Knots 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?

A question which has been vexing astronomers for a long time is whether the forces of attraction between stars and galaxies will eventually result in the universe collapsing back into a single point, or whether it will expand forever with the distances between stars and galaxies growing ever larger. Toby O'Neil describes how the mathematical theory of dimension gives us a way of approaching the question.

Claude Shannon, who died on February 24, was the founder of Information Theory, which is the basis of modern telecommunications. Rachel Thomas looks at Shannon's life and works.

C. J. Budd and C. J. Sangwin show us how to create mazes, and explain why mazes and networks have much in common. In fact the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion and conquest...

Chomp is a simple two-dimensional game, played as follows. Cookies are set out on a rectangular grid. The bottom left cookie is poisoned. Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.

Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic infection parameters. Matthew Keeling describes some of the mathematical developments that have improved our understanding and predictive ability.

Until you understand the basics of functions and algebra, the thought that a number can be predicted is a surprising one. And of course `magic' and `being surprised' are often the same thing. Rob Eastaway shows us how mathemagicians trade off the fact that you can usually predict precisely the outcome of doing something in mathematics, but only if you know the secret beforehand.

Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the second of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses radioactive decay.

Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.

Steven J. Brams uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers.

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.