The Large Hadron Collider at CERN smashes protons
against protons. In these collisions, sometimes a gluon from one proton
scatters off a gluon from the other proton, producing one or more new gluons. What
happens in between depends on who you ask! Most people would say that Feynman
gave us the answer in the form of his famous diagrams involving virtual
particles with real momenta. However, in the past decade, physicists have been
developing stranger and stranger descriptions. I will explain why and introduce
some of these, such as strings moving in twistor space, real particles with
complex momenta, volumes of combinatorial objects such as the Amplituhedron and
points interacting on a Riemann sphere.