My Erdős number is 3

Paul Erdős was a prolific mathematician. Born in Budapest in 1913, he published more than 1500 papers together with over 500 co-authors during his long career. He died in 1996, at the age of 83, while attending a conference in Warsaw.

Mathematician Paul Erdős. Image source: University of St. Andrews, UK.

Erdős never really settled down, but traveled from one place to the next to collaborate with other mathematicians. He relied on his collaborators to host and feed him, and to fund his travels. His entire life was devoted to mathematics.

His large number of co-authors gave rise to the idea of an Erdős number. Imagine a network where the nodes represent mathematicians, and with links between nodes when two mathematicians are co-authors on at least one scientific article. Obviously the node representing Paul Erdős is a well-connected hub at the center of this network.

The Erdős number of any mathematician in this network is the length of the shortest path from their own node to that of Paul Erdős. In other words, those mathematicians who have published an article together with Erdős have an Erdős number of 1. There are 511 of them. Those mathematicians (or other scientists) who have not published together with Erdős himself, but who are a co-author of someone with Erdős number 1, have an Erdős number of 2. There are currently a little more than 11,000 of them. And so on for Erdős numbers of 3, 4, and higher.

A data file listing all scientists with an Erdős number of 1 or 2 is maintained on the website of the Erdős Number Project. Using this data file, I was able to establish that I have an Erdős number of 3, as stated in the following “theorem”.

Theorem: My Erdős number (myE) is equal to 3.

Proof: The proof consists of two parts.

  1. myE > 2.
    This follows easily from doing a search for my own name in the data file, which fails to find a match. Therefore, my Erdős number is strictly larger than 2.
  2. myE <= 3.
    After searching the data file for the names of some of my co-authors, I did find at least one match. My collaborator Prof. Mike Steel, a mathematician at the University of Canterbury (Christchurch, New Zealand), is listed as someone with an Erdős number of 2. Therefore, my own Erdős number is at most 3.

Combining parts 1 and 2, and the fact that it has to be a whole number, it follows that myE is exactly equal to 3.

Q.E.D.    😉

Even though some articles with Erdős as a co-author were still published posthumously, unfortunately it is not possible anymore to achieve an Erdős number of 1 unless you already had one. But there is still somewhat of a (good-natured) competition among mathematicians to achieve as low an Erdős number as possible. It is nice to see that Erdős, who studied the properties of networks extensively, is at the center of one himself.

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