Imagine working nearly 30 years to reach the absolute pinnacle of your field, then voluntarily asking for a demotion. That is exactly what Mary Jackson, NASA's first Black female engineer, did in 1979, and the logic behind that choice is the key to her whole story. Born in 1921 in Hampton, Virginia, she earned dual degrees in mathematics and physical science, then worked a winding string of jobs: schoolteacher, bookkeeper, health department receptionist, army clerk. What looks like career hopping was actually reconnaissance. She was learning exactly how bureaucratic machines classify people and move information, knowledge she would later use to take one apart.

In 1951 she joined the segregated West Area computing pool under Dorothy Vaughan, processing wind tunnel data by hand. Two years later an engineer invited her into the 60,000-horsepow ...