## representation theory

What is group theory and why is it such an exciting area of maths? Two experts explain.

*theorems*are the big important results,

*conjectures*will be important results one day when they are proved, and

*lemmas*are small results that are just stepping stones on the way to the big stuff. Right? Then why has the Fields medal just been awarded to Ngô Bào Châu for his proof of a lemma?