38 Groups
Evariste Galois died in a duel aged 20, but left behind enough ideas to keep
mathematicians busy for centuries. These involved the theory of groups, mathematical
constructs that can be used to quantify symmetry. Apart from its artistic appeal,
symmetry is the essential ingredient for scientists who dream of a future theory of
everything. Group theory is the glue which binds the ‘everything’ together.
Symmetry is all around us. Greek vases have it, snow crystals have it,
buildings often have it and some letters of our alphabet have it. There are several
sorts of symmetry: chief among them are mirror symmetry and rotational
symmetry. We’ll just look at two-dimensional symmetry – all our objects of study
live on the flat surface of this page.