Theorems for sale: an online auctioneer offers math amateurs a backdoor to prestige

Science News, June 12, 2004 by Erica Klarreich

In April, an eBay auction offered math and science aficionados a rare opportunity: to link their names, albeit through 5 degrees of separation, with one of the most famous mathematicians of the 20th century. Trumpeting the title "Decrease your Erdos number!" the auction presented bidders with the chance to collaborate on a research project with the seller, who had collaborated with someone who had collaborated with someone who had collaborated with someone who had collaborated with Paul Erdos, the Hungarian mathematical prodigy who died in 1996.

Erdos was an eccentric, legendary figure with no fixed address. He worked with mathematicians all over the globe, coauthoring papers with more than 500 other researchers during his lifetime. Just as some film buffs calculate movie actors' fame by measuring their degrees of separation from Kevin Bacon, mathematicians calculate their "Erdos numbers." A mathematician who has published a paper with Erdos has an Erdos number of 1. A mathematician who has published a paper with someone who has published a paper with Erdos has an Erdos number of 2, and so on.

The eBay seller was William Tozier, a scientific consultant in Ann Arbor, Mich., whose Erdos number is 4. He launched the auction as a joke, in his words, "one morning before I'd had enough coffee." Quickly, however, the auction took on a life of its own, sparking a vigorous debate both about the limited research opportunities available to amateur mathematicians and about the ethics of selling an Erdos number.

EXCLUSION PRINCIPLE Although Tozier started the auction on a whim, his offer was serious: 40 hours of his time to collaborate on a project of the winning bidder's choosing in one of Tozier's areas of expertise, which include machine learning and complex systems. If the collaboration resulted in a published research paper, which Tozier said was likely but not guaranteed, the auction winner would earn an Erdos number of 5.

Tozier, who is interested in social networks, started the auction as an informal experiment about how news spreads through social and professional circles. He was curious to see how quickly gossip about the auction would spread and whether anyone would actually take him up on his unusual offer.

"It's hard to get real data about social networks without infringing on people's privacy, so I thought it would be interesting to set this out there as something between a joke and an experiment," he says. "I like to approach things in this 'let's see what happens' mode."

Tozier told only four friends about the auction, asking them to pass on the news to their own friends. He also posted a link to the auction on his Weblog (http://williamtozier.com/slurry/2004/ 04/index.html). From there, Tozier says, news about the auction made its way quickly through the "blogosphere," and soon, the mathematics, computer science, and other technical communities were buzzing with the story. Mathematician Jerry Grossman of Oakland University in Rochester, Mich., who maintains the official Web site for the Erdos number project, told Tozier that visits to the site skyrocketed after the auction started.

When Tozier set up the auction, he had no idea who, if anyone, would respond. To his surprise, his offer of collaboration struck a chord in a wide range of individuals, including engineers, teachers, and businesspeople, who had ideas for research projects but felt excluded from the mathematical community. During the 10 days of the auction, Tozier heard from more than 100 would-be researchers, whose frustration echoed complaints Tozier had been hearing for more than a decade. "Through my years as a researcher and corporate consultant, I've met lots of extraordinarily smart people who love math, read about it in books, try things out, and explore, but because they're not members of the [mathematics] community, they can't put their observations back into the pool of collective knowledge," he says. "They do what is arguably research but can't share it with people who would take it further or put it in perspective."

As a result, he adds, "most of these people cannot do anything at all about their ideas, and they cannot apply their skills."

It's hard for people outside of academia to share their ideas with mathematicians, agrees Ronald Graham, a mathematician at the University of California, San Diego who has an Erdos number of 1. "I've run into people who are serious researchers in other areas but have some math idea and don't know what to do," he adds.

Mathematicians get so many letters from crackpots claiming to have proved amazing theorems, Graham says, that it would take too much time to separate the wheat from the chaff.

Spurred by the emotional impact the auction was creating, Tozier decided to devote some of its proceeds to launch a free online community to promote scientific collaboration among laymen and mathematically trained professionals outside of academia. The idea, he says, is to create a forum in which individuals can post research proposals, find collaborators, review each other's work, and publish research findings. He is now talking to nonprofit and governmental groups about the best way to put together such a community.