Katherine Johnson: The Human Computer Who Sent America to Space

23 March, 2026 Siobhan Marie Day 0 Comments 3 categories

When astronaut John Glenn prepared to become the first American to orbit the Earth in 1962, he did not place his trust solely in machines. Instead, he asked for something far more human—and far more precise: “Get the girl to check the numbers.” The “girl” was Katherine Johnson—a mathematician whose calculations would help determine whether Glenn’s spacecraft would successfully return to Earth or vanish into orbit. At a time when computers were still viewed with skepticism, Johnson’s mathematical authority carried decisive weight. Yet her story is not merely one of technical brilliance. It is a case study in institutional invisibility, racial and gender barriers, and the delayed recognition of intellectual labor that powered one of the most celebrated achievements in American history: the Space Race. This is not just the story told in Hidden Figures. This is the deeper history—where precision met prejudice, and where genius went unrecognized for decades.

The Mind Behind the Mission

Born: Aug. 26, 1918 Died: Feb. 24, 2020 Hometown: White Sulphur Springs, WV Education: B.S., Mathematics and French, West Virginia State College, 1937 Hired by NACA: June 1953 Retired from NASA: 1986 Actress Playing Role in Hidden Figures: Taraji P. Henson Biography by Margot Lee Shetterly Being handpicked to be one of three black students to integrate West Virginia’s graduate schools is something that many people would consider one of their life’s most notable moments, but it’s just one of several breakthroughs that have marked Katherine Johnson’s long and remarkable life. Born in White Sulphur Springs, West Virginia, in 1918, her intense curiosity and brilliance with numbers vaulted her ahead several grades in school. By 13, she was attending the high school on the campus of historically black West Virginia State College. At 18, she enrolled in the college itself, where she made quick work of the school’s math curriculum and found a mentor in math professor W. W. Schieffelin Claytor, the third African American to earn a PhD in mathematics. She graduated with highest honors in 1937 and took a job teaching at a black public school in Virginia. More stories on Katherine Johnson When West Virginia decided to quietly integrate its graduate schools in 1939, West Virginia State’s president, Dr. John W. Davis, selected her and two men to be the first black students offered spots at the state’s flagship school, West Virginia University. She left her teaching job and enrolled in the graduate math program. At the end of the first session, however, she decided to leave school to start a family with her first husband, James Goble. She returned to teaching when her three daughters got older, but it wasn’t until 1952 that a relative told her about open positions at the all-black West Area Computing section at the National Advisory Committee for Aeronautics’ (NACA’s) Langley laboratory, headed by fellow West Virginian Dorothy Vaughan. Katherine and her husband decided to move the family to Newport News, Virginia, to pursue the opportunity, and Katherine began work at Langley in the summer of 1953. Just two weeks into her tenure in the office, Dorothy Vaughan assigned her to a project in the Maneuver Loads Branch of the Flight Research Division, and Katherine’s temporary position soon became permanent. She spent the next four years analyzing data from flight tests and worked on the investigation of a plane crash caused by wake turbulence. As she was wrapping up this work her husband died of cancer in December 1956. The 1957 launch of the Soviet satellite Sputnik changed history—and Johnson’s life. In 1957, she provided some of the math for the 1958 document Notes on Space Technology, a compendium of a series of 1958 lectures given by engineers in the Flight Research Division and the Pilotless Aircraft Research Division (PARD). Engineers from those groups formed the core of the Space Task Group, the NACA’s first official foray into space travel. Johnson, who had worked with many of them since coming to Langley, “came along with the program” as the NACA became NASA later that year. She did trajectory analysis for Alan Shepard’s May 1961 mission Freedom 7, America’s first human spaceflight. In 1960, she and engineer Ted Skopinski coauthored Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position, a report laying out the equations describing an orbital spaceflight in which the landing position of the spacecraft is specified. It was the first time a woman in the Flight Research Division had received credit as an author of a research report. In 1962, as NASA prepared for the orbital mission of John Glenn, Johnson was called upon to do the work that she would become most known for. The complexity of the orbital flight had required the construction of a worldwide communications network, linking tracking stations around the world to IBM computers in Washington, Cape Canaveral in Florida, and Bermuda. The computers had been programmed with the orbital equations that would control the trajectory of the capsule in Glenn’s Friendship 7 mission from liftoff to splashdown, but the astronauts were wary of putting their lives in the care of the electronic calculating machines, which were prone to hiccups and blackouts. As a part of the preflight checklist, Glenn asked engineers to “get the girl”—Johnson—to run the same numbers through the same equations that had been programmed into the computer, but by hand, on her desktop mechanical calculating machine. “If she says they’re good,’” Katherine Johnson remembers the astronaut saying, “then I’m ready to go.” Glenn’s flight was a success, and marked a turning point in the competition between the United States and the Soviet Union in space. When asked to name her greatest contribution to space exploration, Johnson would talk about the calculations that helped synch Project Apollo’s Lunar Module with the lunar-orbiting Command and Service Module. She also worked on the Space Shuttle and the Earth Resources Technology Satellite (ERTS, later renamed Landsat) and authored or coauthored 26 research reports. She retired in 1986, after 33 years at Langley. “I loved going to work every single day,” she said. In 2015, at age 97, Johnson added another extraordinary achievement to her long list: President Barack Obama awarded her the Presidential Medal of Freedom, America’s highest civilian honor. She died on Feb. 24, 2020. NASA Administrator James Bridenstine said, “Our NASA family is sad to learn the news that Katherine Johnson passed away this morning at 101 years old. She was an American hero and her pioneering legacy will never be forgotten.”

Katherine Johnson’s mathematical contributions were foundational to NASA’s early space missions. Her work on orbital mechanics enabled the precise calculation of spacecraft trajectories—an area where even minor errors could prove catastrophic.

