# Part II. Erdos Numbers and Bacon Numbers

**Erdos Numbers**

Thanks to his unparalleled impact on mathematics, his hundreds of collaborators have devised an appropriate tribute to him that has taken on a life of its own. The tribute? The ”Erdos Number”. It’s essentially the same idea as Six Degrees of Kevin Bacon, and in fact long preceded the Bacon game. The idea is this: if you’ve published a paper with Paul Erdos (you have, haven’t you?), your Erdos number is 1. If not, then maybe you coauthored a paper with someone who has Erdos number 1, giving you an Erdos number of 2. And so on — if you have an Erdos number of 5 (as I do [note smugness]), then there is a chain of five coauthorships separating you from a paper Paul Erdos has written. Dorky, sure, but among mathematicians (and later, among scientists in general), it has become big-time bragging rights to have a low Erdos number. People with an Erdos number of 1 are literally famous in math circles.^{1} And if you can’t figure out a connection among published papers, then you have an Erdos number of infinity, you poor sap.

Since the guy published so many papers, probably ten times more papers than even the most prolific scientists, it’s actually pretty easy to work out a connection. They say that if you can be connected at all (and most people who publish in math journals can be), your Erdos number will be lower than ten. Just for perspective, I got my Erdos number of five through a minor paper in a middling neuroscience journal, nowhere near math. It’s like a giant interconnected web of math geek publications, with Erdos sitting at the center. What’s more, people this smart can be counted on to not leave well enough alone — some mathematicians now study the mathematical properties of the web of Erdos coauthors, to the point of encouraging new coauthorships among the inhabitants to help fill out the web.

**Hold on to your butts: it’s Erdos-Bacon Numbers**

It didn’t take long for the nerdiness to metastasize out to infect the Six Degrees of Bacon game. The Bacon Game, if you haven’t heard, is just the same idea applied to movie stars. If you have a Bacon number of 1, you’ve starred in a movie with Kevin Bacon. If your number is 2, someone you’ve costarred with also was a costar with Bacon. It’s a fun party game to pick a celebrity at random and try to figure out a path through various movies back to Kevin Bacon — in fact there’s a website that will now do it for you. Well, it just so happens that an occasional mathematician will pop up in a movie here and there, usually a documentary, occasionally in a cameo in movies needing some math credibility, like *Good Will Hunting*. You also see the occasional actor moonlight in mathematics, the most famous example being Danica McKellar (Winnie from the TV show *The Wonder Years*) who is an honest-to-goodness math badass, and Natalie Portman, who has an Erdos number thanks to a neuropsychology paper. So, there are a handful of people who have both an Erdos Number and a Bacon Number. Those hip to the game keep track of the select few who have a non-infinite Erdos-Bacon number, which is just the sum of the two numbers — Danica McKellar’s Erdos-Bacon number is 6, and Natalie Portman’s is 7, meaning I’m going to have to star in a movie with Kevin Bacon *soon* just to keep up.

The current leader in the Erdos-Bacon Number game is a dude name Daniel Kleitman, a mathematician who wrote a paper with Erdos (and so Erdos number 1), and also consulted for and appeared in the movie Good Will Hunting (giving him a Bacon number of 2, thanks to Minnie Driver). This lucky guy therefore has an Erdos-Bacon number of 1+ 2 = 3. Paul Erdos himself has a Bacon number, thanks to his appearance in a documentary – the accounting is apparently controversial, but depending on who you believe Erdos might have an Erdos-Bacon number as low as 3, tying Kleitman. Carl Sagan has an Erdos-Bacon number of 9 (Erdos 6 plus Bacon 3). Once we make TimeBlimp the movie, I ought to be able to get my Erdos-Bacon number down from infinity to around 20 or so. (Anyone have Bacon’s phone digits?)

*Footnotes*

1. Erdos himself has an Erdos number of zero — since mathematicians invented this game, they’ve gotta define all the possible cases.

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