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Ann Varela: Famous Women Mathematicians

Aug 17, 2017 by

An Interview with Ann Varela: Famous Women Mathematicians

Michael F. Shaughnessy –

1) Ann, who was Katherine Goble Johnson and why would she be considered one of the finest mathematical minds of all time?

Katherine Johnson was an extraordinary African-American woman who overcame adversity to succeed in a predominantly dominated man’s world.  Her life was unusual from the start.  For example, she started high school at age 10 and graduated from college at age 18.  To accomplish such a feat, she had to relocate to a city that admitted black students, tolerate segregated bussing rules, and maintain exemplary grades.  Her intellect allowed her opportunities not typical of her contemporaries.  All the while, she endured racism and confronted it unabashedly.

Selection as the first African-American to attend West Virginia University was an honor bestowed upon Johnson back in 1939.  Her skills in mathematics improved and put to the test when she joined the National Aeronautics and Space Administration (NASA) team in 1958.  Her accuracy with mathematical computations was legendary.  John Glenn supposedly trusted her calculations over those of a computer.

Katherine Johnson’s actions and efforts toward equality made it possible for other women at that time to receive improved treatment in the workplace.  She was a voice of reason for equal rights among the races.  Johnson inspired her co-workers and others to treat each other with self-respect and admiration.  She often claimed that she was just doing her job.

2) Let’s look at her foundation – where was she born, where did she go to school, and what challenges did she face in terms of getting a good ground in mathematics and calculations?

Joshua and Joylette Coleman welcomed their fourth child, Katherine, into their family on August 26, 1918.  Johnson’s father made a living as a lumberman, farmer, and repairperson, while her mother was an educator.

Johnson attended public school until the eighth grade, which was the highest level of education offered at that time in Greenbrier County.  Her parents enrolled Katherine and her siblings in high school in Institute, West Virginia.  Although Katherine was only ten years old when she started high school, she thrived and began her college career at the age of fourteen at West Virginia State College.  The founding of West Virginia State College provided higher learning opportunities for black students; however, students of all races could gain admittance.  Several of Johnson’s professors mentored her and provided unique mathematics courses specifically for Johnson.  By the time she was eighteen, Johnson earned her undergraduate degree in Mathematics and French.

After graduation, Johnson remained in Virginia and taught at a black public school.  Within two years, she married her first husband, James Goble, quit her teaching job, and started graduate school with an emphasis in mathematics.  Johnson became the first African-American woman admitted to graduate school at West Virginia University.  After just one year, however, she decided to focus her attention to her family, as she learned of her pregnancy.

3) Apparently her first employment opportunities were with NACA and then NASA- How did she hone her craft at these places?

Johnson fist became involved with the National Advisory Committee for Aeronautics (NACA) in 1958 after the Soviet satellite Sputnik, launched.  Johnson had provided some of the math for the 1958 document Notes on Space Technology, assembled from a series of lectures given by engineers in the Flight Research Division and the Pilotless Aircraft Research Division.

Johnson described herself and the other female employees at NACA, later known as NASA, as human computers.  She and the other women read the data from the black boxes of aircraft.  These data indicated specific mathematical tasks.

Because of her knowledge of analytic geometry, Johnson’s task involved assisting an all-male flight research team.  Her assertiveness gained her access to briefings, which were traditionally off-limits to women; these meetings, meant to be a think-tank for engineers to plan a space mission, did not welcome women.  She declared the computational work was hers and that she deserved to attend the editorial meetings.

4) Her real successes came with NASA and the Apollo space endeavors.  What were her contributions?

Johnson calculated the parabolic flight path for the first American manned mission in space, piloted by Alan Shepard.  Additionally, Johnson published her trajectory analysis, along with Ted Skopinski’s contributions, in a report detailing the equations describing an orbital spaceflight, which specified the landing position of the spaceship.  She also contributed to the orbital mission of John Glenn, the first American to orbit Earth, and with the first human mission to land on the moon, Apollo 11.  Johnson’s computations shaped every major space program beginning with Mercury through the Space Shuttle.  When interviewed about her space exploration contributions, she noted that her greatest contribution was determining the necessary synchronization procedures for Project Apollo’s Lunar Lander with the moon-orbiting Command and Service Module.

