In 1979 Shelah proved that in an oracle-cc forcing extension all automorphisms of P(N)/Fin are trivial. This proof has been adapted to the context of (weaker and weaker) forcing axioms, while keeping its rough form: In three successive steps, the `ideal of trivialities' is shown to be nontrivial, P-ideal, and finally contain N. Over the years, this proof has been adopted to other rigidity contexts, from C*-algebras to (certain) groups. I will discuss recent progress in which the middle step became obsolete and the third step is substantially simplified.