Galois theory
All of the ways of shuffling a field can be turned into a group. There are special types of groups, called the Symmetric Group on n elements labeled Sn, which are all the ways of shuffling n things. Symmetric groups are well behaved and easy to work with when you only shuffle 1, 2, 3, or 4 things. If you use 5 or more, the structure of the symmetric group becomes too chaotic.