Johnson, once known as a human computer, reviews calculations done by a physical computer, at NASA’s Langley laboratory. PHOTO: NASA

Katherine Johnson’s work on the Apollo mission trajectories was the pinnacle of her 33-year career at NASA, where she served as a "human computer". Her mathematical precision was so trusted that she was often called upon to manually verify the outputs of the agency's new electronic computers before high-stakes launches. Key Contributions to Project Apollo Apollo 11 Moon Landing (1969): Johnson calculated the complex trajectories needed to get the spacecraft to the Moon and, crucially, the rendezvous paths between the Lunar Module and the orbiting Command and Service Module for the return trip to Earth. She considered this work her greatest accomplishment. Apollo 13 Emergency (1970): After an oxygen tank explosion crippled the spacecraft, Johnson’s work on backup navigation procedures and charts was used to plot a safe return path for the crew. She helped develop a one-star observation system that allowed astronauts to determine their location accurately without the use of malfunctioning onboard computers. Trajectory Equations: She utilized Euler's Method to solve the differential equations required for orbital mechanics, which involved approximating complex paths through numerous small, finite steps. Early Work & Trust: Before her Apollo contributions, she calculated the trajectory for Alan Shepard's 1961 suborbital flight and famously hand-verified the orbital equations for John Glenn's 1962 mission at his personal request. Wikipedia Wikipedia +8 Impact and Recognition Despite working in a segregated environment at the Langley Research Center, Johnson's work became a foundational part of NASA's mission design. Her legacy was popularized by the book and film Hidden Figures and recognized with the Presidential Medal of Freedom in 2015.

When astronaut John Glenn prepared to become the first American to orbit the Earth in 1962, he did not place his trust solely in machines. Instead, he asked for something far more human — and far more precise:

“Get the girl to check the numbers.”

John Herschel Glenn, Jr. was born July 18, 1921, in Cambridge, Ohio, but considers New Concord, Ohio his permanent home. The son of a plumbing contractor, he attended primary and high schools in New Concord then received a Bachelor of Science degree from Muskingum College there. Glenn entered the Naval Aviation Cadet Program in March 1942, graduating a year later with a commission in the Marine Corps. After advanced training, he joined Marine Fighter Squadron 155 and spent a year flying F4U fighters in the Marshall Islands, including 59 combat missions against the Japanese. After World War II, he was a member of Fighter Squadron 218 on North China patrol and was also stationed in Guam. From June 1948 to December 1950 John Glenn was an instructor in advanced flight training at Corpus Christi, Texas. He then attended Amphibious Warfare School at Quantico, Virginia. In the Korean War, he flew 63 combat missions with Marine Fighter Squadron 311 and 27 while an exchange pilot with the Air Force in F-86 Sabrejets. In the last nine days of fighting in Korea, he downed three enemy jets. After the war, Glenn attended Test Pilot School at the Naval Air Test Center, Patuxent River, Maryland. He was next assigned to the Fighter Design Branch of the Navy Bureau of Aeronautics in Washington from November 1956 to April 1959, during which time he also attended the University of Maryland. In April 1959, Glenn was selected as one of the original seven astronauts for Project Mercury and assigned to the National Aeronautics and Space Administration (NASA) Space Task Group at Langley Research Center in Hampton, Virginia. The Group was moved to Houston and became part of NASA’s Manned Spacecraft Center in 1962. As NASA’s third manned mission, John Glenn and his Friendship 7 spacecraft were launched from Cape Canaveral, now the Kennedy Space Center (KSC), Florida on February 20, 1962. He completed three orbits of the Earth, reaching a maximum altitude of approximately 162 statute miles and an orbital velocity of approximately 17,500 miles per hour. The Mercury spacecraft landed safely in the Atlantic Ocean, 800 miles southeast of Cape Canaveral after a flight of four hours and 55 minutes. As the first American astronaut to orbit the Earth, John Glenn was the nation’s newest hero. Glenn resigned from the Manned Spacecraft Center on January 16, 1964. He retired from the Marine Corps with the rank of colonel on January 1, 1965. Glenn was a business executive from 1965 until his election to the United States Senate as a Democrat from Ohio in November 1974. John Glenn retired from the U.S. Senate in January 1999 after serving four terms. At age 77, John Glenn became the oldest person to travel to outer space when he blasted off from KSC aboard STS-95 Discovery on October 29, 1998. During the mission, the shuttle crew supported a variety of research payloads, including the deployment of the Spartan solar-observing spacecraft, the Hubble Space Telescope Orbital Systems Test Platform, while also conducting investigations on space flight and the aging process. The mission ended with a landing at KSC on November 7, 1998 after 134 Earth orbits, having traveling 3.6 million miles in 213 hours and 44 minutes. In his two flights, Colonel Glenn logged over 218 hours in space. He holds the record for the longest time between space flights at 38 years and two months. John Glenn earned the Distinguished Flying Cross on six occasions and holds the Air Medal with 18 Clusters for his service during World War II and Korea. He also holds the Navy Unit Commendation for service in Korea, the Asiatic-Pacific Campaign Medal, the American Campaign Medal, the World War II Victory Medal, the China Service Medal, the National Defense Service Medal, the Korean Service Medal, the United Nations Service Medal, the Korean Presidential Unit Citation, the Navy’s Astronaut Wings, the Marine Corps’ Astronaut Medal, and the NASA Distinguished Service Medal, In 1978 he was one of the six original recipients of the Congressional Space Medal of Honor, for his Friendship 7 mission.

The “girl” was Katherine Goble Johnson — a mathematician whose calculations would help determine whether Glenn’s spacecraft would successfully return to Earth or vanish into orbit. At a time when computers were still viewed with skepticism, Johnson’s mathematical authority carried decisive weight.

Katherine Johnson at her desk with a calculating machine and a special glober known as a celestial trianing device. Photo Credit: NASA

Yet her story is not merely one of technical brilliance. It is a case study in institutional invisibility, racial and gender barriers, and the delayed recognition of intellectual labor that powered one of the most celebrated achievements in American history: the Space Race.

The Space Race began as an arms race between the respective militaries of the United States and the Soviet Union. World War II had demonstrated to the world that rocket technology would drive modern warfare, and as such the U.S. and Russia locked themselves in a race to have the most superior technology. As technology advanced and powerful intercontinental ballistic missiles (ICBMs) were developed by both countries, the arms race gave way to another race—the Space Race. At the start, there were no set rules for the Space Race. What was the goal? What would count as winning? For Americans, President Kennedy's declaration focused the Space Race on a clear goal: landing a man on the Moon before the Soviets. The Space Race became a race to the Moon. Both countries made announcements to launch the first artificial satellite into space, but it was the Soviet Union that brought humanity into the Space Age with their Sputnik satellite, which was successfully launched on October 4, 1957.

