My Friend Erdös..
After one of my lectures a few weeks ago, a student came up to me and asked whether I had an Erdős number and, if so, what it was. I didn’t actually know what he was talking about but was yesterday reminded of it, so tried to find out.
In case you didn’t know, Paul Erdős (who died in 1996) was an eccentric 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 between colleagues and conference, 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. The Erdős number is 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 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.
A list of individuals with very low Erdős numbers (1, 2 or 3) can be found here.
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. According to the AMS website, mine is 5 – much lower than I would have expected. The path from me to Erdős in this case goes through G.F.R. Ellis, a renowned expert in the mathematics of general relativity (as well as a ridiculous number of other things!). I wrote a paper and a book with George Ellis some time ago.
However, looking at the list I realise that I have another route to Erdős, through the great Russian mathematician Vladimir Arnold, who has an Erdős number of 3. Arnold wrote a paper with Sergei Shandarin with whom I wrote a paper some time ago. That gives me another route to an Erdős number of 5, but I can’t find any paths shorter than that.
I guess many researchers will have links through their PhD supervisors, so I checked mine – John D. Barrow. It turns out he also has an Erdős number of 5 so a path through him doesn’t lower my number.
I used to work in the School of Mathematical Sciences at Queen Mary, University of London, and it is there that I found some people I know well who have lower Erdős numbers than me. Reza Tavakol, for example, has an Erdős number of 3 but although I’ve known him for 20 years, we’ve never written a paper together. If we did, I could reduce my Erdős number by one. You never know….
This means that anyone I’ve ever written a paper with has an Erdős number no greater than 6. I doubt if it’s very important, but it definitely qualifies as Quite Interesting.
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This entry was posted on March 28, 2010 at 12:59 pm and is filed under Biographical with tags Erdos Number, George Ellis, John D. Barrow, Mathematicians, mathematics, Paul Erdos, Reza Tavakol. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
In the Dark 
March 28, 2010 at 4:20 pm
Why do you say he’s eccentric Peter? His behaviour sounds wholly routine for a mathematician. Witness the current furore over Perelman:
http://news.bbc.co.uk/1/hi/world/europe/8585407.stm
March 28, 2010 at 5:23 pm
What’s normal for mathematicians is often eccentric for the rest of us…
March 28, 2010 at 7:41 pm
My Erdös number is NaN according to the AMS website. I guess their bibliographical database doesn’t include much astronomy literature.
BTW, the “author distance” is used by http://www.arxivsorter.org/ which writes: “Arxivsorter uses the network of co-authorship to estimate a proximity between people. It then ranks a list of publications using a friends-of-friends algorithm”. I find it useful.
March 29, 2010 at 1:54 am
Anton and telescoper, your comments are offensive. Mathematicians, and scientists, are normal people. There are weird/eccentric/crazy mathematicians just as there are astronomers, authors, politicians, or mail carriers. But we’re mostly normal and I personally don’t appreciate the perpetuation of that particular myth.
March 29, 2010 at 9:42 am
Ahava,
As someone who is himself openly eccentric, I can assure you no offence was intended.
Peter
March 29, 2010 at 3:31 am
I think you’ll be happy yo know that yours is lower, given that mine is 4 via Tegmark that has 2, and we both published with someone connected to Tegmark.
March 29, 2010 at 9:20 am
anisotropie,
Interesting. The link with Tegmark could be via Cooray but, strictly speaking, those papers aren’t published yet. Unless it’s someone else.
I don’t know who you are, though, so I can’t check.
Peter
March 29, 2010 at 10:22 am
Ahava,
Like Peter I meant no offence. In fact I have delivered an examinable lecture course in a university mathematics department and published mathematical work without any physics applications attached, and I believe that people are entitled to lampoon themselves. The mathematician and lampoon Tom Lehrer always got a laugh with his line about mathematicians.
Anton
March 29, 2010 at 12:29 pm
Yes, I worked in a mathematics department for the best part of a decade. Some of the folks there were quite eccentric, but most of them wouldn’t mind being described by that word. Neither would I. Normality (whatever it is) is highly overrated.
March 29, 2010 at 1:14 pm
It’s certainly possible yours is lower Peter. The AMS route isn’t perfect. I had no idea what my number was, but plugged my name into the site and it came back with 4. However, the path it gave took me first through my advisor and then through one of his other students. Since that person and I published together anyway, it could have avoided going through my advisor at all, but it missed it. So my number is at most 3, which was quite unexpected. Now, if I could only make it 2…
March 29, 2010 at 1:19 pm
Mark,
I have had quite a few emails about this. There are a lot of missing links in the AMS database. I’m pretty sure now that mine is 4 – it certainly is if you count papers in the press. I’m also pretty sure John Barrow’s is less than 5 too…
Peter
March 29, 2010 at 1:21 pm
This routine is unlikely ever to be perfect. Is it Erdos-specific or can it trace a likely shortest path between any two reasonably prolific scientific authors?
Anton
March 29, 2010 at 1:23 pm
Anton,
You can type in any two names, as long as they’re both in the database. Try it here.
Peter
March 30, 2010 at 8:00 pm
Philip,
What are you trying to say with your statement
That flight attendants are not human or that the person the flight attendant caught it from wasn’t human?
Peter
March 30, 2010 at 8:27 pm
A study of mathematically gifted Icelanders demonstrated an increased risk of mental illness in their ranks. (4 times the normal rate!) Google “relation of mathematical ability to psychosis in iceland” … “feynman fredkin wolfram” … “erdos eccentricity”
March 30, 2010 at 8:55 pm
Phillip,
I remember some years ago when pathology specimens of people who had died mysteriously of everything, before the 1980s, were retested for AIDS and the date of first fatality got pushed ever farther back. Genetic mutation rates now suggest that AIDS jumped from monkeys to people in West/Central Africa – most likely when an infected animal was butchered – about a century ago; see
http://en.wikipedia.org/wiki/History_of_AIDS
which also shows that the flight attendant often mentioned in this connection, while infecting many people, was far from being the first.
Anton
December 18, 2011 at 9:09 am
[…] After one of my lectures a year or so ago, a student came up to me and asked whether I had an Erdős number and, if so, what it was. I didn’t actually know what he was talking about but tried to find out and eventually posted about it. […]
July 12, 2012 at 5:25 am
I just discovered that if our paper gets accepted, I will have erdos number 4, which is pretty cool. By the way, in your last paragraph, you must have meant “no less” not “no greater”
July 12, 2012 at 8:05 am
I don’t think so. Friends might have a number less than 6 because of some other connection, but it can’t be greater than six because of mine.
July 12, 2012 at 8:12 am
Yes, you’re right. I got it backwards, I was thinking “no less” than 4 (assuming you’re 5), so the difference has to be 1… Anyways, thanks for correcting my (attempt) to correct you.