I do know that there is a "long proof" (I have read that it is +1000pages) that the Monster group is the largest sporadic simple group. My question is:
Why can we be sure that there is no other bigger group out there?
Beyond that long proof, is there any alternative "proof" of why the Monster group is the largest simple group? After all, the full set of sporadic simple groups seems to have some unexplained and yet mysterious relationships between some of them.