This is not just the story told in Hidden Figures. This is the deeper history — where precision met prejudice, and where genius went unrecognized for decades.

Directed by Theodore Melfi, Screenplay by Allison Schroeder, and Theodore Melfi, Based on "Hidden Figures: The American Dream and the Untold Story of the Black Women Who Helped Win the Space Race" by Margot Lee Shetterly, Produced by Donna Gigliotti, Peter Chernin, Jenno Topping, Pharrell Williams, and Theodore Melfi, Starring: Taraji P. Henson, Octavia Spencer, Janelle Monáe, Kevin Costner, Kirsten Dunst, Jim Parsons, Mahershala Ali, Aldis Hodge, and Glen Powell, with Cinematography by Mandy Walker, Edited by Peter Teschner, with Music by Hans Zimmer, Pharrell Williams, and Benjamin Wallfisch, Production companies: Fox 2000 Pictures, Chernin Entertainment, Levantine Films, and Distributed by 20th Century Fox (2016)

📚 Early Life: A Prodigy in the Segregated South

White Sulphur Springs is a city in Greenbrier County, West Virginia, United States. The population was 2,231 at the 2020 census.[4] The city emblem consists of five dandelion flowers and the citizens celebrate spring with an annual Dandelion Festival.[6] History White Sulphur Springs grew in the first half of the nineteenth century as the southern "Queen of the Watering Places". The springs resort first became the standard summer destination for wealthy Virginia Low Country residents seeking reprieve from heat, humidity, and disease of the "sickly season". As its popularity increased and it gained status as a socially exclusive site, the springs attracted elite guests from all over. The resort, now known as The Greenbrier, remains one of the country's most luxurious and exclusive resorts. For many years, Sam Snead was the resort's golf pro and later golf pro emeritus. The resort has another significant place in golf history; in 1979, it hosted the first Ryder Cup to feature the current competitive setup of the United States and European sides. Golf in the United States began near White Sulphur Springs when the Montague family founded Oakhurst Links in 1884, making it the oldest organized golf club in the country. In 2010, the Greenbrier hosted the inaugural PGA Greenbrier Classic.[7] In 1992 The Washington Post reported that, during the Cold War, the resort had been the site of a "bunker", the Emergency Relocation Center known as Project Greek Island, which was intended to house and protect the U.S. Congress in the event of a nuclear attack.[8] In June 2016, there was a historic severe flood in West Virginia that impacted White Sulphur Springs.[9][10][11] The Greenbrier has also served as a training camp location for the Houston Texans, New Orleans Saints, Cleveland Browns, Arizona Cardinals, New England Patriots, and San Francisco 49ers.

Katherine Johnson as a child. (Makers.com)

Katherine Johnson in college. (Makers.com)

Born in 1918 in White Sulphur Springs, West Virginia, Katherine Coleman (later Johnson) demonstrated extraordinary intellectual ability from an early age. By age 10, she had already advanced to high school — an acceleration that would shape the trajectory of her life.

Her father relocated the family 120 miles so she could attend a school for Black students beyond eighth grade. This decision reflects a critical structural reality: access to education for Black children in the early 20th century was not a given — it was engineered through sacrifice.

At just 18, Johnson graduated from West Virginia State College with degrees in mathematics and French. There, she was mentored by mathematician W.W. Schieffelin Claytor, only the third African American to earn a PhD in mathematics. Recognizing her potential, he created specialized coursework just for her.

This is an important corrective to popular narratives: Johnson was not simply “good at math” — she was operating at a level that required custom academic scaffolding.

