During the Space Race in 1960s, the mission launching a satellite into the space was the most strained competition between two Cold War rivals: The Soviet Union and The United States. After several decays, almost everyone just remembers John Glenn as a hero for the Mercury 7 project and forgets the mathematicians and engineers behind the scene. Three black female mathematicians – Dorothy Vaughan, Katherine Johnson, Mary Jackson – working at the National Advisory Committee for Aeronautics (NACA) at Langley Research Center were the testaments to fight for progress in Negro communities in the intellectual environment, to push for equality for their gender in all aspects of American life.From left: Mary Jackson, Katherine Johnson, Dorothy Vaughan (Edited picture from Internet)Dorothy Johnson Vaughan was an African American mathematician, human computer and supervisor of the West Area Computers. She was born on September 20, 1910 in Kansas City, Missouri and died on February 11, 2005 at the age of 98 in Hampton, Virginia. She was known for the first African-American woman supervisor in a group of staff in West Area Computers of the Langley Research Center. Mary Jackson was an African American mathematician and aerospace engineer at Langley Research Center. She was born on April 9, 1921 and died on February 11, 2005 at the age of 83 in Hampton, Virginia. She was known for being the NASA’s first black female engineer and the strong women who decided her life and matters into her own hands. Katherine Coleman Goble Johnson was an African-American mathematician working at NACA, Spacecraft Controls Branch, the Space Shuttle program, the Earth Resources Satellite. She was born on August 26, 1918 in White Sulphur Springs, West Virginia. She was well known for her critical calculations for the Project Mercury, the John Glenn’s mission, the Apollo 11, a mission to Mars and a first female mathematician had been allowed into the all male meeting. These three women working together in West Area Computers overcame the segregation and the racial discrimination to achieve the victories for them and also for next generations. Their actions, just like Simmel said, were individual actions and they chose what social form they wanted. Usually, all the old social form forced them to work in the categories as women, as black workers under the ethnic racial but they changed it into new cultural form, new categories that they wanted such as first black engineer, first supervisor, first women to bring the difference in NACA.In the beginning, all these three women received a very good education despite the segregation education at that time. The old stereotypes that women shouldn’t study higher and pursue the education were among the society, this just like “The Social Misconstruction of Reality” when the group thinking prevented women to achieve a high quality of education. But Dorothy wouldn’t let that stereotype bothering her, she received the scholarship from Wilberforce University celebrating her work ethic, her natural kind disposition, and her humility. This scholarship somehow inspired other students among the Negro community to overcome the stereotype of society and proved that women could achieve high education if they truly wanted it. Katherine showed her talent for math at a very young age but at that time, the Greenbrier County didn’t have the public school for Negro community past the eighth grade, her family decided to move 125 miles away, this action was the structural fix to change the prevention in education, just only for Katherine’s education in West Virginia. She was a freshman in high school at the age of 10 and graduated from college just at the age of 18. Her action as the first Black female student attending West Virginia State was a symbol of her academic talent in the isolation and scrutiny that came along with being a black student on the front lines of desegregation. Education was always on top of their list of ideas. Before coming to NACA, Dorothy, Katherine and Mary worked as a teacher and their ontologies in education that they had to teach their students shouldn’t put limits on themselves, they had a keen sense of responsibility to advance the race for the Negro community in the society and improved the long-term educational prospects of the young people. Dorothy, as a teacher, had ambitions to maintain an orderly learning environment. “With only eight classrooms; no gymnasium, lockers, or cafeteria; and an auditorium outfitted with folding chairs”, she somehow managed the school to have enough study environment and also she updated her classes with a unit called Wartime Mathematics, teaching students to apply arithmetic operations in the wartime ration books and updating classic word problems with airplanes instead of cars. Her actions were the structural fixes to bring the suitable education for the children to fit the social context. For Mary, life was a long process of raising one’s expectations and she always reminded her idea: “You can do better—we can do better”. At the time, in order to work in the position of NACA engineer, she had to have the degree