Epilogue: The idea of Lie theory as a Galois theory for differential equations

In this epilogue we want to briefly describe the brilliant conception of the Norwegian mathematician Marius Sophus Lie (1842–1899) of transferring Galois’ theory of polynomial equations to an analogous theory of differential equations. In both theories the fundamental underlying idea is that of exploiting hidden symmetries between the (a priori unknown) solutions of an equation (be it an algebraic or a differential equation) to solve this equation; in both cases the mathematical tool to describe these “hidden symmetries” is the concept of a group.