Professor's 'pet project' is Internet's No. 1 source on the Erdös Number, a bit of mathematical folklore

Oakland University professor of mathematics Jerrold W. Grossman explains the Erdös Number Project.

With more than 1 million views, what started as a sabbatical project 20 years ago has become one of Oakland University’s most popular web pages.

Professor Jerrold W. Grossman keeps a coveted list of mathematicians who, through their research publications, are interconnected with the late Paul Erdös.  A famous mathematician (1913-1996), Erdös collaborated with more than 500 people.

Grossman likens the Erdös collaboration network to social networking relationships on sites like Facebook or LinkedIn. For example, LinkedIn identifies its members as having first, second or third degree connections to one another.

“There are people who are short distances to everyone else,” Grossman said. “In some sense it kind of started with mathematicians, this fun thing you do, measuring how far you are from Paul Erdös.”

Erdös himself has an Erdös number of 0, his co-authors have Erdös number 1, co-authors of his co-authors have Erdös number 2, and so on.

“So if you and I do some research and publish a paper together, then we are linked in this network of collaborations,” explains Grossman.  

Using the American Math Society database, Grossman found that approximately 80 percent of mathematicians have an Erdös number, ranging from 1 to 13, the average was about 5. Some people don’t have an Erdös number at all because there is no path from them to Erdös through these links of collaborations. Through his website, Grossman helps mathematicians from around the world determine their Erdös number.

Grossman describes his self-proclaimed pet project as a “silly, fun thing with no real signficiance,” but having a low Erdös number in this academic version of the Kevin Bacon game is a huge point of pride. According to Grossman’s web page, somebody once auctioned off the chance to co-author a paper with him in order to achieve an Erdös number 5.

While Erdös numbers are primarily a brag point for researchers, Grossman said that you could expand the idea of what constitutes a link, which leads to even a horse having an Erdös number.

While completing a crossword puzzle in a magazine, Grossman saw that a clue for a large horse had the intended answer of an Arab horse. Arab horses are generally smaller horses, so Grossman wrote a letter to the editor on behalf of his wife’s fairly small Arab horse.

“So they published this letter, a publication of this horse but I had ghostwritten it for him,” Grossman said. “So I figured, alright, so the horse and I have a joint publication and if I have an Erdös number 2, it gives the horse an Erdös number 3.”

Learn more about the Erdös Number Project at oakland.edu/enp.