Answer: It is unclear which Katherine is being referred to in this question. If you are referring to Katherine Johnson, the African American mathematician and space scientist who worked for NASA during the Space Race, here is an answer:
Katherine Johnson, despite facing discrimination and segregation as an African American woman in the 1950s and 1960s, made significant contributions to NASA's space program. She was part of a team of mathematicians who were responsible for calculating the trajectories that would allow the first Americans to go to space and return safely to Earth.
One example of a complicated problem that Katherine Johnson solved involved the launch of the Atlas Rocket, which was a crucial step in America's quest to put a man on the moon. Despite not having top-secret clearance, Johnson was able to use her knowledge of mathematics and physics to help solve a difficult problem involving the rocket's trajectory.
According to Margot Lee Shetterly's book "Hidden Figures," Johnson learned about the Atlas Rocket when she overheard a conversation between male colleagues discussing the project. Despite not having authorization to work on the project, Johnson's curiosity and knowledge of mathematics allowed her to begin studying the rocket's trajectory in her free time. She eventually made important contributions to the project and was credited with helping to ensure the success of the Atlas Rocket's launch.
Overall, Katherine Johnson's remarkable intelligence, determination, and willingness to work hard in the face of discrimination and obstacles allowed her to make important contributions to the space program, despite not having top-secret clearance or other advantages that many of her colleagues enjoyed.