Indeed it was noticed years ago (especially by Marni) that associahedra alone could not capture the full structure of twistor-super Yang-Mills scattering amplitudes. To capture all the physics, the amplituhedron had to be created. These amplitudes tell more than just physics, however. Breaking free from the chains of unitarity and locality takes one deep into the unification of mathematics itself. The particles dance in projective space, while theorists dream of operads, instantons and infinite Yangian symmetry, followed by a dash of multiple zeta motivic cohomology.