Erdos numbers, itinerant scholars and pilgrims

Students and faculty of the Vatican Observatory Summer 

School, with various members of the Observatory staff on an

outing to Villa d'Este in Tivoli.  

Paul Erdős was an extraordinarily prolific Hungarian mathematician. He wrote over 1400 papers, with more than 500 co-authors; to put that in context, the median publishing mathematician has 2 papers in (all likelihood) his lifetime, with a handful of collaborators, perhaps 5 at most. Erdős was an intinerant scholar, who moved from conference to campus, showing up at a mathematician's door and announcing, "my brain is open." He owned what he could carry.

For most of my visit, I've been packing my backpack for the day and trooping from Castel Gandolfo to Albano, setting up shop on a table in the library, working on my small laptop screen.  I can carry everything I need, including an umbrella in case of sprinkles (or deluge).

As my time at the Observatory this summer comes to an end, I'm thinking about Erdős line, "my brain is open."  This moving to another spot, with different people to talk to, different spaces to work, opens my brain.  "Have you read John M. Staudenmaier, SJ's essay To Fall in Love with the World? Perhaps the introduction would be helpful."  I have now, and it absolutely was helpful.  The lack of screen space, which I thought I might find annoying, has been a gentle nudge to not try to do so much at once.  To leave some room for serendipity.

There is something to walking, to moving, that shakes us up, unsettles us:  am I lost? will I make it to my destination before it gets dark?  before it rains?  before the cafe closes?  To be a pilgrim is to remember that we live in uncertainty.

To be an itinerant scholar is a bit like being a pilgrim in that it's unsettled, but also not quite the same.  It's about figuring out how to enter into community, about finding stability.  With the young astronomers who are here, with the woman at the Pasticceria Al Duomo who recognizes me and knows my favorite sweet roll and who helps my Italian along by making me list my order before I pay for it.  With the group that gathers to celebrate the Eucharist together as we figure when to kneel and when to stand.

My brain is open. Time to go home.

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An Erdős number is the number of edges you have to traverse in a graph of collaborations (where each edge represents a co-authored paper).  Erdős has an Erdős number of 0.  If you were one of the 500 some-odd who co-authored a paper with Erdős, your Erdős number was 1, and so on.  Math Man has an Erdős number of 4, a distinction he shares with about 83,000 other people.  Need to know your Erdős number?  Try this collaboration distance calculator at the American Mathematical Society's MathSciNet, use the button on the right for Erdős.  You can read more about collaboration distance here.

And if Ignatian spirituality is of interest, I highly recommend John M. Staudenmaier, SJ's essay To Fall in Love with the World.  Written for Studies in the Spirituality of Jesuits more than 20 years ago, it remains on point, treating of the American notions of individualism.  Read the preface!