If you are one of the lucky mathematicians (there are 509 of them) who has written a paper with Paul Erdös, then your Erdös number is 1. If you wrote a paper with a person whose Erdös number is 1, then your Erdös number will be 2. And so on.
My Erdös number is 2, because I wrote a paper (see here) with Professor Charles Chui whose Erdös number is 1, because Charles Chui wrote a paper with Paul Erdös (see here: On changes of signs in infinite series).
Erdös number of 2 is the largest it can be for anyone (from now on) since Paul Erdös is no longer alive. Sadly, he passed away in September 20, 1996. The Wikipedia page about him is here.
The Erdös Number Project studies research collaboration among mathematicians. To find out more about it and possibly discover your own Erdös Number, please go to here. Also, the social graph of Erdös is found here.
PS: For a while, I thought my Erdös number is 3 since I wrote several papers with Ömer Eğecioğlu who wrote papers with Charles Ryavec who wrote a paper with Paul Erdös (see here: A characterization of finitely monotonic additive functions). Thanks to Emilie Menard Barnard and Keith Avery for pointing out my paper with Professor Charles Chui of Texas A&M, who by the way was one of the nicest persons I have ever met in my life. He is now retired. Long live Charles. My best wishes. My best wishes to Emily and Keith too, of course.
Taleb asks: “You are rich, how come you are not smart?”
I ask: “You are poor, how come you are smart?”
Answer: I chose not to accumulate.