Hurwitz's automorphisms theorem always astounds me. 84 is such a weird number to see in it. Fun fact: a group for which the maximum of 84(g-1) is reached is cal

Hurwitz's automorphisms theorem always astounds me. 84 is such a weird number to see in it. Fun fact: a group for which the maximum of 84(g-1) is reached is called a Hurwitz group. The Monster Group a Hurwitz group. So there is a Reimann surface of genus 9619255057077534236743570297163223297687552000000001 whose group of automorphisms (via orientation-preserving conformal mappings) is the Monster group. I don't even want to start trying to imagine that surface. For more unlikely Monster Group fun, there's also http://en.wikipedia.org/wiki/Monstrous_moonshine http://en.wikipedia.org/wiki/Monstrous_moonshine. http://en.wikipedia.org/wiki/Monster_group http://en.wikipedia.org/wiki/Monster_group http://en.wikipedia.org/wiki/Hurwitz%27s_automorphisms_theorem http://en.wikipedia.org/wiki/Hurwitz%27s_automorphisms_theor...