I turns out that Paul Erdos was born 100 years ago today. Nowadays his name most often comes up in the context of people’s Erdos numbers, so this happy occasion seems like a good opportunity for two anecdotes.
Anecdote 1. The Bacon number is the distance from Kevin Bacon in the graph where vertices are actors and there is an edge between two actors if they played in the same film. There is also an Erdos-Bacon number, which is the sum of one’s Erdos and Bacon numbers. I once read that Erdos had a Bacon number of 3, which would give him an astounding Erdos-Bacon number of 3; but this is false. Wikipedia tells the story:
He [Erdos] appears in N Is a Number: A Portrait of Paul Erdos (1993) with a Gene Patterson, and a Gene Patterson was in Box of Moon Light (1996) with Sam Rockwell who was in Frost/Nixon (2008) with Kevin Bacon. However, this is incorrect, as the Gene Patterson in N Is a Number: A Portrait of Paul Erdos is not the same person as the one in Box of Moon Light (1996).
According to the Wikipedia article Natalie Portman, Carl Sagan, and Richard Feynman have Erdos-Bacon numbers of 6.
Anecdote 2. My PhD advisor Jeff Rosenschein has an Erdos number of 3, so when I published my first paper with him my number decreased from infinity to 4. A year or two later, I wrote a paper with Bezalel Peleg, who has an Erdos number of 2, and we submitted it as a technical report. At this point I started bragging that my Erdos number is now 3. My office mate Shahar Dobzinski (whose own number is 3, I think) was quick to point out though that a technical report doesn’t count for the purposes of computing one’s Erdos number. Of course we turned to Wikipedia to adjudicate this important dispute. Wikipedia (still) says that the Erdos number is “measured by authorship of mathematical papers”. My paper with Bezalel is clearly a mathematical paper, right? Shahar wouldn’t give up, and looked up the definition of a “mathematical paper”. I couldn’t find the relevant entry now (this was six years ago), but if I remember correctly the (somewhat circular) definition that Shahar was able to find was that a mathematical paper is published in a “mathematical journal”. I was defeated.
Eventually I published a few papers with Noga Alon — whose Erdos number is 1 — including one in the journal Mathematics of Operations Research and one in the journal Discrete Mathematics. Journals with the word “mathematics” in their names are clearly mathematical journals, right?
Turing's Invisible Hand 
Actually, your friend was correct. I once had a brief exchange with Jerrold Grossman (who maintains the Erdos Number Project) and he mentioned that technical reports or papers in arXiv etc don’t count. One has to have that tech report or arXiv preprint accepted to some conference or journal for it to count. I don’t clearly remember what was the initial reason for the exchange with Prof. Grossman.
Shahar is always right.
The mathematician Dan Kleitman has an Erdos-Bacon number of 3, from writing a paper with Erdos, and working on “Good Will Hunting” (http://en.wikipedia.org/wiki/Daniel_Kleitman).
Hmm, if tech reports don’t count for one’s Erdos number, it’s unclear if being a “math advisor and extra” for a film should count for one’s Bacon number 🙂
It was a great shock and a personal set back when I learned that my son Ariel has a lower Erdos number than myself. But may be for a physicist the number should be reconsidered to be \sqrt{N} or any reasonable N^\alpha with \alpha<<1. On the other hand, while I wrote papers with Mathematicians of low Erdos number, like Peter Constantin and J-P Eckmann – they were published in physics journals, so maybe my Erdos number remains infinity irrespective of \alpha?
Itamar Procaccia
I don’t remember Richard Feynman ever complaining about his Erdos number… You can still distinguish yourself number-wise by working on your Erdos-Bacon number after you retire; maybe a second career in Hollywood 🙂