Whenever you smell the lovely smell of fresh coffee or drop a tea bag into hot water you're benefiting from diffusion: the fact that particles moving at random under the influence of thermal energy spread themselves around. It's this process that wafts coffee particles towards your nose and allows the tea to spread around the water. Diffusion underlies a huge number of processes and it has been studied intensively for over 150 years. Yet it wasn't until very recently that one of the most important assumptions of the underlying theory was confirmed in an experiment.
In 1982 Dan Shechtman discovered a crystal that would revolutionise chemistry. He has just been awarded the 2011 Nobel Prize in Chemistry for his discovery — but has the Nobel committee missed out a chance to honour a mathematician for his role in this revolution as well?
How many universes are there? What has made us into who we are? Is there absolute truth? These are difficult questions, but mathematics has something to say about each of them. It can probe the physical reality that surrounds us, shed light on human interaction and psychology, and it answers, as well as raises, many of the philosophical questions our minds have allowed us to dream up. On this page we bring together articles and podcasts that examine what mathematics can say about the nature of the reality we live in.
Paraconsistent mathematics is a type of mathematics in which contradictions may be true.
In such a system it is perfectly possible for a statement A and its negation not A to both be true. How can this be, and be coherent? What does it all mean?
Why can we remember the past and not the future? Why does time appear to move in only one direction when the laws of physics have no preferred direction in time? According to one physicist, it might be because we live in a bubble multiverse.
According to Einstein, the past, present and future have exactly the same character - so why do we feel that there is a particular moment we call "now"? The physicist George Ellis looks for an answer in the curious laws of quantum mechanics.
Convex or concave? It's a question we usually answer just by looking at something. It's convex if it bulges outwards, and concave if it bulges inwards. But when it comes to mathematical functions, things aren't that simple. A team of computer scientists from the Massachusetts Institute of Technology have recently shown that deciding whether a mathematical function is convex can be very hard indeed.