Erdős and me? N(e)(me) = 5 (extended)
Did you read this post where I connected my students to Pierre Fermat (in 5 awkward steps)? That sort of game is familiar.
You know Six Degrees of Separation? (eg, I know someone, who knows someone, who… and I get to almost anyone within six steps.)
How about Six Degrees of Kevin Bacon? (Elvis Presley was in Change of Habit with Ed Asner, who was in JFK with Kevin Bacon…)
Well the mathematics world has an answer to them: The Erdős Number. Paul Erdős was a totally kooky (seriously!) 20th century mathematician. He was prolific: it is likely that no other mathematician has written or co-written so many papers (over 1500), or worked with so many collaborators (over 500 co-authors).
So how do Erdős numbers work? Erdős himself has an Erdős number of 0. Anyone who wrote a paper with him has an Erdős number of 1. Anyone who wrote a paper with someone who wrote a paper with… You get the idea.
(and me? –>)So my Erdős number? Hm, it really needs to be a mathematics paper published in a journal. But there is an Extended Erdős Number, that includes such things as giving Hank Aaron a 1, since he and Erdős signed the same baseball. Now we are in business. I co-authored a mathematics education article with a guy with a real Erdős number of 4. So I get 5 (extended).
JD2718 
“Hm, it really needs to be a mathematics paper published in a journal.”
I think most people would be willing to extend this more broadly to (research?) articles in peer-reviewed journals, not necessarily limited to those on the subject of mathematics. For example, the “readme” at the Erdos Number Project specifically states,
“Paul Erdös has made contributions in many different areas of mathematics; and by the time you go one or two more levels down the tree, essentially all areas of mathematics are represented (as well as computer science, physics, and other natural and social sciences).”