Archive for Erdos Number

What’s your Epstein Number?

Posted in Biographical with tags , , , , , , on February 5, 2026 by telescoper

The release of the latest batch of information relating to disgraced financier and sex offender Jeffrey Epstein got me thinking about the number of physicists on friendly terms with that individual and that in turn got me thinking about the Erdős Number, which I blogged about here, and about constructing some sort of metric relating to a person’s connecttion to Epstein.

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. A list of individuals with very low Erdős numbers (1, 2 or 3) can be found here. As it happens, mine is three.

The main difference between an Erdős Number and a putative Epstein Number is that most people think’s a nice thing to have a low Erdős Number whereas the opposite is probably the case for evidence of close collaboration with Jeffrey Epstein…

It is also difficult to define an equivalent to the Erdős Number for Epstein as the form of “colloboration” is less easily catergorised than publishing a paper. I think it is probably fairer to base a number simply on the number of people you know who met Epstein personally (assuming you didn’t know him yourself). Anyone who did know Epstein personally therefore gets an automatic red card. It would also be very difficult for a typical person to work out how many people they have met who have met someone who has met Epstein, etc.

I was intrigued by this because it is known that Epstein liked hanging out with scientists and, being a scientist myself, I wondered if anyone I knew had been drawn into the Epstein circle. It’s unreasonable to count anyone who appears in the Epstein files as having “known” Epstein because many of the names simply appear on emails sent by Epstein to which no reply was apparently ever received or which were not indicative of a working relationship or personal friendship, sometimes quite the opposite.

Anyway, based on a not very thorough bit of research I came across the following people who I have met in person who met and knew Jeffrey Epstein to a greater or lesser extent.

First, there’s Lawrence Krauss who left his position at Arizona State University as a consequence of a sexual misconduct case. He features prominently in the Epstein correspondence, including many messages about the disciplinary case brought against him at ASU. I met Lawrence Krauss in the 1990s at an Aspen Summer School for Physics, where I shared an office with him for about two weeks. I wouldn’t say that we got on well.

Second, there’s Harvard theoretical physicist Lisa Randall, whom I met at a meeting in South Africa about 25 years ago. The disturbing thing about her case is that she carried on interacting with Epstein even after his conviction for sex offences, visiting Epstein’s island home and travelling on his private jet.

Another name that comes up frequently in the Epstein files is John Brockman, a well-known literary agent. I met him at the Experiment Marathon in Reykjavik in 2008. In fact we were placed next to each other alphabetically speaking in the list of contributors:

Our conversations at that meeting were limited to small talk. As a matter of fact I didn’t really know who he was! He certainly didn’t offer me a lucrative book deal like he did with certain other physicists. The topic never arose.

The files also contain references to Stephen Hawking (who died in 2018), including allegations about him made by Virginia Giuffre. Hawking was never charged with any crime but it is the case that he met Epstein at least once, at a meeting organized by Lawrence Krauss on St Thomas, close to Epstein Island. I met Stephen Hawking on a number of occasions.

Now you can add Lee Smolin, whom I met in Canada when I was on sabbatical in 2005. He has stepped back from his position at the Perimeter Institute after revelations that he maintained contact with Epstein after Epstein’s conviction for child sex offences.

So according to this my Epstein Number is four five. I have had no contact with any people who knew Epstein since 2008 and very little before that. Although it is perhaps indicative of a lack of eminence, I can’t say I’m sorry this number is low. I may have missed some, of course.

P.S. It is worth reading Peter Woit’s blog post on this topic and Scott Aaronson’s here.

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Closer to Erdös…

Posted in Biographical with tags , , , , on December 18, 2011 by telescoper

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.

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.

Anyway, my erstwhile PhD supervisor John D. Barrow recently 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 John’s Erdős number is now  2, mine is consequently no higher than 3, and  anyone I’ve ever written a paper with now has an Erdős number no greater than 4.

I’ll be making sure this new information is included in our forthcoming REF submission.

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My Friend Erdös..

Posted in Biographical with tags , , , , , , on March 28, 2010 by telescoper

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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