divergence

Approximating a function with a divergent series.

If you ignore exponentially small terms they can come back to bite you.

How a question about rainbows led to an entire field of mathematics.

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

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.
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.
The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.

  • How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.

  • Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.

  • Find out why the formula we use to work out conditional probabilities is true!

  • We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.