Apollo was built in the era of "big iron" computer mainframes. The concept of an onboard computer for space missions was radically new. There was only one place in the world that could design the Apollo Guidance Computers, and that was MIT. It took most of the U.S.'s production of integrated circuits, another radical idea replacing individual vacuum tubes, to build the AGC's. It took 2,000 person-years of independent code review and validation to ensure that they would operate properly.
Besides the technical challenges, the Apollo missions were a matter of National Prestige. In the Space Race between the United States and the Soviet Union, President Kennedy said we were going to the Moon and return safely before the end of the (1960's) decade, so we did.
