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Groups: The basics

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

Find out how a story starting with the simple notion of counting ends in a revolutionary new way of doing maths that uses computers to harness the power of human collaboration!
Artificial intelligence and deep learning: Your questions answered

Find out about this important new technology and be part of the conversation.
The murmuration conjecture: finding new maths with AI

Artificial intelligence is changing all our lives - even the lives of mathematicians! Yang-Hui He tells us about his exciting new conjecture, developed with the help of AI, that reveals patterns in the prime numbers that look like flocks of birds.
GO-Science National Numeracy Day challenge!

We're helping the Government Office for Science to bring you an Olympic challenge for National Numeracy Day!
What is a square?

If a shape has equal sides and all 90 degree angles then it's a square, right? Well, wrong! Find out how to draw right-angled triangles and even pentagons in this short article.
Too big to write but not too big for Graham

Meet the number that's bigger than the observable Universe!
The COVID-19 vaccines: Your questions answered

Are they safe? Are they effective? Will they stop the pandemic? Find out with our FAQ informed by experts.
Counting rose petals

The beautiful rose curve has an odd pattern to the number of its petals – this student and teacher team explain why...
Myths of maths: The golden ratio

The golden ratio has many amazing properties. But is it really a secret of nature and the epitome of beauty?

Are you curious about maths and the world? Then explore plus.maths.org to stay connected with mathematics: from the maths of everyday life to the latest current research!

podcast

David Spiegelhalter and the art of uncertainty

We talk to David Spiegelhalter about eggs, politics, coins and his new book The art of uncertainty.
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Euromaths: Avi Wigderson

Should we allow mathematical proofs to contain errors? We find out from Avi Wigderson in our podcast series covering the European Congress of Mathematics 2024.
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Maths in a minute: Cayley graphs

Trying to solve a Rubik's cube? A Cayley graph gives you a road map for doing this — and is similarly useful for dealing with any other type of mathematical group!
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Explaining AI with the help of philosophy

As artificial intelligence becomes increasingly important in our society, can philosophy offer us a way to explain decisions made by AI systems?

podcast

What are groups and what are they good for?

Groups are staples in mathematics and group theory is often described as the study of symmetry. But what does that mean? Find out with Justin Chen!
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Maths in a minute: Measure

Learn how lengths, areas, and volumes generalise to the concept of measure, and how this relates to integration and probability.
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Moduli spaces: A journey into the world of shapes

How many different surfaces are there? The question seems impossible to answer but mathematicians are good at dealing with multitudes. Follow us into the world of moduli spaces!
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Maths in a Minute: Group actions

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.

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