Remembering Erdös

This poster, advertising a forthcoming Summer School in honour of the famous mathematician Paul Erdös arrived this morning, so I thought I’d advertise it through this blog.


In case you didn’t know, Paul Erdős (who died in 1996) was an eccentric yet prolific Hungarian mathematician who wrote more than 1000 mathematical papers during his life but never settled in one place for any length of time. He travelled constantly between colleagues and conferences, mostly living out of a suitcase, and showed no interest at all in property or possessions. His story is a fascinating one, and his contributions to mathematics were immense and wide-ranging, and I’m sure the conference in his honour will be fascinating.

A strange offshoot of his mathematical work is the Erdős number, which is really a tiny part of his legacy, but one that seems to have taken hold. Some mathematicians appear to take it very seriously, but most treat it with tongue firmly in cheek, as I certainly do.

So what is the Erdős number? It’s actually quite simple to define. First, Erdős himself is assigned an Erdős number of zero. Anyone who co-authored a paper with Erdős then has an Erdős number of 1. Then anyone who wrote a paper with someone who wrote a paper with Erdős has an Erdős number of 2, and so on. The Erdős number is thus a measure of “collaborative distance”, with lower numbers representing closer connections. I say it’s quite easy to define, but it’s rather harder to calculate. Or it would be were it not for modern bibliographic databases. In fact there’s a website run by the American Mathematical Society which allows you to calculate your Erdős number as well as a similar measure of collaborative distance with respect to any other mathematician. Also, a list of individuals with very low Erdős numbers (1, 2 or 3) can be found here. I did a quick poll around the Department of Mathematics here at the University of Sussex and it seems that the shortest collaborative distance among the staff belongs to Dr James Hirschfeld who has an Erdos Number of 2. There is a paper of his, with M. Deza and P. Frankl, Sections of varieties over finite fields as large intersection families, Proc. London. Math. Soc. 50 (1985), 405-425 and both Michel Deza and Peter Frankl have joint papers with Paul Erdős.

Given that Erdős was basically a pure mathematician, I didn’t expect first to show up as having any Erdős number at all, since I’m not really a mathematician and I’m certainly not very pure. However, his influence is clearly felt very strongly in physics and a surprisingly large number of physicists (and astronomers) have a surprisingly small Erdős number. Anyway, my erstwhile PhD supervisor Professor John D. Barrow emailed to point out that he had written a paper with Robin Wilson, who once co-authored a paper (on graph theory) with Erdős himself. That means that John’s Erdős number is now 2, mine is consequently 3 (unless, improbably, I have unkowingly written a paper with someone who has written a paper with Erdős). Anyone I’ve ever written a paper with has an Erdős number no greater than 4; they of course may have other routes to Erdős than through me.

Anyway, none of that is important compared to the real legacy of Erdős, which is his mathematical work. I’m sure the Summer School will be both rewarding and enjoyable!

11 Responses to “Remembering Erdös”

  1. “Summer School” link is broken. Two dots after “www”. (Feel free to delete this comment once corrected.)

  2. Brian Schmidt Says:

    Perhaps even more entertaining is the Erdös-Bacon Number
    which is the sum of your Erdös number, and your Kevin Bacon number (which is the number of generations you are away from Kevin Bacon in a film/video based media). So my Erdos Number is 3 – thanks to George Djorgovski (You too – see your post from 2011!) My Bacon number is harder to define. Runaway Universe – our Doco on the accelerating Universe, had the sound done by Kevin Bacon’s brother, Michael. And he and Kevin have done several things together (3). If you feel sounds is not worthy of a Bacon number, then in that production appeared Alex Filippenko, who appeared in Stephen Fry’s ‘Stephen Fry in America’, and Stephen Stephen Fry
    was in A Fish Called Wanda (1988) with John Cleese who was in
    The Big Picture (1989) with Kevin Bacon (4) – so my Erdös-Bacon Number is 6 or 7 (if you accept the Runaway Universe) – otherwise undefined.

    • Mark McCaughrean Says:

      Coming to this very late, and extending beyond what Brian said, there is also the Erdős-Bacon-Sabbath number.

      As with the Erdős and Bacon numbers, your Sabbath number describes how closely linked you are to the band Black Sabbath (yes, Peter, one of those [not so] modern beat combos) in terms of having played / appeared on a piece of music with the intervening links.

      Much like Erdős and Bacon, Black Sabbath are the chosen hypernode on the basis of their having had many members over the years.

      EBS number holders are relatively rare and include the likes of Hawking (his Sabbath number coming via his voice having been used on a track by Pink Floyd), Brian Cox (fairly obviously), Natalie Portman, Carl Sagan, Noam Chomsky, Condoleeza Rice, and so on.

      For what it’s worth, my EBS number is 13: I have an Erdős number of 3 via Eric Feigelson and Gutti Jogesh Babu, a Bacon number of 3 via Dan Riskin (Discovery Channel Rosetta documentary) and Neil Armstrong (!): Riskin did a documentary with him too, and Armstrong appeared in the Apollo 13 film with Bacon.

      Then my Sabbath number is 7, via Atanas Valkov (“Ambition” film soundtrack, on which I’m sampled), Kayah (Kayah & Transoriental Orchestra), Goran Bregovic (Kayah & Bregovic), Iggy Pop (In the Death Car; Arizona Dream soundtrack), David Bowie (The Idiot), Brian May (Under Pressure), and thence Black Sabbath (When Death Calls).

      If only I had been smart enough to record a sing-a-long with Brian May when we gave him an honorary degree at Exeter some years ago: then I could have had a combined EBS number of 8, equal lowest of all on the EBS page.

      Sorry; I’m sure this is of zero interest to anyone but me (!), but since the EBS number webpage seems to have shut down some time ago (too many wannabees like me applying, apparently), so am hijacking your blog to document it at least somewhere on the web 🙂

  3. Phillip Helbig Says:

    “a surprisingly large number of physicists (and astronomers) have a surprisingly small Erdős number”

    In some cases, this might be deliberate, i.e. they looked for appropriate collaborators in order to lower their Erdős number.

    Max Tegmark, who is younger than I am, has an Erdős number of just 2. (So, after I buy Max a beer and write a joint paper, mine will drop to 3—it is 4 now, because I have two-step connections (one intermediary) both to Tegmark and to the ubiquitous Djorgovski.) I’m not sure whether his low Erdős number is deliberate. His father, Harold Shapiro, just happens to be a mathematician, and he wrote a paper with his Dad, as one does. (Max adopted his mother’s surname Tegmark upon discovering that there are many Shapiro’s in astronomy. His family had been the only Shapiros in Sweden. Fortunately, his mother wasn’t named Andersson or Lindquist or whatever but had a rare name, her family being the only Tegmarks in the world.)

  4. Phillip Helbig Says:

    In the folk-rock world, the Pegg number (based—pun, as always, intended) on bass player Dave Pegg) serves a similar purpose.

    On Andy Lawrence’s blog (by the way, whatever happened to the squire—his blog used to be quite active and is now dormant), there is some discussion about 6 degrees of separation.

  5. Anton Garrett Says:

    For a long time I was convinced that “Lorand Eőtvős” was a misprint for “Roland Eőtvős”. But it’s not.

  6. Michael Kenyon Says:

    If you start doing living comedian/dead mathematician posts Barry Cryer is the double of this ex gadgie.

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