Just as actors have their Kevin Bacon, mathematicians have their Paul Erdös. People in each field love to calculate their "degree of separation" from the stars. Now two scientists have shown that all the mathematicians who have won the prestigious Fields medal have a finite "Erdös number." And so do a lot of Nobel laureates.
What's your Erdös number? If you've written a joint paper with the prolific Hungarian mathematician, it's 1; if you've collaborated with an Erdös-1 mathematician, you've earned a 2; and so on. The lower your number, the more closely you're associated with an elite group of extremely well-connected mathematicians (507 Erdös-1 types, at last count).
Mathematicians, being what they are, are fond of analyzing Erdös numbers. The latest effort, appearing in the December issue of the journal of the Colombian Academy of Sciences, shows that winners of the Fields medal--math's Nobel equivalent--"all have a 5 or less, and only one or two have a 5," says co-author Jerrold Grossman of Oakland University in Michigan. In addition, more than 60 Nobel laureates, many in fields far removed from mathematics, can brag of single-digit Erdös numbers. Watson and Crick, for example, have numbers of 7 and 8, says Grossman.
Erdös died in 1996 after publishing close to 1500 papers. But his nonstop travels left a legacy of unpublished work, so his name keeps appearing on papers to this day. According to Grossman, 25 new Erdös papers entered his database this year, promoting 12 new mathematicians to the exalted Erdös-1 status.
