Paul Erdős and the Erdős Number

Mathematicians are well known to be an eccentric bunch. It would be inappropriate for me to present second-hand or higher order accounts of other mathematicians and their eccentricities; there are available numerous articles and books that draw on primary sources for the interested reader. I shall, however, mention the Hungarian mathematician, Paul Erdős (1913–1996).

I did actually meet my mathematical great, great, grand-uncle*, Paul Erdős, one time in passing. It was at Flinders University, Adelaide, in 1985 where I was a Lecturer at the time. Paul Erdős was famously itinerant. He travelled the world, virtually living out of a suitcase, visiting institutions and individuals for only short periods of time on various forms of short-term funding. He was a great problem poser and solver, as opposed to a theorist, and by some measures is the most prolific Mathematics publisher of all time. Moreover, most of his publications were written with collaborators, reflecting his enthusiasm for posing a problem to whomever he was visiting, and then solving it with them.

* My mathematical great, great grandfather, Marcel Riesz, and Paul Erdős were both students of Leopold (Lipót) Fejér at Eötvös Loránd University in Budapest, Hungary; see my Mathematical Genealogy (118KB pdf document).

From this has evolved the concept of a mathematician’s Erdős Number. A mathematician who jointly authored a paper with Erdős has an Erdős Number of 1. A mathematician who wrote a paper with someone with an Erdős Number 1 would then have an Erdős Number of 2, and so on. Of course, the lower one’s Erdős Number, the greater the prestige. So keen are mathematicians to determine their Erdős Number, that the American Mathematical Society even has an Erdős Number calculator on their website!

As a mathematician, I seem to have been blessed with the skill of being in the right place at the right time, rather than any intrinsic mathematical greatness. My Dean of School (an engineer / computer scientist rather than a mathematician) was most impressed to discover that I boast an Erdős Number of 3. So was I to be honest!

Steven F. Brown, Alan J. Branford, William Moran (1997) “On the use of artificial neural networks for the analysis of survival data”, I.E.E.E. Transactions on Neural Networks, 8, 1071-7.

Jean-Marc Deshouillers, Gregory A. Freiman, William Moran (1999) “On series of discrete random variables, 1. Real trinomial distributions with fixed probabilities”, Structure theory of set addition, Astérisque, 258, 411-423.

Gregory A. Freiman, Paul Erdős (1990) “On two additive problems”, Journal of Number Theory, 24, 1-12.