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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!
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!
Artificial intelligence and deep learning: Your questions answered

Find out about this important new technology and be part of the conversation.
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.
Counting rose petals

The beautiful rose curve has an odd pattern to the number of its petals – this student and teacher team explain why...
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.
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!

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Groups today: a whistle-stop tour

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!
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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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The secret to a happy summer: Seville, causality and staircases!

As we head get ready for our summer holidays, we share our mathematical highlights from recent events in Spain and the UK and our recommendations for summer reading and listening!
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How to compute the dimension of a fractal

Find out what it means for a shape to have fractional dimension.

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On the mathematical frontline: Modelling behaviour

Our behaviour impacts not just our daily lives. But how do you mathematically describe the messiness of human behaviour?
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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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Beating bird flu with maths

With bird flu spreading through cattle herds in the US and infecting humans, the diseases poses a severe threat to wild life, poultry and also people. What can mathematical modelling do to help?
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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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