How can mathematicians remain innovative in the dawning new era? As an analyst, I’d like to make a case for the confrontation with concrete experimental phenomena, on a firm modelling basis. 

As a specific example, I’ll focus on domain pattern in ferromagnetic films, namely the magnetization ripple. It is modelled by a non-convex variational problem in the presence of multiple length scales and quenched randomness. 

How to mathematically formulate, and then rigorously establish, a kind of universality of such a pattern? It turns out to rely on an elementary version of a renormalization, and a hidden coercivity, akin to field theories.