Schieffelin Claytor's parents were William Oat Claytor (1880-1956) and Simsie Thorne. William Oat Claytor was the fourth child of thirteen children of William Armstead Claytor and Judith Ann Reynolds. Most the thirteen children went on to become farmers, teachers or medical doctors. William Oat Claytor married Simsie E Thorne of Washington, D.C. She had attended the Hampton Normal and Agricultural Institute, at Hampton, Virginia, graduating around 1900. When Schieffelin Claytor, the subject of this biography, was born his father was a vocational arts teacher at the Southern Norfolk Colored Graded School. The unusual name Schieffelin may have been chosen because of William Jay Schieffelin (1866-1955) who was a Republican of the school of Lincoln and strongly advocated the rights and advancement of African-American citizens. William Oat Claytor was awarded a D.D.S. in dentistry from Howard University in 1916. The family lived at 1350 U Street, Washington, D.C. while he studied at Howard University, a street which became famed as the heart of black culture in America. After graduating William Oat Claytor worked for the U.S. Bureau of Engraving and Printing but, by 1920, was working from his home at 1419 Q Street, Northwest in Washington, D.C. In 1928 the family moved to 1710 P Street, Northwest. The family lived in Washington, D.C. throughout the early years of Schieffelin Claytor upbringing, and naturally he attended schools near his home. Later he studied at the Hampton Normal and Agricultural Institute, Virginia, where his mother had studied. He entered Howard University in September 1925 and graduated with a B.S. in mathematics in 1929. There he was taught by Dudley Weldon Woodard who had been awarded a Master's degree in mathematics from the University of Chicago and then taught at College level for over ten years before being appointed to Howard University in 1920. Woodard took the year 1927-28 away from Howard during which time he studied at the University of Pennsylvania for a Ph.D. advised by John Robert Kline (1891-1955). Woodard, the second African-American to be awarded a doctorate in mathematics, returned to Howard University and set up a graduate programme in mathematics. Claytor joined that programme in 1929, the first year it ran, and took the courses offered on group theory, topology, number theory, real analysis and complex analysis. While taking this graduate course, advised by Woodard, he published the solution to a problem on limits in The American Mathematical Monthly in December of 1929. The problem had been posed in the previous year by James Singer, a student of James Waddell Alexander, of the Graduate College at Princeton. Claytor graduated from Howard University with an M.S. in 1930. Woodard had studied for his doctorate under John Robert Kline, who had been a student of Robert L Moore, at the University of Pennsylvania. He advised Claytor to follow the same route and he wrote to the University of Pennsylvania with a strong recommendation that they accept Claytor onto their graduate programme. He was accepted and, in 1930, began to study for his doctorate at the University of Pennsylvania advised by John Robert Kline. Advised to read the latest topology papers, Claytor wrote to Raymond Wilder in April 1931 (see for example [9]):- May I kindly ask for those of your papers of which you still have reprints. Some of your publications will aid me considerably in my thesis work here at Pennsylvania. Claytor's work progressed well and he was awarded a Harrison Scholarship which he held during his second year as a graduate student and he also won a Harrison Fellowship holding these for his final two years of graduate study. Claytor was awarded a Ph.D. on Wednesday, 21 June 1933 for his thesis Topological Immersion of Peanian Continua in a Spherical Surface. It was published in the Annals of Mathematics. With this Claytor became the third African-American to be awarded a Ph.D. in mathematics and the first to have a research paper published. Kline wrote to Robert L Moore in October 1933 and praised Claytor's thesis highly (see for example [9]):- Claytor wrote a very fine thesis. In many ways I think that it is perhaps the best that I have ever had done under my direction. This quality of Claytor's thesis has been fully attested by the number of papers which have continued to reference it and the resulting papers. For example in 2011 Bruce Richter, Brendan Rooney and Carsten Thomassen proved a generalisation of Claytor's results in their paper On planarity of compact, locally connected, metric spaces. One would have expected that someone with such an outstanding thesis would be able to find a university post where his talents could be fully realised. The best he could achieve was a position in West Virginia State College where he taught a bright student Katherine Coleman (better known today by her married name Katherine Johnson). She wrote [3]:- 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. ... Claytor was a young professor himself, and he would walk into the room, put his hand in his pocket, and take some chalk out, and continue yesterday's lesson. But sometimes I could see that others in the class did not understand what he was teaching. So I would ask questions to help them. He'd tell me that I should know the answer, and I finally had to tell him that I did know the answer, but the other students did not. I could tell. But Claytor did far more that simply encourage Katherine, he made sure she took all the right courses and when he realised that she would need a background in analytic geometry that the College did not offer, he simply put on a course just for Katherine. However, a heavy teaching load and taking on extra work to help his students meant he had no time for research. He wrote in 1936 (see for example [9]):- ... in West Virginia my duties, together with the unfortunate local environment, have made it virtually impossible for me to do any effective mathematical work; so much so even, that I have not succeeded in completing a single problem since doing my thesis. Many mathematicians were aware of his predicament and, a year before he wrote the above, Claytor had applied for a National Research Council fellowship to enable him to work with Oswald Veblen at the Institute for Advanced Study and with other topologists such as Solomon Lefschetz at Princeton University. Others working at Princeton in this area were James Alexander, Deane Montgomery, and Leo Zippin so it would have been an excellent place where Claytor would have flourished. However, Princeton University would not accept a "coloured person", the University administration claiming that the students would object. Leo Zippin, who was at Princeton, wrote to Raymond Wilder at the University of Michigan at Ann Arbor trying to have Claytor accepted there:- I had a letter from Kline asking me to write for Claytor ... which I did with great willingness ... and I spoke to Lefschetz and then to Veblen ... . Veblen ... seemed well impressed with Claytor ... He's heard about him for a full year or two. ... Princeton being out ... Claytor will find other places. I don't know of any better one he could find than Michigan ... Claytor did not get a National Research Council fellowship, Gilbert Bliss having voted against an award being made to him. However, he felt he had to leave West Virginia State College and he wrote himself to Wilder seeking a position at the University of Michigan. After due discussions, Michigan decided to offer Claytor a position for a year but without a stipend. They would not charge him lecture or library fees - a small concession. Having some savings, Claytor thought he could survive, with difficulty, for a year without a stipend so accepted Michigan's offer and arranged to have 1936-37 as leave of absence from West Virginia State College. The difficulties for African-Americans at this time is illustrated by discussions which went on about holding a topology conference in 1936-37 at North Carolina. Wilder, when asked by Whyburn about the organisation of this conference, replied:- There are at least two "offcolor" topologists in existence (Woodard and Claytor) who would undoubtedly like to attend, and I wonder if they would feel very comfortable about attending a meeting in North Carolina. I know that not very long ago there was considerable discomfort caused some negro scholars who attended a meeting of some one of the learned societies in the south. I would probably never think of this objection if it hadn't been for the incident just mentioned, and for the fact that Claytor is apparently going to be here next year [1936-1937] to do some post-doctoral work. Kline, when asked his opinion, wrote to Whyburn:- I do not believe either of these men (Woodard and Claytor) will by any means think of going to Durham. ... I think they will not under the circumstances wish to run the risk of any unpleasant feeling by appearing at a meeting in the south. It is unclear whether Claytor did attend this topology meeting (no list of participants exists) but he did attend the American Mathematical Society meeting in December 1936 in Durham and Chapel Hill immediately afterwards. He was not allowed to stay in the conference accommodation and he was given a room in a private hotel. He did present a paper Peanian continua not imbeddable in a spherical surface to the American Mathematical Society meeting which contained new results he had obtained during the summer of 1936 and completed while at the University of Michigan. He published this paper in the Annals of Mathematics, appearing in 1937. Claytor was successful in an application to the Rosenwald Fund and he was informed in April 1937 that he would receive a fellowship of $1500. One of the conditions was that the fellowship could not be taken abroad and he was advised to take it at the Institute for Advanced Study. However, again Princeton University stated that they would not permit any coloured person to go to the Institute for Advanced Study. Claytor decided to remain at the University of Michigan and, another application to the Rosenwald Fund provided a fellowship for a further year so he was able to remain at Ann Arbor until the end of the 1938-39 academic year. Sadly, worries about his uncertain future meant that Claytor found it difficult to concentrate on his research. Raymond Wilder and his colleagues at the University of Michigan, realising the stress that Caytor was under, tried to get him a permanent position there but the university authorities refused. Wilder did manage to get a non-academic position for Claytor at Michigan which enabled him to remain there until 1941, but he was not able to attend research seminars. When the Institute for Advanced Study opened its own building in 1939 they were able to make their own decisions independently of Princeton University and Veblen offered to accept Claytor at the Institute. However, Claytor turned down the offer saying that he did not want to be a guinea pig. Although in April 1941 the United States was not yet involved in World War I, nevertheless Claytor enlisted in the US Army. He spent the war years teaching in Anti-Aircraft Artillery Schools in Virginia and Georgia. After the war ended, he spent the year 1945-46 at the Southern University in Baton Rouge, Louisiana, and the following year at the Hampton Institute. In 1947 he accepted a position at Howard University and, in the following year married Mae Belle Pullins; they had one daughter Melody Rachel Claytor. In the year they married, Mae was awarded a doctorate in psychology from the School of Education at New York University. Claytor continued teaching at Howard University where he regularly taught around 20 hours a week leaving him no time for research. He was only 59 years old and still in post at Howard University when he died in 1967. The National Association of Mathematicians was founded in 1969 with the aim of:- ... the promotion of excellence in the mathematical sciences and the promotion and mathematical development of under-represented minority mathematicians and mathematics students. In 1980 the Association instituted the Claytor Lecture in honour of William Schieffelin Claytor. Let us end this biography by quoting a letter written by Mae Claytor after Claytor's death (see [2]):- I am sorry about being late with this but it is just difficult for me to write about Bill. I am still at the point where I do not like to go back and think. In order to get much of this material, I had to go to what I call our memory books and looking at pictures and sort of reliving Bill; it just hurts a bit too much. I hope this is O.K. There is so much I just cannot put on paper. Even writing about Bill and his presentation at the Math Society, I thought about the days Bill used to tell me how owing to the Black-White mess, he had to stay at a private home when the others were at the hotel where the Association met. Over the years when the colour-line became less, he never would attend any more meetings. J R Kline used to come to see us periodically and try to get Bill to go with him but I guess the hurt went too deeply with him. After he left, I found old papers and letters he had when Kline was trying to get him in Princeton as a Fellow and whew, again it was the colour mess. At Princeton, the administration said the students might object to a "culud" person which was a laugh, they would never have known it. I do hope what I have written is O.K.

