At
a packed house party of 250plus mathematicians, Robert Barrington
Leigh, a decidedly unscathedlooking 19yearold and thirdyear,
prizewinning mathematics student at the University of Toronto, is
hanging tentatively back from the crowd.
Barrington Leigh has been invited to this invitationonly gathering
honouring Martin Gardner, the
Scientific American writer
who built a cult following of mathematicians, magicians, skeptics, and
puzzlists with his "Mathematical Games" columns from 1956 to 1991.
Gardner,
now 91, lives in Norman, Okla. He did not attend his namesake
conference; he has never liked travel (he spent the weekend at home,
writing his umpteenth book, this one on the works of the "prince of
paradox," G.K. Chesterton).
But the biennial event held last
month in Atlanta — properly called the Gathering for Gardner;
this
being the seventh such gathering, it goes by the short form "G4G7"
— is
all about invoking Gardner's abiding love for the play and fun in math.
G4G7 brought loyal Gardnerites on a pilgrimage from around the
globe, all diehard members of a recreational mathematics subculture, a
group that defies the discipline's stereotypically dry, theoretical,
and arithmetic reputation.
One conference presenter summed it all
up by citing the wisdom of playwright George Bernard Shaw: "We do not
stop playing because we get old, we get old because we stop playing."
As
the math whiz Barrington Leigh gets older, however, he finds he has
less and less time for the kind of fun math that lured him into the
subject initially. That is why he is feeling a little out of place at
G4G7.
"This is not quite my thing. I study all day. I'm in a
different mathematical mood," said Barrington Leigh, contrasting
himself to this playful bunch and hovering in the safe darkness of an
outside deck, looking into the house party's optimal closepacking of
backtoback mathematicians.
The sprawling Japanesestyle
house, in Atlanta's suburban hills, belongs to Tom Rodgers, an Atlanta
businessman and the event's primary organizer. A number of guests sat
on the floor in the living room, digging into a sushi feast, while
Switzerland's Caspar Schwabe entertained. A magician of a mathematician
— a "mathemagician" — and a professor at the
Kurashiki University of
Science and the Arts in Japan, Schwabe pulled out a few of his
trademark toys.
First it's a bouquet of wiry circular rings —
the "Toroflux" — a sort of soupedup slinky that he twists
and winds
around itself and then lets loose to do its thing: travel around a
thin, wobbling, fourfoot tube like a cluster of slippery metallic soap
bubbles.
Then Schwabe assembles the portable kaleidoscope he
invented, with light shining through holes punched on a mirrored cone,
creating a 60fold reflection in which 98 per cent of the composite
image is an illusion.
Another subset of the party have jammed
themselves into Rodgers' puzzle room. Rodgers hasn't counted but he
figures his collection includes more 2,000 puzzles, including Stewart
Coffin's wooden tangles known as "Locked Nest," and Harry Eng's
"Impossible Bottles." To solve Eng's puzzle, you have to figure out how
he crammed a tennis ball, a deck of cards and a pack of cigarettes, not
to mention two sneakers and a dictionary, down the skinny neck of a
glass jug.
The G4G7 conference proper, held in the
ballroom at Atlanta's RitzCarlton hotel downtown, is a fourday
curiosity cabinet of similar brainteasers.
"Curiositydriven
mathematics is where the best mathematics comes from," says Elwyn
Berlekamp, the eminent Berkeley mathematician and coorganizer of the
event (together with Manhattan magician Mark Setteducati). "It expands
the community and increases the appreciation of mathematics. I think
mathematics is more entertaining than most of the stuff I see in the
theatre.
"We do have a few quacks here and there," adds
Berlekamp, though the cult of Gardner at this event includes
mathematical powerbrokers Sir Roger Penrose, Princeton's John Conway,
and Richard Guy from the University of Calgary, as well as Ed Pegg, a
consultant to the TV series
Numbers. And, Berlekamp
adds, "Rookies and novices we encourage."
For
Barrington Leigh, a rookie but no novice, the problem at G4G7 is that
his university syllabus of mathematical study doesn't allow him time to
do playful math. And finding himself among those who do have the time
to indulge makes him a bit apprehensive, at first.
