Andrei Gonchar, George Baker, and Henri Eugene Padé

One of the foci of the school of Andrei Gonchar was, and still is, Padé and rational approximation. We survey a small part of their work – especially related to the Baker–Graves-Morris and Baker–Gammel–Wills Conjectures, and Baker's later patchwork conjecture. We shall also discuss some of the unsolved problems.