We talk to two of the organisers of the ICM 2022 in Saint Petersburg.

The Nevanlinna prize winner Constantinos Daskalakis explains why equilibrium may be unattainable and why it's good to be constructive.

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 the Fields medal for his contribution to algebraic geometry.

Peter Scholze has received the Fields medal 2018 for transforming arithmetic algebraic geometry.

Harvey Friedman tells us about a mathematical movement called constructivism and why we need it.

Spider solitaire is a popular online game. But are users right in their suspicion that some programs are rigged?

How can we get a grip on the uncertainties in mathematical models?

Can a mathematical object be said to exist if you can't construct it?

Physics is all about observation. But how much can we actually see with the naked eye?

The limits to what we can observe are not only a matter of science, but also of politics and economics.

Observing the smallest building blocks of matter doesn't involve seeing in the ordinary sense.