A seemingly unrelated construction is the j -function of number theory. This object belongs to a special class of functions called modular functions, whose graphs form a certain kind of repeating pattern. Although this function appears in a branch of mathematics that seems very different from the theory of finite groups, the two subjects turn out to be intimately related. In the late 1970s, mathematicians John McKay and John Thompson noticed that certain numbers arising in the analysis of the monster group (namely, the dimensions of its irreducible representations) are related to numbers that appear in a formula for the j -function (namely, the coefficients of its Fourier series). This relationship was further developed by John Horton Conway and Simon Norton who called it monstrous moonshine because it seemed so far fetched.