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Erdos Numbers–Nerd World meets “Six Degrees of Kevin Bacon”

Perhaps you remember a parlor game from a few years back, “Six Degrees of Kevin Bacon”.  The game was to connect a chosen movie star to Kevin Bacon in six or fewer links from one actor to another, with the links being films in which the two actors appeared.  There is a version of this divertissement that is enjoyed among mathematicians.  In it, the role of Kevin Bacon is played by Paul Erdos.                                                 Paul Erdos was a Hungarian mathematician, whose dedication to mathematics was so strong that for much of his life he had no fixed home.  He traveled around the world, visiting universities for periods of time and working on mathematical discoveries with the resident faculty.  Over the course of his life, he published a large number of mathematical papers, most of them with joint authorship.  So, in the math nerd world version of “Six Degrees”, the link is provided by writing a joint mathematical paper–rather than appearing together in a movie.                                                                             In this scheme, Paul Erdos gets Erdos number 0.   His 511 co-authors get Erdos number 1.  Their co-authors get number 2 and so on. I wanted to describe all this, because I think that many people believe that math nerds are loners, who sit in our rooms doing calculations with big numbers.  In fact, mathematics is a social activity … mathematicians actually do love to get together and bat ideas around.  It’s  tends to be fairly low key–but there are any number of mathematical papers that got their starts as scribblings on bar napkins.                                                                                                                    Along those lines, there was a story when I was a graduate student that the American Mathematical Society had once had their annual convention in Las Vegas.  Afterward the story goes, the Society was invited not to come back again.  Even though there are about 5000 mathematicians who attend, there wasn’t much gambling [and they were surprised at that?!] and for recreation, the mathematicians sat around talking and drinking a beer or two.  Just not very profitable by Las Vegas standards.  I can’t vouch for the authenticity of the story, but it strikes me as only too true of the way that mathematicians behave.                                                                                                                                                                                                By the way, my Erdos number seems to be 4. 

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