A Rubik's cube, you'll be pleased to hear, can always be solved in at most 20 moves, no matter how badly it was scrambled up to start with. Mathematicians have proved that that's true. But what if you're wrestling with a larger cube that has more than three little cubes in a row?

If you are, then you may be one of the 5 to 7% of the population suffering from dyscalculia, the mathematical equivalent of dyslexia. But unlike many dyslexia sufferers, you probably haven't received the help you need to cope with your condition. As a recent article published in the journal Science points out, dyscalculia is the "poor relation" of dyslexia.

Astronomers have this month trained the world's largest steerable radio telescope on 86 Earth-like planets. The data collected by the telescope will later be analsyed by an estimated one million amateur alien hunters, users of SETI@home, for messages from other civilisations.

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?