The standard model of particle physics is built upon four-dimensional gauge theories. Unfortunately, computations within them are intrinsically hard, and our knowledge is therefore restricted to tiny fractions of their parameter space. In recent years we have made considerable progress towards solving the spectrum of at least one such theory exactly by employing technology well-known from condensed matter physics such as integrable spin chains. Our findings give new insights into string theory and the conjectured duality to gauge theories.

In this talk I will review the connections between gauge theories, string theories and spin chains. For planar maximally supersymmetric gauge theory we were able to show beyond reasonable doubt that the model is integrable. Due to integrability one can make use of the so-called Bethe ansatz to solve the spectrum of the model very efficiently. I will outline and illustrate this procedure and its implications in simple terms.