Sequences of numbers can have limits. For example, the sequence 1, 1/2, 1/3, 1/4, ... has the limit 0 and the sequence 0, 1/2, 2/3, 3/4, 4/5, ... has the limit 1. But not all number sequences behave so nicely. Can we still discern some sort of limiting behaviour?

Yesterday we opened the Plus New York office, amidst snow covered streets at the foot of the Empire State building.

On 14 March at 1.59pm GMT, Marcus du Sautoy will host Pi Day Live, an interactive exploration of the number which has fascinated mathematicians throughout the ages. He wants to rediscover pi using ancient and intriguing techniques, and he needs your help!

They've done it again! GIMPS has discovered the largest known prime number: 257,885,161-1. This massive 17,425,170 digit number was discovered thanks to clever distributed computing software that uses idle computer time donated by volunteers.

How would you go about adding up all the integers from 1 to 100? Tap them into a calculator? Write a little computer code? Or look up the general formula for summing integers?

Sometimes you just can't argue with the evidence. If a large sample of very ill people got better after dancing naked at full moon, then surely the dance works. But hang on a second. Before you jump to conclusions, you need to rule out a statistical phenomenon called regression to the mean.

Scientists find a new method of storing information in DNA.

Climate change is causing populations to sync in different species in the high arctic, increasing their risk of extinction.

Stephen Hawking was once told by an editor that every equation in a book would halve the sales. Curiously, the opposite seems to happen when it comes to research papers. Include a bit of maths in the abstract (a kind of summary) and people rate your paper higher — even if the maths makes no sense at all.

The London Underground turns 150 today! It's probably the most famous rail network in the world and much of that fame is due to the iconic London Underground map. But what makes this map so special?

Without doubt the biggest event in physics and maths this year was the discovery of the Higgs boson. Relive the excitement and understand what it's all about with these Plus articles.

Merry Christmas!