As particle accelerators like the LHC achieve greater precision, computing scattering amplitudes at higher loop orders becomes more and more important. While older methods for calculating these scattering amplitudes were very inefficient, recently a wealth of new techniques have opened up, many of which are first tested in simpler, more symmetric theories like N=4 super Yang-Mills. In particular, six-particle amplitudes in N=4 super Yang-Mills can be described by a basis of transcendental functions called Hexagon Functions. Using this basis, we can begin with a guess for the form of the scattering amplitude at four loops, then constrain it with various physically-motivated restrictions until we arrive at a unique answer. What we find are functions that are paradoxically both very complex (requiring hundreds of pages to write down) and astonishingly simple, behaving very similarly to their lower-loop analogues.