We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.

This is a fascinating book on the application of game theory to situations in philosophy, politics, law, history, literature and even the Bible. The author shows that real insight can be obtained into optimal strategies for dealing with some famous dilemmas.

We often think of mathematics as a language, but does our brain process mathematical structures in the same way as it processes language? A new study published in the journal Psychological Science suggests that it does: the process of storing and reusing syntax "works across cognitive domains."

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.

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.

We like to think of the human brain as special, but as we reported on Plus last year, it has quite a lot in common with worm brains and even with high-performance information processing systems. But how does it compare to online social networks? In a recent lecture the psychiatrist Ed Bullmore put this question to the test.

With twenty skillfully written essays Tony Crilly paints a broad-stroke picture of modern mathematics, focusing on some of the most exciting topics. This book is intended for people whose acquaintance with mathematics is limited to their high school years, but who want to know "what all this fuss is about". It is ideal for those who have heard that mathematicians talk about imaginary numbers and unbreakable codes, and want to know how much of it, if any, is true.

Foraging ants have a hard life, embarking on long and arduous trips several times a day, until they drop dead from exhaustion. The trips are not just long, they also follow complex zig-zag paths. So how do ants manage to find their way back home? And how do they manage to do so along a straight line? Their secret lies in a little geometry.

Computing is at the heart of our modern world, but what are its frontiers? This book presents new trends in this fast growing field. Although the topics covered range from spacecraft control to embedding intelligence in bacteria, they all coincide in one fundamental point: the future of computing is a synthesis with nature.

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

Physicists at the University of California, Los Angeles set out to design a better transistor and ended up with a discovery that may lead to a new explanation of electron spin and possibly even the nature of space.

In some sense, all of maths should come under the label "logic", but mathematical logic has shown that mathematics isn't entirely logical. Makes sense? If not, then this teacher package may help.