Determining the representations of a finite group over the real numbers is an old problem, and is elegantly solved using that complex representations fall into one of three cases – corresponding to the three finite division algebras over R. A natural generalisation, phrased in terms of complex anti-linear maps, was first considered by the physicist Eugene Wigner due to its applications in the physical context of time reversal in quantum mechanics. Astoundingly, the trichotomy that exists between R and C completely generalises to this setting, and results in what Freeman Dyson coined “The Tenfold Way” when the classical theory and its generalisation are considered simultaneously. Another completely surprising application is a method of counting the number of square roots of group elements.