one-sided surface

In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.

Maths in a minute

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

Maths in three minutes: Map projections

Getting a different picture of our planet.
Unlocking the workforce

How can we all get back to work safely in the face of a lingering pandemic?
The agent perspective

How do we learn and understand the world? What separates us from machines? Yoshua Bengio believes it all comes down to our agency.
Football: Was points per game fair?

Would the "points per game" method have led to a fair outcome of the Premier League?
What is constructor theory?

A new way of looking at the physical world promises to shed light on some of the problems physics as we know it can't deal with.