In space, do all roads lead to home?Is the Universe finite, with an edge, or infinite, with no edges? Or is it even stranger: finite but with no edges? It sounds far-fetched but the mathematical theory of topology makes it possible, and nobody yet knows the truth. Janna Levin tells us more.
Extracting beauty from chaosImages based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.
Computing the Mandelbrot setAlmost everyone reading this article has no doubt encountered pictures from the Mandelbrot Set. Their appeal is not limited to the mathematician, and their breathtaking beauty has found its way onto posters, T-shirts and computers everywhere. Yet what is a fractal?
The origins of proof III: Proof and puzzles through the agesFor millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.
Ever-increasing standards: a problem of communication?
A postcard from ItalyEugen Jost is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it.
