Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?

Abstract

About a year ago, a team of physicists reported in Science that they had observed "evidence for E8 symmetry" in the laboratory. This expository article is aimed at mathematicians and explains the chain of reasoning connecting measurements on a quasi-1-dimensional magnet with a 248-dimensional Lie algebra.Comment: v2: Added some material clarifying the word "evidence" and the precise role of E8 in the theory // v3: many small changes to the expositio