This is the first of a series of articles about Erdos’ numbers (EN). We will understand what they are, then we’ll deal with not-mathematics versions, the concept of scale-free network, and some amusing anecdotes.
Paul Erdos was a Hungarian mathematician. A strange person, but a genius. He worked in many different fields: combinatorics, graph theory, number theory, analysis, numerical, …
Thanks to his way of doing and his eccentricity, Paul is certainly one of the most popular mathematics of the twentieth century (he died in the nineties). I talked with italian mathematicians who met him during some conferences in Italy and they have reported that it was a wonderful person. An applicant’s sentence has now become, in our environment, a real say, and even the summary of the mathematician lifestyle:
“A mathematician is a device for turning coffee into theorems.”
After Euler, Erdos is the mathematician who has produced more publications: it is estimated that 511 different mathematicians have had the honor to sign an article with him.
We are not going to explore his main results, concentrating ourselfes on the Erdos’ numbers. The sequence counts the publication distance from the great mathematician. Naturally Erdos is awarded of EN 0, while the 511 mathematicians who have published with him has EN 1. In the same way, mathematicians who have published with at least one of these 511 have EN 2, and so forth. Currently we know that more than 8000 people may have Erdos number of 2.
Of course there are mathematicians in the past (prior to Erdos) owning an EN, eg Frobenius (the morphisms one) EN is 3, Dedekind (the sections one) EN is 7, and it seems that Gauss and Euler (we don’t need to introduce them) have an EN too.
The baseball player Hank Aaron was one of the 511, having been the subject of a mathematical study and having signed with Erdos a baseball ball.