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.

It's International Year of Astronomy and all eyes are on Galileo Galilei, whose astronomical observations 400 years ago revolutionised our understanding of the Universe. But few people know that Galileo wasn't the first to build a telescope and turn it on the stars. That honour falls to a little-known mathematician called Thomas Harriot, who excelled in many other ways too. Anna Faherty takes us on a tour of his work.

A new liquid breaks the laws of physics