What Can We Learn About QCD and Collider Physics from <i>N</i>=4 Super Yang–Mills?

Tremendous ongoing theory efforts are dedicated to developing new methods for QCD calculations. Qualitative rather than incremental advances needed fully exploit data still be collected at the LHC. The maximally supersymmetric Yang-Mills (${\mathcal N}=4$ sYM) shares with gluon sector, which contains most complicated Feynman graphs, but same time has many special properties, and is believed solvable exactly. It natural ask what we can learn from in ${\mathcal sYM addressing difficult problems QCD. With this mind, review here several remarkable developments highlights of recent results sYM. This includes all-order certain scattering amplitudes, novel symmetries, surprising geometrical structures loop integrands, tools calculation integrals, bootstrap methods. While insights have already been carried over contributed state-of-the-art calculations LHC physics, argue that there a host further fascinating ideas waiting explored.