Inverse problems: anniversary and short review of generalized inverse scattering transforms

Three areas are briefly reviewed: how the journal was born, how inverse problems are not ordinary mathematical problems, and how their study either remains connected with the original ‘natural inverse problem’ or extends to mathematical developments which are sometimes not justified by any ‘natural inverse problem’! Examples are given. Related points are also evoked in the second part of the article, where a short topical review of inverse scattering transform extensions is presented.