The world around us is filled to the brim with symmetry – from rotational symmetry in flowers to mirror symmetry in a calm mountain lake. Through inspiration from nature symmetry also unfolds itself in human art, for example the rose window in the Nidaros cathedral. Many paintings are also symmetric, but there are several ways in which they can be so. A curious person could then ask: how many different ways can a painting be symmetric? What happens when we don’t restrict ourselves to a flat painting but a three-dimensional sculpture? What about hypothetical shapes in any possible dimension?
It turns out that mathematicians have perfected this art, and can describe mathematically every possible way something can be symmetric. The story of this result is one of the biggest achievements in mathematical history, and culminates in one of the pinnacles of abstract mathematical achievements – the classification of finite simple groups.
Throughout the talk we will venture through the world of symmetry, exploring their simple mathematical descriptions and their uses in the arts.
Torgeir Aambø is a PhD student in mathematics at NTNU. His research area is topology, a field of mathematics that tries to understand mathematical shapes and abstract geometries.
