The Erdös Number homepage has some interesting information
on this
topic.
For example, the distribution of Erdös numbers is such that almost every mathematician with a finite Erdös number
has a number of less than 8 -- only about 2% are higher, and none is more than 15.
Noether can't help mentioning that his is 4. But there are
more than 62 000 other people with this property.
It seems reasonable that almost all currently publishing mathematicians have a finite Erdös number.
You can find the Erdös Number homepage
at www.oakland.edu/~grossman/erdoshp.html