Now, to keep the Math theme just a little bit longer, but to mix it with a bit of entertainment, I present you the Erdös-Bacon number.

Paul Erdös was a mathematician. Except for the maths, he was famous for being a bit (or a lot) eccentric and having literally hundreds of collaborators.

Kevin Bacon might be a little more known, at least in non-math circles, as the actor, who blessed us with Footloose. And some good movies.

Now, how do these two come together?

Well, developing from the Small World Phenomenon, there first were the Six Degrees of Separation:

Six degrees of separation refers to the idea that, if a person is one step away from each person they know and two steps away from each person who is known by one of the people they know, then everyone is an average of six “steps” away from each person on Earth.

Out of this concept, the Six Degrees of Kevin Bacon came into being – a theory that Kevin Bacon is the center of the entertainment industry. Although later it was discovered that there are better centers (like Sean Connery or Christopher Lee), Kevin Bacon kind of got stuck with it.

With the same background – the Small World Phenomenon – after Erdös’ death, the Erdös number was created, as a tribute to the man.

And then somebody decided that it would be a wonderful idea to combine the two. And I think that someone was right.

The whole thing works like this:

Erdös has an Erdös number of 0, being Erdös. Everybody who collaborated directly with him has an Erdös number of 1. Everybody who collaborated with one of his collaborators has an Erdös number of 2. Etc.

The same for the Bacon number: Kevin Bacon has a Bacon number of 0. Everybody, who worked with him directly, has a Bacon number of 1 and so on.
[Example: Bacon (0) was in Wild Things with Matt Dillon (1), who was in Crash with Don Cheadle (2), who was in After Sunset with Salma Hayek (3)…]

To get the Erdös-Bacon number, you just have to add the Bacon number of a person with their Erdös number.

Natalie Portman, for example, has an Erdös-Bacon number of 7, through various papers she wrote for Harvard.
Other examples:

For a time, the person with the lowest known Erdős-Bacon number was Brian Greene. He appeared in Frequency with John Di Benedetto, who was in Sleepers with Kevin Bacon, for a Bacon number of 2. He also wrote a paper with Shing-Tung Yau, who wrote a paper with Ronald Graham, who wrote a paper with Paul Erdős, for an Erdős number of 3 and a combined Erdős-Bacon number of 5. Greene was later outdone by Dave Bayer, mathematical consultant to A Beautiful Mind who received a minor role on screen in the movie. Rance Howard was also in A Beautiful Mind and in Apollo 13 with Kevin Bacon to give Bayer a Bacon number of 2. Bayer wrote a paper with Persi Diaconis, who has an Erdős number of 1 due to a jointly authored 1977 Stanford University technical report, later published in a 2004 compilation.[10] As such, Bayer’s Erdős-Bacon number is 4. Diaconis himself has an Erdős-Bacon number of 5, and Bacon number of 4. He was in the documentary The Math Life[11] with Freeman Dyson, who was in A Glorious Accident[12] with Oliver Sacks. Sacks has a Kevin Bacon number of 2.[13]

 And there’s even a horse with an Erdös-number…

Now, what’s your Erdös-Bacon number? :)