in engineer but at that time no black colleges offered the engineering course so that she had no choice to attend the white university. Instead of doubting herself about her decision, she moved forward to convince the judge with her cognitive fix in order to change the social structure in Virginia. Even though Virginia was still a segregated state, she used the cognitive fix to remind the importance of being the first: “And I, sir, plan on being an engineer at NASA. But I can’t do that without taking those classes at that all-white high school. And I can’t change the color of my skin. So…I have no choice but to be the first. Which I can’t do without you.” In the end, she was granted this permission to be able to take the classes at Hampton High in the evening. This action gave an important step for the Negro students to attend the white colleges and somehow blur the border in the segregation education at that time.During the 1960s in the United States, the demand for aircraft exploded due to the fear of Russia conquering the space race and spying from the sky. At this space race, the United States could not be starting it with a disadvantage. Also, the segregation was still in place under the control of Civil Rights and Financially Struggling. Most of the woman at that time, especially the black women were supposed to work as domestic servants. The black college-educated women were expected to go into teaching, the highly prestigious job without high salary at that time, not mathematicians or engineers. This issue began to change during the World War II. At that time the government struggled with the shortage of male workers due to the war, which allowed unheard of numbers of women and African Americans to enter the restricted industries. NACA wasn’t an exception to the law. Due to the shortage of male workers, NACA hired a lot of women to compensate for a shortage of male mathematicians. That was the time for the first African American women computers hired at Langley. The job at the aeronautical laboratory in their minds was very new and also had a higher salary than teacher’s salary. Although the industries and several government’s offices were opening to African Americans male and female, segregation still continued and presented every corner of society: colored bathroom, colored cafeteria, segregated office. The black women working as computers were called the “West Area Computers” or “Computer wearing a shirt” because they were restricted to the West Area of the Langley facility. Also their work was considered as “women’s work” due to the stereotype of social, just like what Hamilton mentioned in “The Social Misconstruction of Reality”, with the group thinking that their work was not valued. These social and cultural form, like Simmel mentioned, suppressed their opportunities so that they actioned to change these forms around them and rose up new question among the community: How could some simple actions change the social and cultural form in the intellectual environment?In the noble environment of the NACA laboratory, a place that had selected the black women for their intellectual talents, the sign “colored computers” in the cafeteria and in front of the bathroom seemed especially ridiculous and somehow more offensive. Dorothy and her West Computers’ colleague, Miriam Mann, had their structural fix to change this issue among their working environment. They banished the cardboard sign on a table in the cafeteria to the recesses of Miriam’s purse until management of the research team gave up and stopped labeling the table. Also Dorothy in three years at Langley had proven to be more than equal to the job, gained excellent ratings from her bosses and be the first African-American supervisor in NACA. Their action somehow inspired the anxiety and a sense of empowerment not only among the community in NACA but also among the local gentry outside NACA. There were some black people sitting at the front of the Ogden Hall, apart from the school’s black faculty and administrators. When Katherine moved from the West Area Computers to the Guidance and Control Division of Langley’s Flight Research Division in the other building, she had to work among all white male engineers. If she wanted to use the bathroom, she had to run all the way back to the West Area Building just only for the colored bathroom label. But in the new building, most of the bathrooms were unmarked so that Katherine thought that there was no reason why she shouldn’t use those bathrooms and ignored the rules. She also made her own decision to bring a bag lunch and eat at her desk without going to the colored cafeteria and simply determined to pluck those unevolved, backward rules out, willing into existence a work environment. At that time, the female salary was way lower than male salary. In order to raise the salary, Dorothy talked to Katherine’s manager and insisted he either give her a raise or send her back to West Computing. After that cognitive fix to change the manager’s mind, Katherine’s job was made permanent with a corresponding increase in salary. Her small victory also had a