Title: Zooming into Catalan's conjecture.

Abstract: We give a historically motivated introduction to the study and solution of Catalan's conjecture - which consists in the statement that the only consecutive perfect powers are 8 and 9.

In the first part of the talk, we will give a historical overview of the various approaches - and respective results - to the study of Catalan's conjecture. In the second part, the zooming in will consist in an increasingly technical, magnifying focus on the central consequences of the presumable existence of unknown solutions to Catalan's equation. The way these consequences lead to a contradiction should become clear or at least plausible to the audience (depending upon time, technical prerequisites ... and, maybe, chemistry of the moment).