At just 18, Johnson graduated from West Virginia State College with degrees in mathematics and French. There, she was mentored by mathematician W.W. Schieffelin Claytor, only the third African American to earn a PhD in mathematics. Recognizing her potential, he created specialized coursework just for her.

NASA’s Project Mercury, culminating in John Glenn’s orbital flight in 1962, represented a critical milestone — not just scientifically, but symbolically. And at the heart of that mission were calculations performed by Katherine Johnson.

🚀 Enter NASA: The West Area Computing Unit

The West Area Computers (short for West Area Computing Unit) were the African American women who worked as human computers at the Langley Research Center of NACA (predecessor of NASA) from 1943 through 1958. Most of their work involved reading, analyzing, and plotting data for aircraft testing, supersonic flight research, and, later, the space program. In the era before digital computers, they worked by hand, one-on-one with engineers or in computing sections.

In 1953, Johnson joined the National Advisory Committee for Aeronautics (NACA), which would later become NASA.

The National Aeronautics and Space Administration (NASA /ˈnæsə/) is an independent agency of the U.S. federal government responsible for the United States' civil space program and for research in aeronautics and space exploration. Headquartered in Washington, D.C., NASA operates ten field centers across the US and is organized into mission directorates for Science, Space Operations, Exploration Systems Development, Space Technology, Aeronautics Research, and Mission Support. Established in 1958, NASA succeeded the National Advisory Committee for Aeronautics (NACA) to give the American space development effort a distinct civilian orientation, emphasizing peaceful applications in space science. It has since led most of America's space exploration programs, including Project Mercury, Project Gemini, the 1968–1972 Apollo program missions, the Skylab space station, and the Space Shuttle. The agency maintains major ground and communications infrastructure including the Deep Space Network and the Near Space Network. NASA's science division is focused on better understanding Earth through the Earth Observing System; advancing heliophysics through the efforts of the Science Mission Directorate's Heliophysics Research Program; exploring bodies throughout the Solar System with advanced robotic spacecraft such as New Horizons and planetary rovers such as Perseverance; and researching astrophysics topics, such as the Big Bang, through the James Webb Space Telescope, the four Great Observatories (including the Hubble Space Telescope), and associated programs. The Launch Services Program oversees launch operations for its uncrewed launches. NASA supports the International Space Station (ISS) along with the Commercial Crew Program and oversees the development of the Orion spacecraft and the Space Launch System for the lunar Artemis program. It maintains programmatic partnerships with agencies such as ESA, JAXA, CSA, Roscosmos (for ISS operations), NOAA, and the USGS. NASA's missions and media operations—such as NASA TV, Astronomy Picture of the Day, and the NASA+ streaming service—have maintained high public visibility and contributed to spaceflight outreach in the US and abroad. A subject of numerous major films, NASA has maintained an influence on American popular culture since the Apollo 11 mission in 1969. For FY2022, Congress authorized a $24.041 billion budget, with a civil-service workforce of roughly 18,400; since December 2025, the administrator is Jared Isaacman.

She was assigned to the West Area Computing Unit, a segregated group of Black female mathematicians responsible for performing complex calculations by hand.

Here, the term “computer” was literal.

At Langley, Black female mathematicians were assigned to the West Area Computing Unit, a segregated division responsible for performing complex calculations by hand. These women — referred to as “human computers” — were essential to aeronautical research long before electronic computers became reliable.

These women:

Calculated flight trajectories
Processed aerodynamic data
Verified engineering outputs

To understand Hidden Figures, one must first understand the institutional paradox it depicts: The National Aeronautics and Space Administration (NASA), the pinnacle of American scientific progress, operated within a segregated social order.

Despite their essential role, they worked under:

Segregated bathrooms
Separate dining facilities
Limited authorship credit in reports

Unlike her colleagues, Johnson quickly broke through these barriers. Her assertiveness — asking questions in male-dominated briefings — led to her inclusion in the all-male Flight Research Division meetings.

