convergence

We take the real numbers for granted, but what are they really?

Compound interest is the curse of debt and the blessing of saving. Find out how it works and what it has to do with one of the most important numbers in mathematics.

This problem about an infinite sum has a surprising answer.

What is 1-1+1-1+1-1+...? How infinite sums challenge our notion of arithmetic.

What do you get when you add up all the natural numbers 1+2+3+4+ ... ? Not -1/12! We explore a strange result that has been making the rounds recently.

The number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.

Usain Bolt, the "fastest man on the planet", aims to get his 100 metre world record of 9.58 seconds down to 9.40 seconds. What has mathematics got to say about this quest?

Mathematics takes to the stage with A disappearing number, a work by Complicite, inspired by the mathematical collaboration of Hardy and Ramanujan. Rachel Thomas went to see the play, and explains some of the maths. You can also read her interview with Victoria Gould about how the show was created.
Victoria Gould has always known she would be an actor, and went straight from studying arts at school to running her own theatre company. But she eventually had to come clean about her guilty secret - she loves maths - and has since managed to combine a career as a research mathematician and teacher with a successful acting career on television and in theatre. She tells Plus why she needs to use both sides of her brain.
Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.