If you are not a Mathematician you may be asking yourself - 'What the heck is an Erdös number?'
Well, the most functional way to describe it is that it measures the distance (a.k.a. the collaborative distance) between a particular author and Dr. Paul Erdös. To explain a little further, in order to be assigned an Erdös number you must be a coauthor with someone who currently has an Erdös number. Your Erdös number will be one higher than your coauthor. Dr. Paul Erdös' number is zero so all of his coauthors have an Erdös number of 1, their coauthors (who have not published with Dr. Erdös) have an Erdös number of 2 and so on. As a personal example...
My Erdös number is a three. Its sequence is the following:
(3) Coker to Tatusov
(1) Székely to Erdös
So why an Erdös number and not a Smith, Ramanujan, etc. number?
Dr. Erdös published more papers than any other mathematician in his lifetime. Basically, the Erdös number was started by Dr. Erdös' friends and colleagues as a way to pay tribute to him.
This may seem like a 'silly' academic exercise or just an esoteric thing that really doesn't mean much at all. However, studies (http://link.springer.com/article/10.1007%2FBF03025416) have shown that leading mathematicians tend to have a lower Erdös number. For example, recipients of the Field Medal (often called the Nobel for Mathematics) have a median Erdös number of 3.