collateral effect to win promotions for both Katherine and her white colleague. Just like Katherine, after 2 years working at West Computing, Mary was assigned to work on a project on the East Side. When she asked the white colleague: “Can you direct me to the bathroom?”, he just laughed at her because how would they know where to find HER bathroom? Angry and humiliated, she ran back and forth between buildings just to go back to West Building to use a bathroom. She told Kaz, an assistant section head in the four-by-four-foot Supersonic Pressure Tunnel, about her issue. In the end, he invited her to work for him so that she didn’t have to use the segregation bathroom anymore and use the unmarked bathroom. All of them, Dorothy, Katherine, Mary, broke the Langley’s color barrier with their cognitive and structural fixes. All of these actions, somehow just like Simmel said about the cultural structural, refused the unreasonable cultural rules and changed the social structural inside NACA.In NACA at that time, women were not allowed to have names on research papers even though all the numbers were calculated by them. “Getting one’s name on a research report was a necessary first step in the career of an engineer. For a woman, it was a significant and unusual achievement”. After several actions to prove her ability, Katherine was the true heroic calculation for the projects. In some of her projects, she had to analyze the data for the flying subject. She had to deeply understand why the plane with the previous formula fell out of the flying path. She spent days analyzing and looking at the black box and the top secret data that she was not allowed to see to recalculate the formula. She just simply flashed the black hidden data under the bright light to see through the paper. Also, in order to calculate more accurately, she had to go and see all the new information in the meeting. But she was not allowed to attend the meeting with all white male engineers since she was a woman. She felt that it was unfair since all the numbers were her number, after all. She thought that she had to change this old stereotype. She questioned her male colleague: “Why can’t I go to the editorial meetings?”, “Is there a law against it?” she asked the engineers. In fact, there wasn’t. “There were laws telling which fountain to drink from. There were laws restricting her ability to apply for a credit card in her own name, because she was a woman. But NO law applied to the editorial meeting. It wasn’t personal: it was just the way things had always been done”Finally, all the engineers allowed her to attend the meeting. Her way of using structural and cognitive fixes changed the way people thought about women, especially black women in NACA at that time. Having the data from several tests and prototypes, she used the deductive method to solve the issue and came up with the new formula. Somehow she assumed that our world was surrounded by math and we could see the issue related with the flying capsule under the math basic formula. When the engineers analyzed Katherine’s new data, they were fascinated and realized they were uncovering something they had not quite seen before: a new path of subject to changing forces, new formula to calculate the destination point of Astronaut John Glenn’s capsule, calculate the trajectories for many NASA missions. She just only used some old but efficient theory, the Euler’s method, to come up with new formula. Euler’s method was among all techniques she applied to describe the path of a flying object and this method was best suitable to calculate the landing point of John Glenn’s capsule. All of her projects proved and acknowledged to the public that she had given a lot of efforts and contributions to some first steps in the aeronautical community. At that time, all of the women in West Computer Building were celebrating and whispering about a remarkable story: “Mary Jackson—a former West Computer!—had faced down the brilliant John Becker and won.”. Mary was given an assignment and when the numbers did not come out as expected, the division chief believed she had made an error. The stereotype about women were computers, men gave the orders and women just followed that and all the mistakes were from the women’s tasks. She and her division chief went back and forth over the wrong data. She somehow used the IDEAL steps in problem solving to look back at the data and identify the wrong step in the formula. Finally, they discovered that the division chief gave her the wrong starting numbers. After that, he apologized to Mary, which earned Mary a really high reputation. No one at that time could do like what Dorothy, Katherine, and Mary did in order to transform the American workplace. Despite all the difficulties, these women had a real love and passion for their works in NACA. All of these brave actions formed an amazing base for the people, especially Negro community in later generations in the STEM fields. These three mathematicians built up a fingerprint in the histories of the Negro community to be the lead engineers and mathematicians who taught humans to fly.