People ask, from time to time, what is your Erdős number? For a long time I’ve said I haven’t got one because I haven’t published a mathematical research paper. When I gave this answer to Samuel Hansen last year he told me that any research paper counts, not just those in mathematics. This left me idly wondering and today, having listened to Samuel discussing social network theory on the Big Science FM podcast, I finally decided to have a go. There are a few possibilities, none of which seem, to me, entirely satisfactory.

Short answer: At most 4. Probably.

Long answer:

My list of publications is on my website. I do not appear on MathSciNet.

MathSciNet tells me Edmund Harriss wrote ‘Flattening functions on flowers‘ with Oliver Jenkinson, who wrote ‘Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type‘ with R. Daniel Mauldin , who wrote ‘The nonexistence of certain invariant measures‘ with Paul Erdős. This gives Edmund an Erdős number of 3. Edmund and I are both authors on the paper ‘The unplanned impact of mathematics‘ in Nature, which would make my number at most 4. However, this was a strange piece and although it is listed as one paper on the Nature website it was actually a series of seven short pieces under a common title and introduction. It is difficult to say whether this counts as a collaboration.

From the same root article, MathSciNet tells me Mark McCartney has an Erdős number of 5, Graham Hoare has 4 (although this is via a biography ‘Stefan Banach (1892–1945). A commemoration of his life and work’ in Mathematics Today which may not count (see below)), Juan Parrondo has 5, Julia Collins has 5 and Chris Linton has 4. These all have the same problem as Edmund above and are all greater numbers than Edmund’s anyway.

For another route, MathSciNet tells me Joel Feinstein wrote ‘A fixed-point theorem for holomorphic maps‘ with Richard Timoney, who wrote ‘An extremal property of the Bloch space‘ with Lee Rubel, who wrote ‘Tauberian theorems for sum sets‘ with Paul Erdős. This makes Joel’s Erdős number 3. Joel and I have a paper ‘Media Enhanced Teaching and Learning‘, in the new issue of MSOR Connections. This would make my number 4. MSOR Connections is a mathematics education practitioner journal and I am not sure if this counts.

Stephen Hibberd and Cliff Litton, with whom I collaborated on some of my first articles, including ‘MELEES – Managing Mayhem?’ (Proc. Mathematical Education of Engineers IV), both have an Erdős number of 4. Going this route, mine would be 5. Being a paper in conference proceedings, this seems the most ‘real’ route.

So what are the rules? The Erdős Number Project says:

Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional coauthors is permitted. Not normally included are joint editorships, introductions to books written by others, technical reports, problem sessions, problems posed or solved in problem sections of journals, seminars, very elementary textbooks, books on history, memorial or other tributes, biography, translations, bibliographies, or popular works.

The Nature article perhaps doesn’t count then, even if it counts as a collaboration, as it is a history or perhaps even popular article (exposition rather than original research). By this definition, the article with Joel Feinstein does seem to count. We’ve collaborated for a couple of years on using tablet PCs to deliver mathematics lectures, both while I was at Nottingham and since then, and have run several workshops on this topic. This collaboration led to this paper on Joel’s use of this technology in his lectures. So I suppose that would make my Erdős number 4.

Of course, like any social network analysis, the members of a network may not be able to find the shortest path through it. For example, I co-authored with Claire Chambers who has a healthy number of co-authors but as her work now is in education around geography they are not included in MathSciNet. I have other co-authors on my list of publications that don’t appear in MathSciNet but may, as I appear to, have a number. Indeed, any of the authors listed above could have a shorter route found by leaving MathSciNet’s database. So I should say my Erdős number is “at most 4”.

I find you can only go so far down this rabbit hole before it all seems far too preposterous to go on, so I will stop.