Marianne Freiberger

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.

The human genome is represented by a sequence of 3 billion As, Cs, Gs, and Ts. With such large numbers, sequencing the entire genome of a complex organism isn't just a challenge in biochemistry. It's a logistical nightmare, which can only be solved with clever algorithms.

On March 14 2010 a mathematician and a magician teamed up to perform what they believed to be the world's largest live magic trick. The trick involved a thousand volunteers from the around the world who, using free choice, each came up with a number that was only known to themselves. And although the volunteer might be on the other side of the globe, the mathematician and the magician were able to read their mind and tell them which number they had chosen.

One advantage of the UK voting system is that nobody could possibly fail to understand how it works. However, the disadvantages are well-known. Differently sized constituencies mean that the party in government doesn't necessarily have the largest share of the vote. The first-past-the-post system turns the election into a two-horse race, which leaves swathes of the population un-represented, forces tactical voting, and turns election campaigns into mud-slinging contests. There are many alternative voting systems, but is there a perfect one? The answer, in a mathematical sense, is no.

A Galileo of number theory

The state of the Arctic

E8 symmetry discovered in lab for the first time

Keeping up with temperature

Experiment discovers evidence for dark matter

Making sure that vaccination works