Articles

Mathematical mysteries: Strange Geometries

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.
Looking at life with Gerardus 't HooftNobel 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.
Mathematical mysteries: Survival of the nicest?

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.
Catching waves with Kip ThorneWhat 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.
Natural born mathematiciansNeuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!
Maths in the dockChemists John Watling and Allen Thomas talk to Plus about the vital role of maths in presenting criminal evidence.
An infinite series of surprisesInfinite 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.
New designs from AfricaPaulus Gerdes takes us on a tour of the mathematical properties of some beautiful designs inspired by the traditional art of Angolan tribespeople.
Mathematical mysteries: Painting the Plane

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.
Three Colours and Seven Colours
Backgammon, doubling the stakes, and Brownian motionBackgammon is said to be one of the oldest games in the world. In this article, Jochen Blath and Peter Mörters discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double.
Why knot: knots, molecules and stick numbersKnots crop up all over the place, from tying a shoelace to molecular structure, but they are also elegant mathematical objects. Colin Adams asks when is a molecule knot a molecule? and what happens if you try to build a knot out of sticks?