Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.
Chemists John Watling and Allen Thomas talk to Plus about the vital role of maths in presenting criminal evidence.
Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.

Suppose you have an infinitely large sheet of paper (mathematicians refer to this hypothetical object as the plane). You also have a number of different colours - pots of paint, perhaps. Your aim is to colour every point on the plane using the colours available. That is, each point must be assigned one colour.