This week the International Symposium on Mathematical Programming (ISMP) took place in Berlin. It's the world congress of mathematical optimisation, which drew over 2,000 scientists and members of industry to Germany's capital. But what exactly were they talking about?

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.

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