Monstrous Moonshine - Why "monstrous Moonshine"?

Why "monstrous Moonshine"?

The term "monstrous moonshine" was coined by Conway, who, when told by John McKay in the late 1970s that the coefficient of (namely 196884) was precisely the dimension of the Griess algebra (and thus exactly one more than the degree of the smallest faithful complex representation of the Monster group), replied that this was "moonshine" (in the sense of being a crazy or foolish idea). Thus, the term not only refers to the Monster group M; it also refers to the perceived craziness of the intricate relationship between M and the theory of modular functions.

However, "moonshine" is also a slang word for illegally distilled whiskey, and in fact the name may be explained in this light as well. The Monster group was investigated in the 1970s by mathematicians Jean-Pierre Serre, Andrew Ogg and John G. Thompson; they studied the quotient of the hyperbolic plane by subgroups of SL₂(R), particularly, the normalizer Γ₀(p)+ of Γ₀(p) in SL(2,R). They found that the Riemann surface resulting from taking the quotient of the hyperbolic plane by Γ₀(p)+ has genus zero if and only if p is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 or 71. When Ogg heard about the Monster group later on, and noticed that these were precisely the prime factors of the size of M, he published a paper offering a bottle of Jack Daniel's whiskey to anyone who could explain this fact.