This was not standard practice. It was a disruption of institutional norms.

Taraji P. Henson as Katherine Goble Johnson, mathematician, in "Hidden Figures" (2016) Photo Credit: 20th Century Fox

🛰️ Orbital Mechanics: Explaining the Math That Made Spaceflight Possible

At the heart of Johnson’s work was orbital mechanics — the mathematical discipline governing how objects move through space under gravitational forces.

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from laws of motion and of universal gravitation derived by Isaac Newton. Astrodynamics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbit dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).

Key Concepts (accessible breakdown)

1. Trajectory Calculation

To send a spacecraft into orbit, engineers must calculate:

Launch angle
Velocity (approx. 17,500 mph for low Earth orbit)
Earth’s rotation

In 1961, Project Mercury Astronaut Scott Carpenter underwent a simulated mission in the procedures trainer at Langley Research Center, which at the time was headquarters for NASA’s manned spacecraft operations. Credits: NASA

A small miscalculation could mean:

Missing orbit entirely
Burning up on reentry
Drifting into space indefinitely

Orbital mechanics failures in NASA missions typically stem from errors in trajectory calculation, unit conversion, or insufficient velocity during critical mission phases. While most modern failures are mechanical or software-related, specific historic missions highlight how miscalculating the physics of motion in space can be catastrophic. Notable Orbital Mechanics Failures Mars Climate Orbiter (1999): Unit Conversion Error The Failure: The spacecraft approached Mars at a lower altitude than planned and was destroyed by the Martian atmosphere. The Cause: A "metric vs. imperial" mismatch. Ground software from a contractor used English units (pound-force seconds), while NASA’s system used metric units (newton-seconds). This led to a cumulative navigation error that placed the craft's orbit within 57 km of the surface instead of the safe 140–150 km. Gemini IV (1965): Counter-Intuitive Orbital Maneuvering The Failure: Astronaut Ed White attempted a "station-keeping" maneuver (flying alongside the spent Titan II rocket stage) but failed to get closer. The Cause: This demonstrated the non-intuitive nature of orbital mechanics. Thrusting directly toward an object to "catch up" raises an orbit and slows the craft relative to the target. Successful rendezvous requires lowering an orbit to increase speed and then rising back up. Orbiting Carbon Observatory (2009): Insufficient Velocity The Failure: The satellite failed to reach its planned orbit and fell back into the ocean near Antarctica. The Cause: The payload fairing (protective nose cone) failed to separate during ascent. The extra mass of the fairing prevented the launch vehicle from reaching the orbital velocity needed to sustain its trajectory, resulting in atmospheric re-entry. Space Exploration Stack Exchange Space Exploration Stack Exchange +8 Summary of Physics-Related Factors Orbital Insertion: Missions like the Mars Climate Orbiter fail if they enter the "capture" phase at the wrong angle or speed, leading to either burning up or "bouncing" off the atmosphere back into deep space. Station-Keeping: Lessons from early missions like Gemini IV led to the development of precise rendezvous techniques used in Apollo and for the International Space Station. Atmospheric Drag: Satellites in Low Earth Orbit (LEO) can fail prematurely if they do not maintain enough velocity to overcome the "high drag" of the outer atmosphere, as seen with some Starlink launches during solar storms.

2. Elliptical Orbits

Animation of Orbit by eccentricity 0.0 · 0.2 · 0.4 · 0.6 · 0.8 Two bodies with similar mass orbiting around a common barycenter with elliptic orbits. Two bodies with unequal mass orbiting around a common barycenter with circular orbits. Two bodies with highly unequal mass orbiting a common barycenter with circular orbits. An elliptical orbit is depicted in the top-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy decreases as the orbiting body's speed decreases and distance increases according to Kepler's laws. Part of a series on Astrodynamics Orbital mechanics Orbital elements Types of two-body orbits by eccentricity Equations Celestial mechanics Gravitational influences N-body orbits Engineering and efficiency Preflight engineering Efficiency measures Propulsive maneuvers vte In astrodynamics or celestial mechanics, an elliptical orbit or eccentric orbit is an orbit with an eccentricity of less than 1;[citation needed] this includes the special case of a circular orbit, with eccentricity equal to 0. Some orbits have been referred to as "elongated orbits" if the eccentricity is "high" but that is not an explanatory term. For the simple two body problem, all orbits are ellipses. In a gravitational two-body problem, both bodies follow similar elliptical orbits with the same orbital period around their common barycenter. The relative position of one body with respect to the other also follows an elliptic orbit. In the solar system the dominant mass of the sun ensures planets each follow nearly circular elliptic orbits (e near 0) with the sun at the main focus while comets such as Halley is highly eccentric or elongated orbit (e near 1). Examples of elliptic orbits or trajectories for satellites include Hohmann transfer orbits, Molniya orbits, and tundra orbits.

Spacecraft follow elliptical paths, not perfect circles. Johnson calculated:

Apogee (farthest point from Earth)
Perigee (closest point to Earth)

An apsis (from Ancient Greek ἁψίς (hapsís) 'arch, vault' (third declension); pl. apsides /ˈæpsɪˌdiːz/ AP-sih-deez)[1][2] is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the apogee, and at the nearest point the perigee, as with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named aphelion for the farthest and perihelion for the nearest point in a heliocentric orbit.[3] Earth's two apsides are the farthest point, aphelion, and the nearest point, perihelion, of its orbit around the host Sun. The terms aphelion and perihelion apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of the Solar System.

3. Reentry Windows

Sketch of a circumlunar free-return trajectory (not to scale), plotted on the rotating reference frame rotating with the Moon (Moon's motion only shown for clarity)

Returning to Earth required hitting a narrow “corridor”:

Too steep → incineration
Too shallow → skipping off the atmosphere

In orbital mechanics, a free-return trajectory is a trajectory of a spacecraft traveling away from a primary body (for example, the Earth) where gravity due to a secondary body (for example, the Moon) causes the spacecraft to return to the primary body without propulsion (hence the term free).[1] Many free-return trajectories are designed to intersect the atmosphere; however, periodic versions exist which pass the Moon and Earth at constant periapsis, which have been proposed for cyclers.

