Many sci-fi books, shows and movies incorporate the idea of faster-than-light (FTL) travel. The first appearance of the term “warp-drive” was in John W. Campbell’s novel Islands of Space (all the way back in 1931), but the accepted value of the Speed of Light (c) had only been discovered 51 years earlier (in 1879). That is not to say that people had not thought about or attempted to measure this limit. Aristotle argued with Empedocles about the speed of light in the first known discourse on the subject (and as with many of his ideas about physics, Aristotle was wrong-he thought light traveled instantaneously).
Even as early as Galileo, people were attempting experiments to measure the speed of light- usually these experiments failed because they were carried out at distances that were too small to be able to detect any differences.
Finally, Albert Michelson (a former Navy Officer) came up with the accepted speed of light after his experiment with Edward W. Morley proved that there was no aether to cause drag.
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