"Mathematics is a science of structures and the main equations of physics are some of the most beautiful structures we can find." Clément Mouhot, from the University of Cambridge, gave an invited lecture at the International Congress of Mathematicians 2018 (ICM). We talk to him about his work on differential equations and mathematical physics.

Ivan Smith is Professor of Geometry at the University of Cambridge and gave an invited lecture at the International Congress of Mathematicians 2018 (ICM). We talk to him about his work and what he likes about the ICM.

The next International Congress of Mathematicians will take place in 2022 Saint Petersburg. We were lucky to catch up with two of its organisers, Stanislav Smirnov and Andrei Okounkov, during a very busy break at the current ICM, to ask them why they wanted to bring the ICM to Russia, what exactly they are planning, and what they have learnt from Rio.

You can also listen to this interview as a podcast.

Constantinos Daskalakis has been awarded the Rolf Nevanlinna Prize at the International Congress of Mathematicians 2018. The prestigious prize is awarded every four years for outstanding contributions in mathematical aspects of information sciences. In this video Daskalakis tells us about the work he is being honoured for, which involves complexity theory, game theory, online dating and traffic jams.

Caucher Birkar has been awarded a Fields medal for his contributions to a field of maths called algebraic geometry. The area does exactly what its name suggests: it tries to understand geometric objects using equations that describe them.

It's an idea you might be familiar with from school. The equation