Get on a commuter train these days and you can virtually see people's brains crunching away at filling the numbers from 1 to 9 into a square grid. As the Sudoku craze shows no sign of slowing, Hardeep Aiden investigates its relatives and predecessors.

Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how not only shapes, but also laws of nature can be symmetrical, and how this aids our understanding of the universe.

6174 is a very mysterious number. Yutaka Nishiyama explains why, and how beautiful mathematical oddities can inspire us to discover new mathematics.

To arm or to disarm? This is the question in Phil Wilson's article, which explores the maths behind a cold war in slug world.

What is the cosmological constant?

The travels of bank notes give important clues to epidemiologists

Is geometry hard-wired into our brain?

Mathematicians may make the "invisibility cloak" more powerful

Carla Farsi is both an artist and a mathematician, who declared 2005 her Special Year for art and maths. Find out what she got up to, and what it's like being a part of both worlds.

Kurt Gödel, who would have celebrated his 100th birthday next year, showed in 1931 that the power of maths to explain the world is limited: his famous incompleteness theorem proves mathematically that maths cannot prove everything. 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.