the best description of the monster is to say, "It is the automorphism group of the monster vertex algebra". This is not much help however, because nobody has found a "really simple and natural construction of the monster vertex algebra". Wilson with collaborators has found a method of performing calculations with the monster that is considerably faster. Let V be a 196,882 dimensional vector space over the field with 2 elements. A large subgroup H (preferably a maximal subgroup) of the Monster is selected in which it is easy to perform calculations. The subgroup H chosen is 31+12.2.Suz.2, where Suz is the Suzuki group. Elements of the monster are stored as words in the elements of H and an extra generator T. It is reasonably quick to calculate the action of one of these words on a vector in V. Using this action, it is possible to perform calculations (such as the order of an element of the monster). Wilson has exhibited vectors u and v whose joint stabilizer is the trivial group. Thus (for example) one can calculate the order of an element g of the monster by finding the smallest i > 0 such that giu = u and giv = v. This and similar constructions (in different characteristics) have been used to find some of its non-local maximal subgroups. Martin Seysen has implemented a fast Python package named mmgroup, which claims to be the first implementation of the monster group where arbitrary operations can effectively be performed. The documentation states that multiplication of group elements takes less than 40 milliseconds on a typical modern PC, which is five orders of magnitude faster than estimated by Robert A. Wilson in 2013. Moonshine The monster group is one of two principal constituents in the monstrous moonshine conjecture by Conway and Norton, which relates discrete and non-discrete mathematics and was finally proved by Richard Borcherds in 1992. In this setting, the monster group is visible as the automorphism group of the monster module, a vertex operator algebra, an infinite dimensional algebra containing the Griess algebra, and acts on the monster Lie algebra, a generalized Kac–Moody algebra. Many mathematicians, including Conway, have seen the monster as a beautiful and still mysterious object. Conway said of the monster group: "There's never been any kind of explanation of why it's there, and it's obviously not there just by coincidence. It's got too many