We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy.

If you like mathematics because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. In this article Phil Wilson looks at constructivist mathematics, which holds that some things are neither true, nor false, nor anything in between.

Phil Wilson continues our series on the life and work of Leonhard Euler, who would have turned 300 this year. This article looks at the calculus of variations and a mysterious law of nature that has caused some scientists to reach out for god.

In last issue's Graphical methods I Phil Wilson used maths to predict the outcome of a cold war in slug world. In this self-contained article he looks at slug world after the disaster: with only a few survivors and all infra-structure destroyed, which species will take root and how will they develop? Graphs can tell it all.

The three door problem has become a staple mathematical mindbender, but even if you know the answer, do you really understand it? Phil Wilson lets his imagination run riot in this intergalactic application of Bayes' Theorem.

It has often been observed that mathematics is astonishingly effective as a tool for understanding the universe. But, asks Phil Wilson, why should this be? Is mathematics a universal truth, and how would we tell?

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.