# representation theory

What exactly do we mean when we say group theory is the study of symmetry? Group actions make precise what it means for a group to act by symmetries on an object.

Explore the mathematical study of symmetry with this collection of content, which includes short introductions, in-depth articles, a podcast, and some magic!
What is group theory and why is it such an exciting area of maths? Two experts explain.
Groups occur all over mathematics, so it makes sense to find a common language to talk about them all.
Results in mathematics come in several flavours — 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?
Results in mathematics come in several flavours — 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?