We talk to Maryna Viazovska, who in 2016 made a breakthrough in the theory of sphere packings.

How to arrange oranges in higher dimensions.

How to optimally fill a box with eight-dimensional oranges.

How chickens' eyes solve a subtle maths problem.

A new foam with medical potential

The Eternity puzzle is back with a $2 million prize

Has mathematics become an experimental science?

In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.

Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.

Sir Walter Raleigh is perhaps best known for laying down his cloak in the mud for Queen Elizabeth I. But, he also started a mathematical quest which to this day remains unsolved.