R. W. Richardson wrote a number of papers which constructed geometric characterisations of group-theoretic notions (and/or vice-versa depending on your taste). In his 1988 paper ‘Conjugacy classes of n-tuples in Lie algebras and algebraic groups.’ he introduces a notion of Strong Reductivity of a reductive group G to characterise when orbits of a subgroup H<G acting by conjugacy on G^n are closed. I’ll explain how I came to be aware of the notion of Strong Reductivity, motivated by group theory, and then sketch how Richardson used it to to solve the problem he was working on. Many of the concepts involved in the latter are standard in GIT.