Physicist and cosmologist Paul Davies has made an unusual move into the infant discipline of astrobiology. He tells Plus about his interest in the big questions: what is life, how would we recognise aliens - and are they all around us?

Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the first of two articles, he talks about connections between algebra and geometry, and the importance of lateral thinking in mathematics.

The 2003 Dirac Lecturer, distinguished physicist Freeman Dyson, tells Plus why he is an optimist, what makes life interesting and why old-fashioned maths is what you need for physics.

If you had a crystal ball that allowed you to see your future, what would you arrange differently about your finances? Plus talks to the Government Actuary, Chris Daykin about the pensions crisis, and how actuaries use statistical and modelling techniques to plan for all our futures.

Currently, disabled computer users have a hard time inputting text, using laborious word-completion. Plus find out how this is changing, thanks to Dasher, a new open-source text-entry system based on arithmetic coding.

In 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, Plus looks at the case and finds out how courts deal with statistics.

Theoretical physicists are searching for a 'Theory of Everything' to reconcile quantum mechanics and relativity - the two great physical theories of the twentieth century. String theory is a current hot favourite, and some of the world's most eminent physicists tell us why.

Suppose you walk past a barber's shop one day, and see a sign that says
"Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else."
This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.

One of the most puzzling aspects of human behaviour is cooperation, in situations where backstabbing and selfishness would seem to be more rewarding. From the point of view of evolutionary theory, the very existence of altruism and cooperation appear mysterious.