Johnson’s calculations ensured that astronauts could reenter safely — a problem as complex as reaching orbit itself.

🧮 Project Mercury & John Glenn’s Flight

Astronaut John Glenn enters the Mercury spacecraft, Friendship 7, prior to the launch of Mercury-Atlas 6 (MA-6) on Feb. 20, 1962. The MA-6 mission was the first crewed orbital flight and Glenn became the first American to orbit the Earth during the three-orbit, five-hour MA-6 mission. Image Credit: NASA

Liftoff of the Mercury-Atlas 6 mission on Feb. 20, 1962. On this mission, John Glenn became the first American to orbit Earth. As part of the preflight checklist, Glenn asked engineers to get NASA research mathematician Katherine Johnson to check the orbital equations by hand on her desktop mechanical calculating machine. Photo Credit: NASA

Johnson’s most famous contribution came during Project Mercury, the United States’ first human spaceflight program.

he seven Mercury astronauts. From left: Wally Schirra, Alan Shepard, Deke Slayton, Gus Grissom, John Glenn, Gordon Cooper and Scott Carpenter. Credits: NASA

For Glenn’s mission aboard Friendship 7, early electronic computers were used to calculate orbital trajectories. However, these machines were new — and not fully trusted.

Before launch, Glenn requested:

“If she says the numbers are good, I’m ready to go.”

Johnson manually verified:

Orbital coordinates
Capsule positioning
Reentry timing

This was not redundancy — it was mission-critical validation.

NASA's original mission control, the Mercury Control Center, as it looked when staffed and operational in 1963. (NASA)

Her calculations ensured:

Glenn successfully orbited Earth three times
The capsule reentered safely
The U.S. secured a symbolic victory in the Cold War Space Race

🎬 Fact vs. Fiction: The “Check the Numbers” Moment

The film Hidden Figures dramatizes this moment as a climactic turning point — and while rooted in truth, the reality is more nuanced.

✅ What the Film Gets Right

Glenn did request Johnson’s verification
There was skepticism about early computers
Johnson’s calculations were essential

⚠️ What’s Compressed or Altered

The timeline is condensed for narrative urgency
Johnson was already deeply embedded in flight analysis work — not a last-minute savior
Collaboration is underplayed; spaceflight was a team effort

🎯 Accuracy Takeaway

This is a classic case of “emotional truth vs. procedural reality.”

The film captures the stakes — but simplifies the workflow.

Taraji P. Henson, Octavia Spencer, and Janelle Monáe in "Hidden Figures" (2016) Photo Credit: 20th Century Fox

🏅 Recognition Delayed: Why It Took Decades

Despite her contributions, Johnson remained largely unknown to the public for decades. Why?

WASHINGTON, DC- NOVEMBER 24: President Barack Obama presents Katherine G. Johnson with the Presidential Medal of Freedom during the 2015 Presidential Medal Of Freedom Ceremony at the White House on November 24, 2015 in Washington, DC. (Photo by Getty Images)

Katherine G. Johnson Computational Research Facility ribbon-cutting ceremony in the Reid Conference Center. Honored guests include Katherine G. Johnson and members of her family, Mayor Donnie Tuck, Senator Warner and Governor McAuliffe. Margot Lee Shetterly, author of “Hidden Figures,”

Artist's rendering of the 40,000-square-foot Katherine G. Johnson Computational Research Facility at the Langley Research Center in Hampton, Virginia. (NASA)

Structural Factors:

NASA reports often excluded female authors
Black women were rarely centered in scientific narratives
The Space Race spotlight focused on astronauts — not mathematicians

For Women's History Month we are highlighting mathematicians Katherine Goble Johnson, Dorothy Vaughan, and Mary Jackson. These three are among the many women of color whose skills helped make American space exploration possible.

The #1 New York Times bestseller The phenomenal true story of the black female mathematicians at NASA whose calculations helped fuel some of America’s greatest achievements in space—a powerful, revelatory history essential to our understanding of race, discrimination, and achievement in modern America. The basis for the smash Academy Award-nominated film starring Taraji P. Henson, Octavia Spencer, Janelle Monae, Kirsten Dunst, and Kevin Costner. Before John Glenn orbited the earth, or Neil Armstrong walked on the moon, a group of dedicated female mathematicians known as “human computers” used pencils, slide rules and adding machines to calculate the numbers that would launch rockets, and astronauts, into space. Among these problem-solvers were a group of exceptionally talented African American women, some of the brightest minds of their generation. Originally relegated to teaching math in the South’s segregated public schools, they were called into service during the labor shortages of World War II, when America’s aeronautics industry was in dire need of anyone who had the right stuff. Suddenly, these overlooked math whizzes had a shot at jobs worthy of their skills, and they answered Uncle Sam’s call, moving to Hampton, Virginia and the fascinating, high-energy world of the Langley Memorial Aeronautical Laboratory. Even as Virginia’s Jim Crow laws required them to be segregated from their white counterparts, the women of Langley’s all-black “West Computing” group helped America achieve one of the things it desired most: a decisive victory over the Soviet Union in the Cold War, and complete domination of the heavens. Starting in World War II and moving through to the Cold War, the Civil Rights Movement and the Space Race, Hidden Figures follows the interwoven accounts of Dorothy Vaughan, Mary Jackson, Katherine Johnson and Christine Darden, four African American women who participated in some of NASA’s greatest successes. It chronicles their careers over nearly three decades they faced challenges, forged alliances and used their intellect to change their own lives, and their country’s future. -WINNER OF ANISFIELD-WOLF AWARD FOR NONFICTION -WINNER BLACK CAUCUS OF AMERICAN LIBRARY ASSOCIATION BEST NONFICTION BOOK -WINNER NAACP IMAGE AWARD BEST NONFICTION BOOK

It was not until:

The publication of Margot Lee Shetterly’s Hidden Figures (2016)
The success of its film adaptation

…that Johnson’s story entered mainstream recognition.

