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.

It's Monty Hall, only better!

Comparing and communicating small lethal risks is a tricky business, yet this is what many of us are faced with in our daily lives. One way of measuring these risks is to use a quantity called the micromort. David Spiegelhalter and Mike Pearson investigate.

When you flip a coin we assume it has equal chance of coming up head or tails, so any coin flipping game should be a fair one. But Yutaka Nishiyama and Steve Humble can give you the winning advantage.