Wise old birds win the numbers game

<i>The Parrot's Theorem</i> by Denis Guedj, trans. Frank Wynne (Weidenfeld &amp; Nicolson, &pound;12.99, 344pp)

A Thousand and One Pages: the name of the bookshop run by the 84-year-old, wheelchair-bound lay philosopher, Mr Ruche. He lives above the shop with single mother Perrette, her twins Lea and Jonathan, and her deaf son Max. The tranquillity of the Ruche household is disturbed when, simultaneously, Max finds a parrot and Mr Ruche receives a letter from Elgar, an old friend from university days. Elgar's letter is a mathematical enigma wrapped in a constellation of riddles. Sydney, the parrot, is a talking professor of maths.

A Thousand and One Pages: the name of the bookshop run by the 84-year-old, wheelchair-bound lay philosopher, Mr Ruche. He lives above the shop with single mother Perrette, her twins Lea and Jonathan, and her deaf son Max. The tranquillity of the Ruche household is disturbed when, simultaneously, Max finds a parrot and Mr Ruche receives a letter from Elgar, an old friend from university days. Elgar's letter is a mathematical enigma wrapped in a constellation of riddles. Sydney, the parrot, is a talking professor of maths.

Elgar claims that he has proved two of the oldest and the most famous theorems of mathematics - Fermat's Last Theorem and Goldbach's Conjecture. But a ruthless gang is after the proofs. All Mr Ruche has to do is to decode the explanation in the letter and make sure the proofs do not fall in the wrong hands. Elgar provides two aids: a library of classics of mathematics; and a mysterious "loyal friend" to guide Ruche in the right direction.

The Parrot's Theorem starts as a rather conventional fictional journey through the history of maths. But a pedestrian beginning is soon transformed into a richly textured narrative. Half way through, it turns into an uncut diamond, polished to a brilliant shine towards the end. En route, we are confronted with complex formulae and intricate proofs. But Denis Guedj is so accomplished that he makes most quite accessible. The pace of mathematical complexity is pitched squarely at the level of 12-year-old Max, who has to lip-read proofs.

The fervent research begins with the geometric ideas of Thales, around 600 BC; and ends with Andrew Wiles and his recent proof of Fermat's Last Theorem. In between, they tackle Pythagoras, Euclid, Descartes and Pascal; wrestle with algebra, trigonometry, spherical geometry and calculus; and struggle with imaginary and irrational numbers.

The stroll through history is used to show how mathematics starts as a way of looking at the world of experience and proceeds by focusing on the quantity, shape and structure of things. But then it develops wings, and takes off to explore relationships among ideas such as numbers and symmetry.

Guedj is careful not to represent mathematics as though it was nothing but True. Instead, Ruche discovers that at crucial points in its evolution, mathematics experienced deep crises leading to serious confusion about its very foundation. These episodes, never discussed in front of the children, were very fruitful for the progress of the mathematical imagination. It is through these events that characters and readers to come to appreciate the beauty of mathematics.

There are obvious parallels here with Jostein Gaarder's Sophie's World. But there are also important differences. Gaarder presents philosophy as purely a European enterprise; Guedj's approach to mathematics is much more inclusive. Moreover, he has a real plot, reminiscent of the Arabian Nights, with stories unfolding within stories, deftly combined with the urgency of a thriller.

Over a third of the narrative - as indeed a third of the history of mathematics itself - is concerned with Muslim mathematicians. Guedj has a long string of colourful Muslim characters - from Al-Khwarizimi, the founder of algebra, to Omar Khayyam, the Persian poet and mathematician, to Nasir al-Din al-Tusi, who laid the foundation for the Copernican revolution. But he is not content with simply bringing the "golden age" of Islam and maths vividly to life.

To dethrone the Eurocentric approach, Guedj offers a new, more accurate classification scheme for the history of mathematics. Mr Ruche's first job is to classify the books he has acquired. This he does with the help of the librarians at the famous Institut du Monde Arabe in Paris. The result, laid out in loving detail, will bring tears to the eyes of those who champion Dewey Decimal and Library of Congress classifications.

Guedj wants to show that the history of mathematics is not just the history of numbers and theorems; but the enchanting stories of gifted individuals as well of civilisations. It is a universal history, perhaps the only one that binds humanity together. Moreover, like music, it is universally accessible. We can all dance to mathematics just as we do to music.

The stories of Arab mathematicians make yet another point. Guedj interweaves the historic events surrounding the friendship of Omar Khayyam, Nizam al-Mulk (the Vizir who build the celebrated House of Wisdom library in 11th-century Baghdad) and Hassan Al Sabbah (founder of the Ismaeli sect and leader of the "Order of the Assassins") with the Paris-based narrative of Mr Ruche, Elgar, and their shadowy, villainous friend. As Ruche and Max discover, abstruse mathematical ideas have an uncanny ability to become very practical indeed.

Elgar's concealed proofs become more understandable, if still excruciatingly beyond reach. But the reader is left in no doubt that there is nothing to be proud of in being bad at maths. Sydney, the parrot, escapes the clutches of the gang and returns to the jungle. Back in the Amazon, he relates humanity's greatest achievement to other birds, echoing the 13th-century philosopher Roger Bacon. People who do not know mathematics do not know the depth of their own ignorance. Reading The Parrot's Theorem would be an excellent antidote to that ignorance.

Ziauddin Sardar co-wrote 'Introducing Mathematics' (Icon)