Director Theodore Melfi and Taraji P. Henson filming "Hidden Figures" (2016) Photo Credit: 20th Century Fox

In 2015, she was awarded the Presidential Medal of Freedom by Barack Obama.

By then, she was 97 years old.

⚖️ The Ethical Lens: Recognition, Labor, and Historical Memory

Katherine Johnson’s story raises a broader question central to MoviestoHistory.com:

Who gets remembered — and who gets footnoted?

Her work was never hidden from NASA. It was documented. It was essential. But it was not amplified.

This reflects a systemic pattern:

Intellectual labor by women and minorities is often absorbed into institutions without attribution
Recognition is often retroactive rather than contemporaneous

In cinematic terms, Hidden Figures corrects the historical record — but it also reveals how incomplete that record was to begin with.

Octavia Spencer as Dorothy Vaughan, mathematician and supervisor, in "Hidden Figures" (2016) Photo Credit: 20th Century Fox

📊 Accuracy Meter: Hidden Figures (2016)

Historical Accuracy: 8.5 / 10

What’s Accurate:

✔ Johnson’s role in trajectory calculations

✔ Glenn’s trust in her verification

✔ Segregation at NASA

Taraji P. Henson, and Janelle Monáe in "Hidden Figures" (2016) Photo Credit: 20th Century Fox

What’s Dramatized:

✖ Timeline compression

✖ Individualization of collaborative work

✖ Certain workplace conflicts heightened for narrative

Octavia Spencer and Kirsten Dunst in "Hidden Figures" (2016) Photo Credit: 20th Century Fox

🧠 Legacy: The Mathematics That Still Matters

Katherine Johnson’s calculations extended beyond Project Mercury.

Katherine Johnson (1918–2020) was a pioneering NASA mathematician who, in addition to her work on the Mercury and Apollo programs, calculated trajectories and provided essential mathematical support for the early Space Shuttle program. Her work, which included expertise in computerized navigation, spanned over 30 years at NASA before her retirement in 1986. NASA (.gov) NASA (.gov) +4 Key Contributions to the Space Shuttle Program Trajectory Calculations: She helped determine the flight paths and trajectories essential for the launch and operation of the Space Shuttle. Technical Expertise: As a "human computer," she helped transition NASA from human-led calculations to digital systems, bringing her expertise to the Shuttle era. Research & Development: She authored or co-authored 26 research reports during her career, with her later work focusing on the Space Shuttle and the Earth Resources Technology Satellite (ERTS/Landsat). NASA (.gov) NASA (.gov) +4 Johnson worked at the Langley Research Center from 1953 until her retirement, during which she witnessed NASA’s transition from early space exploration to the Shuttle era, consistently providing vital mathematical accuracy.

She contributed to:

Apollo missions
Space Shuttle program groundwork

Her work helped define:

Computational verification standards
Trust frameworks between human and machine calculation

Today, as we rely on advanced AI and automation, her story remains strikingly relevant:

When systems fail, human judgment still matters.

✨ Precision as Power

Katherine Johnson did not walk on the moon. She made it possible for others to get there.

Her story is not just about mathematics — it is about precision as a form of power, and about the quiet authority of those whose work determines outcomes without ever occupying the spotlight.

For decades, her contributions existed in the margins.

Today, they define the center of the story.

SEPTEMBER 2016 CHARLES BOLDEN ANNIE LEIBOVITZ When I was growing up, in segregated South Carolina, African-American role models in national life were few and far between. Later, when my fellow flight students and I, in training at the Naval Air Station in Meridian, Mississippi, clustered around a small television watching the Apollo 11 moon landing, little did I know that one of the key figures responsible for its success was an unassuming black woman from West Virginia: Katherine Johnson. Hidden Figures is both an upcoming book and an upcoming movie about her incredible life, and, as the title suggests, Katherine worked behind the scenes but with incredible impact. When Katherine began at NASA, she and her cohorts were known as "human computers," and if you talk to her or read quotes from throughout her long career, you can see that precision, that humming mind, constantly at work. She is a human computer, indeed, but one with a quick wit, a quiet ambition, and a confidence in her talents that rose above her era and her surroundings. "In math, you're either right or you're wrong," she said. Her succinct words belie a deep curiosity about the world and dedication to her discipline, despite the prejudices of her time against both women and AfricanAmericans. It was her duty to calculate orbital trajectories and flight times relative to the position of the moon—you know, simple things. In this day and age, when we increasingly rely on technology, it's hard to believe that John Glenn himself tasked Katherine to double-check the results of the computer calculations before his historic orbital flight, the first by an American. The numbers of the human computer and the machine matched. With a slide rule and a pencil, Katherine advanced the cause of human rights and the frontier of human achievement at the same time. Having graduated from high school at 14 and college at 18 at a time when African-Americans often did not go beyond the eighth grade, she used her amazing facility with geometry to calculate Alan Shepard's flight path and took the Apollo 11 crew to the moon to orbit it, land on it, and return safely to Earth. I was so proud of Katherine as I sat with hundreds of other guests in the East Room of the White House and watched as she received the Presidential Medal of Freedom from President Obama last year. Katherine's great mind and amazing talents advanced our freedoms at the most basic level—the freedom to pursue the biggest dreams we can possibly imagine and to step into any room in the country and take a seat at the table because our expertise and excellence deserve it. Katherine, now 97, took her seat without fanfare. As far as not being equal was concerned, she said, "I didn't have time for that. My dad taught us 'you are as good as anybody in this town, but you're no better.'" I'd posit that Katherine was better—not only at math but also at applying her talents with the precision and beauty possible only in mathematics. She achieved the perfect parabola—casting herself to the stars and believing she could chart the journey home.

https://moviestohistory.com/wp-content/uploads/2022/03/cropped-d3d0f4de5c874cf7a06b2f50e0bc7820-2-10.png

Want more “Reel vs. Real” breakdowns like this?

Explore our full Hidden Figures series on MoviesToHistory.com

📊 Dive into Fact vs. Fiction

🎬 Compare Hollywood vs. History

🗳️ Join the debate: Does emotional truth justify historical compression?

👉 Read more. Watch smarter. Question everything.

Hidden Figures is available now to watch with a subscription to HBO Max…

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