`(Playful
math)
helps keep you sharp. But right now my work
is more about remembering than
being creative'
Robert Barrington Leigh
Math whiz

"I used to be more [into playful math] when I was younger,"
said Barrington Leigh. "It helps keep you sharp. But right now my work
is more about remembering than being creative."
Barrington
Leigh's mentor, Andy Liu, a professor of mathematics at the University
of Alberta in Edmonton and a devoted mathematics educator, noted that
therein lies the value of G4G7, and the weakness in typical mathematics
education.
"The worst thing the education system does is take
away students' natural curiosity," said Liu, who runs a math club for
kids called SMART — Saturday Mathematics Activities,
Recreations, and
Tutorials. (The program has been running for 25 years, and Barrington
Leigh, being from Edmonton, met Liu when he joined SMART at age 10.)
Liu
said that Barrington Leigh was able to maintain his mathematical
curiosity through his first two years at university. As a result, in
both those years the breadth and depth of his inquisitiveness placed
him in the top 10 in the William Lowell Putnam Mathematical Competition
— a North American faceoff of 2,000 university mathematics
students
from all the best schools, including Princeton, Harvard and MIT.
Barrington
Leigh didn't expect to do as well in the Putnam in his third try, since
as he gets further in his studies, his focus is forced to narrow. He
was right. He finished in a threeway tie for 11th13th, out of the top
10 for the first time.
"My performance on the Putnam has been steadily decreasing," he said.
"Normally
our vision is narrow," said Liu. "Here [at G4G7] our minds are opened;
it's mindboggling. Everybody feels outclassed. We are here to learn.
And we don't care if what we learn is useful. If it is good it will
become useful, but we don't care when, how, or by whom.
"Unlike
academic conferences," Liu continued, "the talks here are not given for
the benefit of the author; talks at those conferences are given to
sustain careers, and the speaker doesn't care whether anyone listens.
Here the talks are for the benefit of the audience."
And soon
enough Barrington Leigh was rediscovering his funloving side and
getting into the playful mood. He checked out the exhibits and sales
rooms, which featured tables of mathematical art — "I'm not
so
interested in the art," he confessed, "but I'll try to be; I don't want
to be too onedimensional" — as well as origami quilts,
knitted
hyperbolic planes, MC Escher Tshirts, and NorthBiloxibased Lou
Zocchi's candystore assortment of polyhedral dice, including a
patented version of a 100sided die, the "Zocchihedron."
The
rapidfire conference schedule allowed for talks of 10, 20, or 30
minutes maximum. Barrington Leigh admitted to preferring presentations
that were more "mathy." He passed on the antigravitational jugglery by
Akihiro Matsuura, a lecturer in computer science at Tokyo Denki
University in Japan.
Instead, he took to Englishman Adrian
Fisher's presentation on the proliferation of mirror mazes. "They were
fun, with pretty pictures. And they are mathematically interesting,"
said Barrington Leigh.
Fisher has created more than 500 mazes
in 23 countries. The latest, which opened in January, is a
worldrecordbreaking maze in a mall in Dubai with three "thematic
episodes"— a palm forest, a palace, and a garden conservatory
(Fisher
has set six Guinness world records with his mazes).
Peter
Winkler's "simple but fiendish" problems also nabbed Barrington Leigh's
attention. A typical reaction to a good problem, said Winkler, from the
department of mathematics at Dartmouth, is either "Wait a minute, I
must be missing something, this is too obvious!" or "Wait a minute,
this is completely impossible!'"
And Barrington Leigh watched
John Conway, as much an entrancing showman as a worldclass
mathematician, who spoke about his "Doomsday Rule," a mental algorithm
he devised for calculating the day of the week for any given date (a
handy party trick for impressing people with the day of the week on
which they were born). Barrington Leigh tried to learn the Doomsday
Rule when he met Conway once before. He was nervous and intimidated by
the professor, and he made an embarrassing error in calculation.
"Some
mathematicians are really bad at arithmetic — I'm one of
them," said
Barrington Leigh, who on the last day of G4G7 was in the thick of all
the playful schmoozing, even after the marathon of presentations had
concluded. There could be no better way for an upandcoming
mathematician to celebrate his 20th birthday.
Siobhan
Roberts is a Toronto freelancer writer. Her book "King of Infinite
Space: Donald Coxeter, The Man Who Saved Geometry" is being published
by Anansi this fall.