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In this busy time why not put your feet up and learn some maths in just a few minutes with this year's *Plus* advent calendar. Now what's behind today's door?

This year's Nobel Prize for Physics brings together the physics of materials with one of our favourite areas of maths – *topology*.

Can the very act of observing something change what's being observed? This series of articles and videos explores some basic questions about the role of the observers in physics.

If only the fittest survive, how can we explain the evolution of altruism? Mathematics has some answers.

Computer scientists have made a breakthrough in the theory of cake cutting.

A model of the interaction between predators and prey explains why sometimes frogs appear to eat snakes.

In these two short videos the legendary Andrew Wiles talks about what it was like to prove Fermat's Last Theorem, and what it feels like to do maths.

Image © Heidelberg Laureate Forum Foundation / Flemming – 2016

Five favourite problems inspired by Leonhard Euler, one of the greatest mathematicians of all time.

An insightful look at the climate models that predict our future.

With intelligent machines taking over more and more of our jobs, what does the rise of AI mean for humanity?