To coincide with the 100th International Women's Day two new competitions to find the best young female mathematical minds in the UK and Europe have been launched.

When insects go foraging, they zoom off from their nest in complex zig-zag paths. How do they manage to find their way back home? And how do they manage to do so along a straight path? These questions are explored in an exhibit at the Royal Society Summer Science Exhibition, currently taking place at the Southbank Centre in London.

Water is essential for life on Earth, and it is a resource we all take for granted. Yet it has many surprising properties that have baffled scientists for centuries. Seemingly simple ideas such as how water freezes are not understood because of water's unique properties. Now scientists are utilising increased computer power and novel algorithms to accurately simulate the properties of water on the nanoscale, allowing complex structures of hundreds or thousands of molecules to be seen and understood.

People have been using gold particles dispersed in water — gold hydrosols — for medical purposes for over 1000 years. Recently, hydrosols containing gold nanoparticles have become particularly popular because they have exciting potential in cancer therapies, pregnancy tests and blood sugar monitoring.

What have muesli, social networking sites and flocks of birds got to do with mathematics? Scientists and students from the University of Bath will be explaining all at the Royal Society's prestigious Summer Science Exhibition, which opens today.

This year the Royal Society celebrates its 350th anniversary and Plus is joining in the celebrations. The annual Royal Society Summer Science Exhibition is this year part of a festival called See Further: The Festival of Science + Arts, which explores the links between science and the arts. The festival is taking place at the Southbank Centre in London from the 25th of June to the 4th of July 2010.

The shadow of the late Martin Gardner looms large in Manchester this week as the workshop How to talk maths in public, organised by the Institute of Mathematics and its Applications, draws to a close. The question on everyone's mind is "who will fill the enormous hole left by his absence"?

One in nine women will get breast cancer in her lifetime, and it seems sensible to screen women for breast cancer to treat them as early as possible. But, as David Spiegelhalter explains, screening is a controversial issue.

Maths conquers the summer festivals

Would you prefer a game with a 90% chance of winning, or one with a 10% chance of losing? You might scratch your head and say it's the same thing, and you'd be right, but research has shown that people's perception of risk is surprisingly vulnerable to the way it's presented. In this article David Spiegelhalter and Mike Pearson explore how risk can be spun and there's an interactive animation for you to have a go yourself.

Innumeracy costs UK taxpayers up to £2.4 billion a year.

The UK Statistics Authority fulfills its duty to keep the government honest