# Russell's Paradox

Paraconsistent mathematics is a type of mathematics in which contradictions may be true.
In such a system it is perfectly possible for a statement
A and its negation not A to both be true. How can this be, and be coherent? What does it all mean? |
When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on. |

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. |
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." |

For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are.
Jon Walthoe explains the tricks involved and how great thinkers like Pythagoras, Newton and GĂ¶del tackled the problems. |