Imaginary numbers

The fictional maths in Denis Guedj's The Parrot's Theorem just doesn't add up, finds Simon Singh

Imaginary numbers


The Parrot's Theorem by Denis Guedj 350pp, Weidenfeld, £12.99
Buy it at BOL

The last year has seen an unprecedented boom in the publishing of novels about mathematics. Number Nine by Cecil Balmond, The French Mathematician by Tom Petsinis and Leaning Towards Infinity by Sue Woolfe all caused minor stirs; earlier this year Apostolos Doxiadis's Uncle Petros and Goldbach's Conjecture hit the headlines by offering a $1m prize for whomever could solve the eponymous problem. Now we have The Parrot's Theorem by Denis Guedj and, coming next year, The Wild Numbers by Philibert Schogt.

These books are neither as gripping as a Stephen King novel nor as literary as a Booker Prize winner, but they have a different objective from most other fiction - to smuggle mathematical concepts into the mind of the unsuspecting reader by wrapping the maths inside an engaging plot. The question is, does this new genre of fictional maths succeed?

The boom in maths books began when non-fiction authors started to write about mathematicians as well as mathematics, placing the intellectual concepts within a framework of history and human stories. The intention was to capture the reader's imagination for long enough to persuade him or her that understanding mathematical ideas and proofs can be a rewarding and enthralling experience.

Some of the finer exponents of this style of mathematical writing include Paul Hoffman (author of The Man who Loved Only Number ) and Sylvia Nasar (A Beautiful Mind). In the wider area of general science, Dava Sobel has succeeded in introducing the work of John Harrison (inventor of the marine chronometer) and the ideas of Galileo to hundreds of thousands of readers. This style of writing has been dubbed narrative non-fiction.

The majority of popularisers are attempting to convey the wonder of an esoteric subject to readers who would normally run a mile at the mere mention of trigonometry. The good news is that narrative non-fiction has been relatively successful in taking mathematics to a new readership, but perhaps the new pure-fiction approach can reach out to an even wider audience.

There is inevitably a level of compromise. The novelist seems doomed either to have the flow of the plot interrupted by equations or to omit the meaning of mathematics; without the nitty-gritty of maths it is impossible to convey any of the beauty of the subject. In Uncle Petros and Goldbach's Conjecture , Doxiadis is fortunate in having at the heart of his story a problem that is simple to explain. In 1742, the Prussian-born Christian Goldbach suggested that every even number bigger than 2 is the sum of two prime numbers: 6=3+3, 8=5+3, 10=7+3... (A prime number is one that cannot be divided by any number except 1 and itself, such as 5 or 7.)

For 200 years every even number that has been tested has obeyed Goldbach's conjecture, but nobody has ever been able to prove that the conjecture holds true for every even number up to infinity. Having established the problem without traumatising the reader, Doxiadis spends the rest of the novel concentrating on his characters and plot, in particular Petros Papachristos and his quest to prove the conjecture. The result is a highly readable novel about what drives mathematicians to spend decades searching for solutions to apparently insoluble problems.

By comparison, The Parrot's Theorem contains considerably more mathematics. Denis Guedj, Professor of the History of Science at Paris VIII University, has constructed a Sophie's World -type schema that enables him to use a child as a channel for explaining numerous mathematical ideas to his readers. The bizarre plot concerns a mathematical hermit in the Amazon jungle, an evil criminal genius, a murder mystery, a Parisian bookseller and a deaf child called Max who encounters an exceptionally eloquent parrot.

Along the way Max learns about 2,000 years of mathematics, which means that there are large sections discussing topics such as geometry, arithmetic, zero, imaginary numbers and calculus. Non-mathematicians will find some of these pages heavy going, but if they can persevere and comprehend the lines of logic, the consequence will be a genuine insight into the wonder of numbers. Unfortunately, no easy alternative exists when it comes to learning about mathematics, as Ptolemy II learned when he asked Euclid if there was a shortcut to understanding geometry. Euclid replied: "There is no royal road to geometry."

The plot is just about engaging enough to maintain the reader's momentum through the didactic sections. If further sustenance is required, one can look forward to Guedj's charming historical detours. For example, he describes the ethos of the Pythagorean Brotherhood. When a disciple entered the Brotherhood, he had to give all his worldly goods to the community. For five years students could only listen to Pythagoras's teaching from behind a curtain . . . Those who failed the tests of the Brotherhood were expelled, but were given twice the value of the goods that they had originally contributed. If they could not gain intellectually, then they should be compensated materially. A grave was dug within the grounds of the school, symbolising the tragedy of having lost a potential mathematician.

So Guedj's novel contains a pleasant plot, some excellent mathematical lectures and great historical tales, but how does it compare to books about real mathematics? I may be biased, but none of the fictional mathematics that I have so far read quite matches the standard of the narrative non-fiction currently being published. Hoffman's The Man Who Loved Only Numbers is a brilliant biography of Paul Erdös, one the great mathematicians of the 20th century, who dedicated his entire life to proving mathematical theorems. Erdös also had a penchant for one-liners that are as witty as any that a novelist could fabricate.

Sylvia Nasar's A Beautiful Mind is the story of John Nash, who did his greatest mathematics in his twenties before succumbing to paranoid schizophrenia. The book is an elementary introduction to game theory, but it is also a romance, a tragedy and an examination of madness and its treatments in the 1950s and 1960s. In both these cases, the truth is stranger than any mathematical fiction.