Power in Numbers: Katherine G. Johnson

Dr. Talithia Williams is an Associate Professor of Mathematics at Harvey Mudd College and cohost of the PBS series NOVA Wonders, premiering in April 2018. Her upcoming book, Power in Numbers: The Rebel Women of Mathematics, takes aim at the forgotten influence of women on the development of mathematics over the last two millennia. Here’s the story of NASA mathematician Katharine G. Johnson. Sound familiar? You may know her from the Oscar-nominated movie, Hidden Figures.

Katharine G. Johnson

b. August 26, 1918

Lives Depended on the Accuracy of Her Calculations

“Everybody was concerned about them getting there. We were concerned about them getting back.”—Katherine G. Johnson on the Apollo 13 mission

The mathematical calculations that sent Alan Shepard into space—and safely brought him home—were a matter of life and death. It was Katherine Johnson whose painstaking precision guided that 1961 mission, Freedom. Her work was essential to sending the first American into space and to America’s successful space program overall. The youngest of four children, Johnson (born Katherine Coleman in 1918) was the daughter of a lumberman and a teacher and grew up in West Virginia. Signs of her mathematical talent became apparent at an early age. She told author and interviewer Margot Lee Shetterly, “I counted everything. I counted the steps to the road, the steps up to church, the number of dishes and silverware I washed . . . anything that could be counted, I did.” Johnson was so academically advanced that by age ten she was ready for high school. At fifteen she entered West Virginia State College, where she studied English, French, and mathematics.

One of her professors, W. W. Schieffelin Claytor, the third African American to earn a PhD in mathematics, told Johnson that she would make a great mathematician and offered to help her become one, even going so far as to create a course on the analytic geometry of space just for her. Johnson recognized his contribution to her success: “Many professors tell you that you’d be good at this or that, but they don’t always help you with that career path. Professor Claytor made sure I was prepared to be a research mathematician.”³

In 1937, at the age of eighteen, Johnson graduated summa cum laude with two bachelor’s degrees: one in mathematics and one in French. She began teaching at an African American public school (one of the only options open to her at the time). She left teaching after two years when she was offered a spot at West Virginia University as part of the state’s decision to integrate its graduate schools. Katherine left the graduate program early, however, to start a family with her husband, James Goble. Goble and Johnson had three daughters before he died of a brain tumor in 1956.

At a family gathering in 1952, Johnson learned that the National Advisory Committee for Aeronautics (NACA) was hiring mathematicians for its Guidance and Navigation Department. She was hired in 1953 and moved with her family to be near the Langley Memorial Aeronautical Laboratory in Hampton, Virginia. There she performed mathematical calculations, including analyzing data from flight tests, along with other women in the “pool.” Her extensive knowledge of analytic geometry as well as her inquisitive nature led to a temporary assignment on an all-male flight research team. She became an invaluable member, attending editorial meetings (a taboo for women at that time) and contributing to various projects. There she performed mathematical calculations from 1953 to 1958 in the West Area computer section and the Guidance and Control Division of Langley’s Flight Research Division.

Despite the fact that all those working at the division did research, Johnson and the other African American women in the computing pool had a work area—“Colored Computers”—separate from their white counterparts. Although NASA disbanded segregated work areas in 1958, disparities remained. Johnson recalled:

In the early days of NASA, women were not allowed to put their names on the reports—no woman in my division had had her name on a report. I was working with Ted Skopinski and he wanted to leave and go to Houston . . . but Henry Pearson, our supervisor—he was not a fan of women—kept pushing him to finish the report we were working on. Finally, Ted told him, ‘Katherine should finish the report, she’s done most of the work anyway.’ So Ted left Pearson with no choice; I finished the report and my name went on it, and that was the first time that a woman in our division had her name on something.

In 1959, Johnson married Colonel James A. Johnson, a veteran of the Korean War. She contributed to the mathematics of the 1958 document Notes on Space, which featured lectures given by engineers in the Flight Research Division and the Pilotless Aircraft Research Division. The core of the Space Task Group was made up of engineers from these divisions, and Katherine Johnson, who had worked with many of them, joined the program as NACA became NASA in 1958. Not only did she calculate the trajectory for Alan Shepard’s May 5, 1961, spaceflight, but her work helped to ensure that the Freedom 7 Mercury capsule would be quickly found after landing, using the accurate trajectory that had been established. Johnson also calculated the launch window for Shepard’s 1961 Mercury mission and performed calculations for a planned mission to Mars.

So trusted was Johnson as a mathematician that when NASA used electronic computers for the first time to calculate John Glenn’s orbit around Earth, Glenn requested that Johnson verify the computer’s numbers by hand on her desktop mechanical calculating machine. The computers had been programmed with the orbital equations that would control the trajectory of the capsule in Glenn’s Friendship 7 mission, from blastoff to splashdown, but the astronauts were leery of the electronic calculating machines, which were prone to hiccups and blackouts. Thanks in large part to Johnson, Glenn’s flight was a success, and marked a pivotal moment in the Space Race between the US and the Soviet Union.

Johnson also helped to calculate the trajectory for the 1969 Apollo 11 flight to the moon. In 1970, she worked on the Apollo 13 moon mission as well. When the mission was aborted after two oxygen tanks exploded, Johnson had to calculate a safe route for the astronauts still on board. She described this moment in a 2010 interview: “Everybody was concerned about them getting there. We were concerned about them getting back.” Her work on Apollo 13 helped to establish a one- star observation system that would allow astronauts to determine their location in space with accuracy.

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Prepare to be inspired. Power in Numbers: The Rebel Women of Mathematics is a full-color volume that takes aim at the forgotten influence of women on the development of mathematics over the last two millennia.

You’ll see each eminent mathematician come to life on each page, women like the astronomer-philosopher Hypatia, theoretical physicist Emmy Noether, and rocket scientist Annie Easley.

Power in Numbers: The Rebel Women of Mathematics is an affirmation of female genius and a celebration of the boundless applications of mathematics. See their stories!