Plus is very proud to present Professor Stephen Hawking's own Birthday Symposium address.

Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.

Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.

Nobel Prizewinning Physicist Professor Gerardus 't Hooft has always been fascinated by the mathematical mysteries of nature. He tells Plus about his early life, and what our Universe might really be like.

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.

Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!

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.

Chemists John Watling and Allen Thomas talk to Plus about the vital role of maths in presenting criminal evidence.

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.

Paulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.

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.