At a packed house party of 250-plus mathematicians, Robert Barrington Leigh, a decidedly unscathed-looking 19-year-old and third-year, prize-winning mathematics student at the University of Toronto, is hanging tentatively back from the crowd.

Barrington Leigh has been invited to this invitation-only 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 Gardner-ites 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 close-packing of back-to-back mathematicians.


The sprawling Japanese-style 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 souped-up slinky that he twists and winds around itself and then lets loose to do its thing: travel around a thin, wobbling, four-foot 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 60-fold 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 Ritz-Carlton hotel downtown, is a four-day curiosity cabinet of similar brainteasers.

"Curiosity-driven mathematics is where the best mathematics comes from," says Elwyn Berlekamp, the eminent Berkeley mathematician and co-organizer 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 power-brokers 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 three-way tie for 11th-13th, 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 mind-boggling. Everybody feels out-classed. 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 fun-loving 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 one-dimensional" — as well as origami quilts, knitted hyperbolic planes, MC Escher T-shirts, and North-Biloxi-based Lou Zocchi's candy-store assortment of polyhedral dice, including a patented version of a 100-sided die, the "Zocchihedron."

The rapid-fire 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 anti-gravitational 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 world-record-breaking 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 world-class 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 up-and-coming 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.