February 1962: John Glenn is strapped into Friendship 7, about to become the first American to orbit the Earth, and he refuses to launch. NASA’s brand-new IBM computers have produced his trajectory, but Glenn does not trust the black box. “Get the girl to check the numbers,” he says. “If she says they are good, I’m ready to go.” The girl was Katherine Johnson, and it took her a day and a half of nonstop hand calculation to verify what the machine spat out in minutes. This episode traces how a Black woman from the segregated South became the ultimate safety net for the American space race.

Born in 1918 in White Sulphur Springs, West Virginia, where public education for Black students simply stopped after eighth grade, she counted everything, started high school at 10, and graduated college summa cum laude at 18 with a professor inventing new courses just to keep her challenged. Her path included a deliberate detour into motherhood and teaching before she joined the segregated West Area computing pool in 1953, worked a temporary assignment with the all-male flight research team, and, as she put it, “they simply forgot to return me to the pool.” What made her indispensable was not calculating speed. It was analytic geometry: she could see the physical shape of a flight path behind the equations, and spot what a machine would blindly accept.

• The family that split itself in half: moving 100 miles every school year during the Depression so their children could get an education Jim Crow refused to provide
• How she got her name on the research: the azimuth angle report of 1960 that made her the first woman in her division credited as co-author
• What checking the machine’s math actually meant: numerical integration by hand, recalculating a shifting trajectory step by agonizing step, thousands of times
• The Apollo 13 lifeline: her one-star observation method that let a powerless, tumbling spacecraft find its way home, plus the Presidential Medal of Freedom, Hidden Figures, and a life that reached 101