5) In a sense, her mathematical acumen was sorely tested due to the travels in space- and the fact that she was computing math for a different environment (space) and had to take multiple factors into consideration. What kind of mathematical thinking is needed for such an endeavor?

When calculating the height and speed of objects, Johnson used geometry.  She said the early trajectory was parabolic in shape and predictions about where it would be at a given point in time would be easy to calculate.  See Figure 1.

Figure 1

https://i1.wp.com/upload.wikimedia.org/wikipedia/commons/5/5a/Mr3-flight-timeline.png?resize=412%2C219&ssl=1

https://upload.wikimedia.org/wikipedia/commons/5/5a/Mr3-flight-timeline.png

By 1962, NASA used electronic data processors to calculate launch conditions for the Friendship 7 mission.  The calculations necessary for orbiting the Earth were definitely more complicated than the ones needed for the first mission in space.  Apparently, John Glenn insisted that Johnson check over the computer’s calculations for accuracy.

Johnson used mathematical equations dating back to Sir Isaac Newton and Henry Cavendish.  More specifically, the laws of gravity provided Johnson with the necessary information to calculate the force of gravity between the Earth and the spacecraft.  See Figure 2.  Spacecraft in low orbits travel at higher speeds because the gravitational pull is powerful.  In higher orbits, spacecraft travel at lower speeds because the force of gravity diminishes.

Figure 2

http://sdsu-physics.org/physics180/physics195/images_physics_195/13_gravitation1.jpg

6) I understand that she also published 26 mathematical papers-what was her area of interest and how were her papers received?

Katherine Johnson co-authored 26 scientific papers relating to her NASA career.  These publications were the result of her attendance and participation in the briefings at NASA.  During her career at NASA, Johnson wrote about her calculations concerning such topics as trajectory of spacecraft, orbital behavior, optical measurements, nonlinear aircraft maneuvers, and space antenna.  She eventually gained notoriety and respect for her efforts.

7) Obviously she worked during a period of racial discrimination. What were some of her accomplishments in this regard?

Attempts at acquiring an education beyond the eighth grade was Johnson’s earliest encounter with discrimination.  Luckily, her parents valued education enough to find a way for their children to obtain a high school education, even though it meant dividing their time between two cities.

Johnson attended graduate school at West Virginia University.  Integration of the races was not typical during this period.  The Supreme Court ruling Missouri ex rel. Gaines v. Canada (1938) changed history, as it stated that any state offering higher education to white students must also provide it to black students.  Now, whether states integrated students or established separate colleges was up to the state.

Johnson’s employment at NASA broke race and gender barriers.  Although she started out working in a team of African-American women, she ultimately ended up working in a mixed-gender and mixed-race environment.  Something as simple as using the restroom also challenged Johnson and the other African-American women at that time.  Johnson’s office sign read “Colored Computers.”  Segregation also existed for eating areas and restrooms.

The inclusion of a woman’s name on a report at that time at NASA was unprecedented.  That sounds ludicrous to me in the twenty first century, or at any time for that matter, but it was standard operating procedure back then.  Johnson changed that SOP when she had her name included on a report that she contributed to and finished writing.  She stated the necessity for assertiveness and aggressiveness on the job at varying degrees, depending on one’s desired goal.

8) She was obviously a role model for many women. What recognition did she receive, and what were some of her awards and honors?

Katherine Johnson received numerous awards and honors, some as recently as this year, such as the Medal of Honor from the Daughters of the American Revolution.  In Hampton, Virginia, there is a building named the Katherine G. Johnson Computational Research Facility.  She received several honorary degrees from various universities such as Doctor of Laws, Doctorate of Science, and Doctorate of Humane Letters.  Johnson even received the Silver Snoopy award for her exceptional contributions to flight safety and mission success.  In 2015, she received the nation’s highest civilian honor, the Presidential Medal of Freedom, which she proclaimed to be her most prized honor.

Johnson devoted her life to mathematical and scientific pursuits.  Her teaching career and her time at NASA provided her love of learning an opportunity to grow and flourish.

9) What have I neglected to ask?

After her tenure with NASA, Johnson spent her time traveling and being with her family.  She has three daughters.

Johnson also devoted some of her time on the lecture circuit speaking to students about studying math and science and to working persistently toward their dreams and goals.

The movie Hidden Figures portrays Johnson’s experiences during her NASA employment and the obstacles faced by African-American women during that era.

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