What do young researchers in maths and computer work on? We find out at the Heidelberg Laureate Forum 2019. From crime scene investigation to theoretical investigations of computer algorithms, the range is wide.

How do green algae manage a perfect breaststroke even though they haven't got a brain? The maths of synchronisation explains and even sheds light on evolution.

Many things in nature seem to be striving for a purpose — the carefully choreographed flocking of birds is an example. Are these birds smart enough to follow a common goal or is the apparent purpose an illusion? Find out with these articles. (Photo: Walter Baxter.)

Machine learning is the most important recent development in artificial intelligence. Find out how it works, what it can do, where it comes from and whether it's ethical with this collection of articles.

Wim Hordijk recently sent us a digital postcard from Vienna, where he had traced the steps of the eminent mathematician Kurt Gödel. Here is what he discovered.

Keats complained that a mathematical explanation of rainbows robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.