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, "Robert Karl Stonjek"
Nature 454, 580-581 (31 July 2008) | doi:10.1038/454580a; Published
online 30 July 2008
Maths and mad hatters
BOOK REVIEWED-Lewis Carroll in Numberland: His Fantastical
Mathematical Logical Life
by Robin Wilson
Allen Lane/Norton: 2008. 237 pp./208 pp. £16.99/$24.95
Legend has it that Queen Victoria was so enchanted by Alice's
Adventures in Wonderland that she insisted on Lewis Carroll's next
work being sent to her. One can imagine her expression as she opened
the book that arrived, entitled An Elementary Treatise on Determinants.
Charles Lutwidge Dodgson had many careers. He is best remembered for
the sublime nonsense verse he wrote under the name Lewis Carroll. He
was a pioneering childrens' photographer and a lay clergyman admired
for his sermons. Before all else he was a mathematician who taught
generations of students at the University of Oxford, UK, contributed
to the fields of geometry, algebra and logic, and used games and
puzzles to entertain and instruct. In Lewis Carroll in Numberland,
mathematician Robin Wilson reveals Dodgson to be the grandfather of
He was precocious, orthodox and craved variety. Born in 1832 in
Cheshire, UK, Dodgson was a lecturer at Oxford by his early twenties.
At a time when non-Euclidean geometries were catching on, he wrote a
four-act play stubbornly arguing that Euclid should remain at the
centre of the Oxford curriculum. He invented a method to find the
determinants of large matrices, but his strange notation meant that it
never caught on. Later, he sought mathematical remedies for real
injustices, suggesting tie-break methods for parliamentary elections
to his friend Lord Salisbury, and devising a way to make lawn tennis
tournaments fairer to the runners-up.
Some work was ahead of its time, especially his efforts to bring
mathematics to young people. Although pupils complained of his
"singularly dry and perfunctory manner" in the classroom, Dodgson's
gift for teaching shone through in dozens of self-published guides for
students, and in his letters to children. Wilson shows that he found
humour in the plainest of subjects and did not underestimate his young
correspondents, once commenting that intelligence seemed to vary
inversely with size. In person, he drew their attention using guessing
games and feats of memory. He could recite the first 71 digits of pi
using a series of nonsense couplets as memory aids, and once contrived
an algorithm that could give the date of every Easter Sunday until 2499.
Sooner or later every child who knew Dodgson would receive a brain
teaser. Published in collections with titles such as A Tangled Tale
and Pillow Problems Thought Out During Sleepless Nights, many of these
word problems required the dutiful application of algebra,
trigonometry or geometry. Some needed mere patience and common sense.
One devious puzzle asked how many guests would come to a dinner party
if a man invited his father's brother-in-law, his brother's
father-in-law, his father-in-law's brother, and his brother-in-law's
father. Others were in the form of fallacies to debunk. Dodgson once
asked a 14-year-old boy to find the flaw in his proof that 2 + 2 = 5,
which Wilson reveals to be a stealthy division by zero. A few problems
hinged simply on a pun.
Later in life, Dodgson taught symbolic logic with a board game that
used red and grey counters on a set of nested squares, which he
believed superseded the overlapping circles championed by British
logician John Venn. In Dodgson's Game of Logic, published under his
pen name to gain a wider audience, one can see some of the punctilious
lunacy of the Mad Hatter. Following chains of inference he called
'sillygisms', he led readers from reasonable premises to conclusions
such as "Babies cannot manage crocodiles", "No banker fails to shun
hyaenas" and "No bird in this aviary lives on mince-pies". These
examples are perhaps less interesting as logic than as the stirrings
of a systematic kind of literature, also apparent in his symmetrical
poem that can be read vertically and horizontally.
Lewis Carroll in Numberland is not a conventional biography. Robin
Wilson has winnowed Dodgson's prodigious output into a first-rate
scrapbook of proofs and puzzles. Sadly, his tone is often fawning and
flat - not up to the standard of mathematical storytelling he set in
his previous book, Four Colours Suffice (Allen Lane, 2002), on the
history of the conjecture that four colours can fill any map without
any bordering countries sharing a colour. By immersing us in Dodgson's
correspondence, however, Wilson conjures the spirit of a man who
delighted in paradox yet insisted on precision, who held fiercely to
the ancients while straining to understand the world around him, and
who wanted most of all to stump everyone he knew. Writing for work or
pleasure, for children or adults, Wilson shows that Dodgson turned the
most sober of problems into child's play.
"Some perhaps may blame me for mixing together things grave and gay,"
he wrote as Lewis Carroll in an insert to his nonsense poem The
Hunting of the Snark. But, he continued, "I do not believe God means
us thus to divide life into two halves."
Robert Karl Stonjek
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