When NASA first decided to put a man on the Moon they had a problem: once the Apollo spacecraft was in flight, they would not be able to observe its exact location and neither would they be able to predict it using physics. How could they send astronauts to the Moon if they didn't know where they were? An ingenious mathematician came up with an answer.
In a major and expensive setback for NASA's Mars program, both the Mars Climate Orbiter and Mars Polar Lander spacecraft appear to have been lost. Soberingly, while the fate of the Mars Polar Lander is unclear, it appears that the Mars Climate Orbiter was lost due to a simple mathematical error.