# symmetry

Groups have become a core part of the language of modern mathematics and theoretical physics. On this page, find out how groups can help describe roots of polynomials, holes on a surface, and even the laws of physics!

Group theory is the mathematics of symmetry and structure. On this page, find out what a group is and how to think about them.

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.

Our neighbour Oscar Randal-Williams tells us about his exciting work at the frontiers of mathematics and the fundamental question he might be just about to answer!

What is group theory and why is it such an exciting area of maths? Two experts explain.
2018 is the centenary of a mathematical result that changed the character of physics.
Symmetry is one of the two guiding principles in understanding probabilities – if different outcomes are equivalent they should have the same probability.
How to get massive particles from gold.
After having explored our economic analogy for the force of electromagnetism, let us turn to the weak force.
Current physical theories suggest that beautiful symmetries underly the fundamental particles and forces of nature. We describe those symmetries using an analogy from economics, and even rediscover the famous Higgs boson.
Now let's look at the economic analogy for electromagnetism.
And finally, here is how the famous Higgs boson gets into the picture.