Reflections and symmetries in space and time

A personal view is presented of developments in the non-linear mechanics of structural buckling over more or less the past four decades. The era has been one of unprecedented change and development in the world of science as a whole, and this is acknowledged by describing ways in which the field has interacted strongly with other areas of study, including mathematics, non-linear dynamics and chaos and structural geology. A framework is provided through two key conferences that have emerged as pivotal moments in time when ideas seemed to take shape in a collective sense rather than just with individuals. Throughout most of the paper, the buckling of the axially compressed cylindrical shell is used to illustrate key features, including the breaking of hidden symmetry, localization and snaking solutions leading to a minimum energy periodic state that accords with a revitalized Maxwell stability criterion. The paper closes with some thoughts to the future, including the modelling of layered structures in geology and potential uses of modern composites.