The Erdős-Bacon Number


What do Carl Sagan, Richard Feynman, and Natalie Portman have in common?

They all have the same Erdős-Bacon number:  six.

Natalie Portman collaborated (as Natalie Hershlag) with Abigail A. Baird, who wrote mathematical papers in a further collaborative path which leads to Joseph Gillis. Gillis, having co-written a paper with Paul Erdős himself, has an Erdős number of one. This gives Portman an Erdös number of five. Bacon and Portman both appear a movie (which one?  See the details in this Wikipedia article:, which gives Portman a Bacon number of one.

The Erdős-Bacon number is simply the sum of these two numbers — hence Natalie Portman’s six:  five plus one.

Feynman’s and Sagan’s sixes are more balanced. Richard Feynman’s is the most so, since his Erdős and Bacon numbers are both three.

I haven’t been able to determine who first thought of an Erdős-Bacon number, but . . . wow. It came from the blogosphere (Where else?) — Wikipedia reveals that much.

Some blogger might be obsessive enough, someday, to exhaustively determine exactly how many people even have such numbers. However, that person will not be me.

Meet Paul Erdős


Meet Paul Erdös

As was written in The New York Times when his biography, The Man Who Loved Only Numbers, was reviewed (1998), Paul “Erdős (pronounced “air-dish”) structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down.”

This was during most of the Cold War between, at the forefront of each side, swaggering mightily like something straight out of a comic book, the USA and the USSR. Except … this wasn’t a comic book. You really could die. Younger people don’t really know what this is like, for the simple reason that the threat of imminent. sudden extinction hasn’t been present since the Cold War ended. The world faces disasters, of course, but a sudden one, greater than the large-city scale, is unlikely in the extreme — now.

Erdős had little regard for Uncle Sam (that’s the United States), nor Uncle Joe (the Soviet Union, with “Joe” being a caricature of Josef Stalin), but he did enjoy clever ridicule, so he heaped contempt, publicly, on both sides, during the Cold War. He wasn’t a big fan of the S.F., either (that’s Supreme Fascist — of the Universe. Guess who. Yep. That’s the guy. Why is God always a guy?)

Erdős just wanted to do math, and this native of Hungary simply dismissed all else. Mathematicians need other mathematicians to talk to, for they are already crazy, in very specific and sometimes unintentionally useful ways, and need other people also so afflicted to talk to, lest they torment the uninterested with mathbabble. That is only one way of looking at it, of course, as people have explained to me about my own mathbabble, which is insufficiently advanced to allow me to comprehend that of Erdős himself.

Life was viewed differently by Erdős, and I do not mean in any way that would seem “normal” to any mathematics professor you might have met (feel free to ask them). If you worked on proving theorems, solving problems, proving certain problems can’t be done — all of which are varied ways of describing the same activity — then you were, to Erdős, “alive.” If you stopped doing mathematics, you “died.” I don’t know what he thought of those who never did mathematics, because he avoided interacting with them. With no home, he could simply get on a plane when all the local mathematicians were exhausted, their brains tired, and he would then go to another continent — there were several available, and he did this for decades — and the local mathematicians would welcome him with open arms, for it was an honor to have Erdős as a guest in one’s home.

Sources, and further reading:

The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth, biography by Paul Hoffman, 1998.ös

More Erdős vocabulary:
“Women” were “bosses,” with “men” translating as “slaves,” in Erdős’s unique language of his own invention. Children were “epsilons,” and if you laughed at that, I do hope you are happy with the fact that you, too, are a math nerd. (For the benefit of those who aren’t, “epsilon” is a symbol often used, in mathematics, for variables with very small values.) There’s a lot more — and links to use to help you find it, right up there.