Author: Marianne Freiberger

Guilt, so some people have suggested, is what makes us nice. When we do someone a favour or choose not to exploit someone vulnerable, we do it because we fear the guilt we'd feel otherwise. A team of neuroscientists, psychologists and economists have this month produced some new results in this area, using a model from psychological game theory.

If you are prone to forgetting your passwords, you're not alone. To make sure we remember all our passwords, many of us take measures that defeat the purpose. These include, as studies have shown, using the same password for everything or writing them down on post-it notes and sticking them to our computer. But such sloppiness makes easy work for evil agents out to steal our data and identities. Now physicists from the US and Germany have devised a safer way of using passwords that takes account of the human need for memorability.

The Abel Prize 2011 goes to John Willard Milnor of Stony Brook University, New York for "pioneering discoveries in topology, geometry and algebra".

When you try to put democracy into action you quickly run into tricky maths problems. This is what happened to Andrew Duff, rapporteur for the European Constitutional Affairs Committee, who was charged with finding a fair way of allocating seats of the European Parliament to Member States. Wisely, he went to ask the experts: last year he approached mathematicians at the University of Cambridge to help come up with a solution. A committee of mathematicians from all over Europe was promptly formed and today it has published its recommendation.

In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics?

It requires only a little processing power, but it's a giant leap for robotkind: engineers at the University of Southampton have developed a way of equipping spacecraft and satellites with human-like reasoning capabilities, which will enable them to make important decisions for themselves.

It's been nearly 18 months since the Large Hadron Collider at CERN started up and scientists are eagerly awaiting their first glimpse into the cosmic mysteries it was designed to explore. But when can we realistically expect the first ground-breaking discoveries to come through? Last week, John Ellis, outgoing leader of the theory division at CERN, addressed an audience of physicists at the University of Cambridge to update them on the current state of play. Plus went along and also managed to catch Ellis for a quick interview.

Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin.

This book is a mixture between an encyclopedia and a collection of intriguing ideas. In some sense, it's a plain English encyclopedia of maths, embellished with some examples for entertainment. So whether you're trying to get at the "true" meaning of something textbooks only define using passionless symbols, or are looking for a little diversion before going to sleep, this book can give you both.

This book tells the fascinating story of strange geometric objects that have achieved some fame outside of maths and even inspired a Woody Allen joke: they're called Calabi-Yau manifolds. When Plus recently interviewed one of its authors he was adamant that maths should be brought to the masses without dumbing down or glossing over the tricky parts. And this is just what this books sets out to achieve.