Hamilton was a software engineer before the position was even existed—in fact, she's the one who coined the term. She was one of the first people who distinguished software engineering as a legitimate field worthy of respect.

In the 1960s, she led the team that developed the in-flight software for the Apollo missions. Her team's hand-written software played a critical role in landing the astronauts of Apollo 11 on the moon, one of the first times a computer was trusted with the real-time execution of a mission-critical task.