## proof

What are mathematical proofs, why do we need them and what can they say about sheep?

**Gregory Chaitin**explains why he thinks that Gödel's incompleteness theorem is only the tip of the iceberg, and why mathematics is far too complex ever to be described by a single theory.

**David Acheson**? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.

**Robert Hunt**concludes our Origins of Proof series by asking what a proof really

*is*, and how we know that we've actually found one. One for the philosophers to ponder...

**Jon Walthoe**explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems.

**J.V. Field**continues our series on the origins of proof with an examination of Kepler's astronomy.