What is the cosmological constant?

Mario Livio's new book tells the story of the elusive quintic equation and how, from the mysteries of this unsolvable puzzle, group theory was born. This branch of mathematics describes and defines symmetry, and at the core of the book is a strong sense of just how much of our behaviour and appreciation of the world around us depends on our ability to perceive symmetrical proportions.

This is a new edition of an old classic. Abbott wrote this beautiful tale over a hundred years ago under the pseudonym A Square. It still is one of the best introductions to a mathematical world of higher dimensions, and it's an amazingly imaginative social satire, too.

Edward Burger and Michael Starbird are both Professors of mathematics and have won numerous teaching and writing awards for their work. Burger has even performed stand-up comedy in night-clubs and is no stranger to appearing on television and radio broadcasts. In their company the reader is clearly in safe hands and these achievements are reflected in the quality of the book. The text is also written with a charm that is lamentably rare in maths literature.

Duplex difference Sudoku

Teaching a machine to understand music is an incredibly difficult task, which uses all the mathematical power of digital signal processing. But teaching a machine to compose music is quite another matter, and the wonderful world of mathematical patterns proves to be a gold mine. Nick Collins talks to Plus about his artificial musician.

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.

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