Which African American mathematician's orbital calculations John Glenn insisted on rechecking by hand?

Katherine Johnson. Before Glenn's 1962 orbital flight, NASA had switched to IBM computers for the trajectory, and he did not trust them; he asked for the girl to run the numbers by hand, and said that if she confirmed the machine, he was ready to go. She spent a day and a half on it.

She had started in the segregated West Area Computing unit at Langley, where Black women worked apart, ate apart and used separate bathrooms. She got out of it by asking to attend the editorial meetings that women were not admitted to, repeatedly, until the objection wore out, and eventually by having her name put on a report - which was not done for the computers.

The work was orbital mechanics: the equations for a spacecraft's path, the launch window that puts a capsule at a particular splashdown point, and later the Earth-Moon trajectories for Apollo. She also worked on the backup procedures that let the Apollo 13 crew navigate home with the main systems dead. She received the Presidential Medal of Freedom in 2015, at 97, and the story reached the public mainly through a book and film fifty years after the flight.