P versus NP
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.
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.