# Articles

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

*Plus*is very proud to present

**Professor Stephen Hawking**'s own Birthday Symposium address.

*Plus*talks to

**Sir Roger Penrose**about all this and more.

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.

**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.

One of the most puzzling aspects of human behaviour is cooperation, in situations where backstabbing and selfishness would seem to be more rewarding. From the point of view of evolutionary theory, the very existence of altruism and cooperation appear mysterious.

**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.

**Professor Kip Thorne**shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.

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

**John Watling**and

**Allen Thomas**talk to

*Plus*about the vital role of maths in presenting criminal evidence.

**C. J. Sangwin**shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.

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.