## Unclaimed Accounts: A Mathematical Interlude with Paul Erdos

October 2, 2010Ever heard of the Six Degrees of Kevin Bacon?

Twenty-five years before that, there was the Erdos Number.

One of the highlights of my series on unclaimed bank accounts was a little over $2,000 in a Bank of Montreal account right by the University of Calgary. An eager *Journal* reader, Natasha Schiebelbein, brought this late mathematician’s account to my attention:

# Math genius left unclaimed sum

At first glance, there was little to connect Erdos and the U of C. He never taught there, never lived in Canada, and was by all accounts, an itinerant. My initial thought was that Erdos had simply visited the U of C for a conference or the like, where a stipend was collected on his behalf. But I was intrigued.

Anyway, the article was a complete pleasure to write and wound up going from an anecdote of a story, to a colossal 30″ long feature (My average story is probably less than half of that).

That meant editors trimmed down some copy I was sad to see go:

- Microsoft board member Maria Klawe, a former Edmontonian and president of Harvey Mudd College, spoke about Erdos as “everybody’s favourite weird uncle.”
- Discussion of Erdos-Bacon numbers and “Six Degrees of Kevin Bacon,” actually derived from the Erdos Number phenomenon.

So here, uncut and unedited, is the bottom half of the story:

*It’s been nearly three decades since Guy’s last shared paper with Erdos, though he penned a pair of tributes when his friend died. Now approaching 94, Guy has since slowed down, though he still maintains office hours, grad students, researches interests, and speaking engagements.*

*Collaborations with Erdos remain a badge of honour in the world of mathematics, where one’s “Erdos Number” — akin to the “six degrees of Kevin Bacon” — signifies closeness of collaborations. Erdos himself was a 0, while Guy, Graham, and select few hundred are 1s, their co-authors are 2s, and so on. According to Oakland University researchers, the average mathematician has a Erdos Number of 4.65.*

*The idea of linking Bacon’s co-stars was actually derived from Erdos Numbers, later spawning the bizarre “Erdos-Bacon Number,” calculated by adding the two scales together.*

*The Erdos Number is a dangerous lure, says Graham, since scholars may be tempted to pen a paper based on a fuzzy decades-old conversation.*

*It’s been 14 years since his death, but Graham says the publications and collaborations are still coming.*

“*It didn’t stop him, it only slowed him down a little,” said Graham. “I think he just published one or two papers last year.”*

*No spectre of doubt clouds former Edmontonian Maria Klawe’s Erdos Number. The Microsoft board member and president of the prestigious Harvey Mudd College couldn’t resist lending a few minutes in her hectic schedule to speak about “everybody’s favourite weird uncle.”*

“*One of the wonderful about the mathematical community is that he was like their child,” said Klawe. “They embraced him, and loved him and took care of him and admired him.”*

*A star-struck Klawe first met Erdos as an undergraduate at the University of Alberta, where she went on to complete a PhD. She earned her Erdos Number through a graph theory paper examining a problem Erdos once posed in an Australian taxi cab. Klawe frequently gets requests to co-author papers — from aspiring students to the founder of Netflix — to land an Erdos Number of 2.*

*Apart from his unusual lifestyle, Erdos was also known for posing math problems with corresponding bounties. Cheques ranged from a few dollars to $25,000, proportionate to the difficulty of the problem. Guy, for instance, once won $5.*

*One of Graham’s ongoing duties has been to dole out cheques whenever a riddle is cracked. In the fascinating 1993 documentary, N is a Number, Erdos is a silhouette at Graham’s shoulder, signing blank cheques for future claimants. In 1998, Graham and his mathematician wife Fan Chung co-authored Erdos on Graphs, a compendium of approximately 100 unsolved problems posed in Erdos lectures. Only two have been solved in a dozen years.*

“*As Erdos liked to say, if you hoped to earn a living by solving his problems, you’d be paid way below minimum wage,” Graham said.*

*Graham initially suggested the unclaimed bank account could be put toward the unsolved problems. But faced with the paperwork necessary for the claim, the money may be as difficult to grasp as one of Erdos quandaries. Not only did Erdos leave no heirs, he was not one to bother with the paper work of a will. His Wikipedia entry, which declares Graham “the (informal) administrator of solutions,” is probably insufficient for Bank of Canada criteria.*

*Like so many other unclaimed accounts, then, the money will most likely remain in the Bank of Canada database, a sizable bounty for an unsolvable problem, and a century-long record of a truly unique human being.*

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