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What are mathematical proofs, why do we need them and what can they say about sheep? 
This year's Abel prize shows you can wrap anything, no matter how weirdly shaped. 
Can you measure information? It's a tricky question — but people have tried and come up with very interesting ideas. 

Can a mathematical model of zombies' movements allow the human race to survive impending doom? 
Two mathematicians' visit to the desert sheds new light on avalanches. 
Observers are, of course, vital in physics: we test our theories by comparing them to our observations. But in cosmology, as Jim Hartle explains, we could be one of many possible observers in the Universe and knowing which one we are is vital in testing our theories. 

What is 11+11+11+...? How infinite sums challenge our notion of arithmetic. 