Integrable lattice models in 1+1 dimensions have been a topic of much fascination in physics since the early days of quantum mechanics. Recently, a work by Costello has offered a new perspective on these models based on a 4D topological gauge theory. An interesting aspect of this proposal is the close connection with 3D Chern-Simons theory and knot invariants. I will explain how to derive the 4D topological theory using string dualities and localization techniques for a 5D twisted super Yang-Mills theory. Finally, I will explain how this construction might relate to other appearances of Yangian symmetry which played a prominent role in AdS/CFT physics. This is a joint work in progress with Joe Minahan.