Paul Erdös (1913-1996) was one of the most prolific mathematicians of all time, having authored over 1500 articles. The Erdös number measures the shortest distance of a researcher from Erdös on a graph whose edges represent co-authorship. See the Erdös Number Project Page for details.

The above graph was generated from this DOT file and this Makefile.

How challenging is it to have a small Erdös number? It's not as hard as you might imagine. As per Facts about Erdös numbers, the distribution in Dec 2010 was:

      Erdös number  0  ---      1 person
      Erdös number  1  ---    504 people
      Erdös number  2  ---   6593 people
      Erdös number  3  ---  33605 people
      Erdös number  4  ---  83642 people
      Erdös number  5  ---  87760 people
      Erdös number  6  ---  40014 people
      Erdös number  7  ---  11591 people
      Erdös number  8  ---   3146 people
      Erdös number  9  ---    819 people
      Erdös number 10  ---    244 people
      Erdös number 11  ---     68 people
      Erdös number 12  ---     23 people
      Erdös number 13  ---      5 people