I begin by explaining to non-specialists why resolution of singularities in characteristic 0 works. Then I go into some ideas telling how it actually works. I finish with a brief discussion of related results on foliations. I report on work with Andr\'e Belotto da Silva, Michael Temkin, and Jaros{ \l}aw W{ \l}odarczyk; any claim to originality is joint with them and appears in the paper [AdSTW25].
Categories: math.AG