"Mathematics is not yet ready for such problems." This is what the mathematician John Conway reportedly said about the Collatz conjecture, a simple-looking, yet unsolved mathematical mystery. This week Plus hosted two intrepid work experience students, Sabrina Qian and Joe Dickens, who decided to have a go at this fiendish problem nevertheless. And they made some intriguing discoveries. Here is what they came up with.
If you are (or were) an England fan and don't feel like watching Germany's unstoppable advance to take the ultimate trophy, why not use the freed-up time to look at the maths behind the beautiful game...
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.
Obesity has reached epidemic proportions and the World Health Organisation estimates that, by 2015, about 3 billion adults will be overweight or obese worldwide. These individuals will be at increased risk of cardiovascular disease, type 2 diabetes, cancer and osteoarthritis.
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.
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.