Tracing the path of invading species using a famous problem in graph theory.

How many possible genetic relationships are there between a collection of different species? The answer is mind-bogglingly large.

In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics?

Next year is a great one for biology. Not only will we celebrate 150 years since the publication of On the origin of species, but also 200 years since the birth of its author, Charles Darwin. At the heart of Darwin's theory of evolution lies a beautifully simple mathematical object: the evolutionary tree. In this article we look at how maths is used to reconstruct and understand it.

Underlying our vast global telecommunications networks are codes: formal schemes for representing information in machine-readable and transmissible formats. Kona Macphee examines the prefix property, one of the important features of a good code.