All of science can be regarded as motivated by the search for rules behind the randomness of nature, and attempts to make prediction in the presence of uncertainty. Chris Budd describes the search for pattern and order in chaos.
To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
The Riemann Hypothesis is probably the hardest unsolved problem in all of mathematics, and one of the most important. It has to do with prime numbers - the building blocks of arithmetic. Nick Mee, together with Sir Arthur C. Clarke, tells us about the patterns hiding inside numbers.