Does infinity exist? — John D. Barrow gives us an overview, from Aristotle's ideas to Cantor's never-ending tower of mathematical infinities, and from shock waves to black holes. You can also listen to the podcast accompanying this article.

A glimpse of Cantor's paradise — In the 19th century the mathematician Georg Cantor revolutionised the mathematical notion of infinity by discovering a never-ending tower of them, one bigger than the other.

Cantor and Cohen: Infinite investigators Part I and Part II — What's the nature of infinity? Are all infinities the same? And what happens if you've got infinitely many infinities? These two articles explore how these questions brought triumph to one man and ruin to another, venture to the limits of mathematics and find that, with infinity, you're spoilt for choice.

Searching for the missing truth — In mathematics things are either true or false. Or are they? It turns out that you can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a correct set of rules to use? It turns out that the answer hinges on notions of infinity.

Taming infinity — Quantum mechanics and general relativity are incompatible — and this has led to a decades-long search for a theory of quantum gravity that could combine the two. But the particle physicist Richard Woodard thinks that the mismatch between the two could be nothing more than an illusion, created by the complicated maths techniques used in attempts to unite them. This article is from the FQXi community website.

Phantasms of infinity — Infinity is a pain. Its paradoxes easily ensnare the unsuspecting reasoner. So over the centuries, mathematicians have carefully constructed bulwarks against its predations. But now cosmologists have developed theories that put them squarely outside the mathematicians' "green zone" of safety. This article is from the FQXi community website.