London, September, 1854. A cholera outbreak has decimated Soho, killing 10% of the population and wiping out entire families in days. Current medical theories assert that the disease is spread by "bad air" emanating from the stinking open sewers. But one physician, John Snow, has a different theory: that cholera is spread through contaminated water. And he is just about to use mathematics to prove that he is right.

In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.

Simon Singh, the well-known physicist-turned science and maths communicator, has been awarded the Leelavati Prize for outstanding contributions to public outreach in mathematics by an individual.

What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.

The work of Fields Medallist Stanislav Smirnov will take mathematics and physics into a new phase with his mathematical proof of the understanding of phase transitions.

Eron Lindenstrauss got the Fields Medal for developing tools in the area of dynamical systems and using them to crack hard problems in the seemingly unrelated area of number theory.

Results in mathematics come in several flavours — theorems are the big important results, conjectures will be important results one day when they are proved, and lemmas are small results that are just stepping stones on the way to the big stuff. Right? Then why has the Fields medal just been awarded to Ngô Bào Châu for his proof of a lemma?

Over 3000 mathematicians have gathered to sounds of the tabla and bansuri playing traditional Indian music in the Hyderabad International Convention Centre, and they are all baiting their breath. They are all waiting for the announcement of the Fields medals, the highest honour in mathematics, and the prestigious Gauss, Nevanlinna and Chern Prizes. The hall is a colourful scene filled with mathematicians from around the world, including many local participants in beautiful saris and suits. You can hear a pin drop as the entire hall stands for the entrance of Pratibha Patil, the President of India, who will award the medals to the prize winners...

Researchers have unveiled the first prototypes of robots that can develop emotions and express them too. If you treat these robots well, they'll form an attachment to you, looking for hugs when they feel sad and responding to reassuring strokes when they are distressed. But how do you get emotions into machines that only understand the language of maths?

Two computer geeks claim to have calculated the number pi to 5 trillion digits — on a single desktop and in record time. That's 2.3 trillion digits more than the previous world record held by the Frenchman Fabrice Bellard.

It's not just evil villians who can blow smoke rings, it seems peat moss has been doing it for millennia.

Two lines in a plane always intersect in a single point ... unless the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements. Burkard Polster and Marty Ross explain how to get around the problem.