http://en.wikipedia.org/wiki/47_(number)
Forty-seven has been the favorite number of Pomona College, California, USA, since 1964. A mathematical proof, written in 1964 by Professor Donald Bentley, supposedly demonstrates that all numbers are equal to 47.[4] However, Bentley offered it as a "joke proof" to further a popular student research project that listed real and imaginative "47 sightings". Bentley used the invalid proof to introduce his students to the concept of mathematical proofs.[5]
Joe Menosky graduated from Pomona College in 1979 and went on to become one of the story writers of Star Trek: The Next Generation. Menosky "infected" other Star Trek writers with an enthusiasm for the number 47.
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The joke transcends Trek, also showing up in J.J. Abrams shows from
Alias to
Fringe (so it's an interesting convergence that he ended up doing Trek).