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.
What's the nature of infinity? Are all infinities the same? And what happens if you've got infinitely many infinities? In this article Richard Elwes explores how these questions brought triumph to one man and ruin to another, ventures to the limits of mathematics and finds that, with infinity, you're spoilt for choice.
Richard Elwes continues his investigation into Cantor and Cohen's work. He investigates the continuum hypothesis, the question that caused Cantor so much grief.
When the famous diagram fails
Runner up in the general public category. Great minds spark controversy. This is something you'd expect to hear about a great philosopher or artist, but not about a mathematician. Get ready to bin your stereotypes as Rebecca Morris describes some controversial ideas of the great mathematician David Hilbert.
When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life.
What do computers and light switches have in common? Yutaka Nishiyama illuminates the connection between light bulbs, logic and binary arithmetic.
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?

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?

When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
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