## Articles

**Yutaka Nishiyama**explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.

**Chris Budd**investigates.

**Christine Currie**explains how your airfare is calculated.

**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.

**Yutaka Nishiyama**illuminates the connection between light bulbs, logic and binary arithmetic.

**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?