## P versus NP

The simple act of packing your luggage can open a complex can of worms.

A famous question involving networks appears to have come closer to an answer.

What will quantum computers be able to do that ordinary computers can't do?

*Travelling Salesman* is an unusual movie: despite almost every character being a mathematician there's not a mad person in sight. Moreover, the plot centres on one of the greatest unsolved problems in mathematics. We were lucky enough to speak to the writer/director Tim Lanzone about creating drama from mathematics.

Struggling to solve today's sudoku? Is your tried and tested method hitting a brick wall and you feel like you are going around in circles? New research might make you feel a bit better: you might not necessarily be stuck... perhaps you are just in a patch of transient chaos on your way to the solution.

The *Travelling Salesman* movie is coming to the UK! Get your tickets here and find out about the P vs NP problem.

Convex or concave? It's a question we usually answer just by looking at something. It's convex if it bulges outwards, and concave if it bulges inwards. But when it comes to mathematical functions, things aren't that simple. A team of computer scientists from the Massachusetts Institute of Technology have recently shown that deciding whether a mathematical function is convex can be very hard indeed.

*Plus*contributor Lewis Dartnell reports on the scramble for million-dollar prizes that made mathematical headlines at the BA Festival of Science in September 2004.

**grand mathematical challenges**of the 21st century. But be warned...these problems are hard. In the first of two articles, Chris Budd explains how to hit the bigtime.