 2019.