## Erdős number

16 July 2011A while ago I read about the Erdős number, which is a measure of the “collaborative distance” between a researcher and the late, prolific Hungarian mathematician Paul Erdős. (His surname is pronounced something like *air-desh*, with a slightly rolling “r” in the first syllable, a bit like a Scot saying “err”…) It is related to the concept of six degrees of separation, a hypothesis that everyone in the world is linked to everyone else through no more than six mutual acquaintances, except that the criteria when calculating an Erdős number are more stringent, as two people must have co-authored a scientific paper together for the link to count. Anyone who wrote a paper with Erdős has an Erdős number of 1, their collaborators have an Erdős number of 2, and so on.

Erdős numbers are primarily for mathematicians, but it is possible for researchers in other fields to have an Erdős number as much collaboration cuts across the boundaries of different disciplines. So I decided to see if I had an Erdős number myself. The American Mathematical Society have a collaboration distance calculator which can take the names of any two mathematicians, but has a shortcut to add Erdős as the second person. As it is a Mathematical Society, the database only covers mathematical journals.

I tried a few names in the calculator, and eventually found that the key to finding my Erdős number is Derek Raine, a professor in the Leicester physics department who has published research in more mathematical areas such as cosmology and quantum field theory. He has an Erdős number of 4, thanks to a collaboration from when he was at Oxford University. Unfortunately, I am still three more connections away from Derek, which means **I have an Erdős number of 7**. Here are the seven steps:

- Alladi, K.;
*Erdős, P.*;**Vaaler, J. D.**Multiplicative functions and small divisors. Progr. Math., 70, 1–13 (1987) **Rodriguez-Villegas, F.**; Toledano, R.;*Vaaler, J. D.*Estimates for Mahler’s measure of a linear form. Proc. Edinb. Math. Soc. (2) 47, no. 2, 473–494 (2004)**Candelas, P.**; de la Ossa, X.;*Rodriguez-Villegas, F.*Calabi-Yau manifolds over finite fields. II. Fields Inst. Commun., 38, 121–157 (2003)*Candelas, P.*;**Raine, D. J.**Quantum field theory on incomplete manifolds. J. Mathematical Phys. 17, no. 11, 2101–2112 (1976)- Brandt, D.; Fraser, G. W.;
*Raine, D. J.*;**Binns, C.**Superconducting Detectors and the Casimir Effect. J. Low Temp. Phys. 151, Nos. 1–2, 25–31 (2008) *Binns, C.*;**Howes, P. B.**et al. Loss of long-range magnetic order in a nanoparticle assembly due to random anisotropy. J. Phys. Cond. Mat. 20 055213 (2008)**Rawle, J. L.**;*Howes, P. B.*; Alcock, S. G. Crystal Truncation Rod Measurements from Buried Quantum Dots. Surf. Rev. Lett. 10, Iss. 2–3, 525–531 (2003)

Apparently, most people with an Erdős number have one lower than 8. Of course, I may have another, as of yet undiscovered, path to a lower Erdős number, through connections either with the same or different people. So perhaps I should say that my *maximum* Erdős number is 7.

There is also the question of what counts as a publication. I did once produce an Institute of Physics branch newsletter with Derek Raine, so if I could count that, I would have a quite respectable Erdős number of 5! In any case, six degrees of separation holds true: in terms of acquaintance I’m less than six steps away from the great mathematician.