An Erdős number is a fun and nerdy way to count connections between oneself and the eccentric and prolific mathematician, Paul Erdős. Most of what I know about Erdős is from a cute children’s book, The Boy Who Loved Math: The Improbable Life of Paul Erdos, by Deborah Heiligman, which I recommend.
As a nerd, I am very proud to have an Erdős number, despite not being a mathematician. Physicists may be more likely than those in other fields to have one. According to some statistics of Wikipedia, about 80% of Nobel Laureates in Physics have an Erdős number, larger even than the the Nobel Laureates in Economics (only 62%).
My maximum Erdős number is 5. It is a maximum, because there may be a connection that I don’t know about. I calculate my lineage based on the information published in Albert-László Barabási’s fun book, Linked (p48). Here is the breakdown:
0: Paul Erdős has an Erdős number of 0, by definition.
1: Joseph E. Gillis was one of 511 distinct coauthors of Erdős. According to the Erdős Number Project, they published a single paper together in 1937. (I haven’t been able to find the name of this article, but I will update when I do.) Gillis was a British Jewish mathematician who received his PhD at the University of Cambridge. He worked as a codebreaker at Bletchley Park, breaking the German code that the Nazi’s used to send weather reports. (Interesting article here.)
2: George H. Weiss first published with Gillis in 1959 (according to the MathSciNet website). The paper was titled “Nature of the singularities in the spectrum of a one-dimensional ionic lattice,” in Physical Review. Weiss is a mathematician and a physicist, working in the Division of Computational Bioscience at NIH. This collaboration, then, brings the lineage squarely into the realm of physics, and in particular into the realm of statistical physics. They also published at least two more papers together: “Products of Laguerre polynomials” in 1960, and “Expected number of distinct sites visited by a random walk with an infinite variance” in 1970. All of this happened before I was born.
3: Gene Stanley is a Professor of Physics at BU, where I received my PhD. So Gene is the first person in my Erdős lineage that I actually know. According to the CV published on his website, he coauthored 13 scholarly papers with Weiss on statistical physics topics, so this link is quite strong, if you want to weight links according to the number of collaborations. I don’t think that weighting links for this graph is really a thing, though as the Erdős Number Project website explains, there is a different, more pure, kind of Erdős number, called the Erdős number of the second kind. For this number, which Erdős himself apparently preferred, a link is only established if a paper has only two coauthors. Using this definition, Stanley and Weiss would not be linked at all, since all papers that they worked on together had 3 or more authors (as you can see in the list below).
Having a large average number of coauthors fits well with what I know of Gene. During my time at BU, Gene always had a large research group, with a number of post-docs or visiting scientists working with graduate students on projects. He publishes A LOT. His CV lists (at the time that posting) a whopping 1385 publications. He has supervised 114 PhD theses, and hosted 211 Research Associates or Visiting Scholars. He is evidently a publication ‘hub,’ in the network theory sense, and has allowed for the connection of many a physicist like me to Paul Erdős!
For your reading pleasure, and for my own reference, I’ve listed the (very fun!) titles of the 13 papers that Gene and George Weiss worked on together. I include the publication date, and the total number of authors for each paper in parentheses.
- Probability Distribution of the Interface Width in Surface Roughening: Analogy with a Levy Flight, 1991. (4)
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Territory Covered by N Diffusing Particles, 1992. (5)
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Some Recent Variations on the Expected Number of Sites Visited by an n-Step Random Walkers, 1992. (7, with Weiss as first author)
- Fractal Landscapes in Physics & Biology, 1993. (15, with Stanley as first author)
4: Bill Klein was my PhD advisor at Boston University, so basically my academic father. (It’s funny that he his daughter is the same age as me and also has the same first name as me.) Bill worked with Gene on percolation topics. My very first project with Bill was a little percolation exploration. Bill and Gene (again, according to Gene’s published CV) published 11 articles together between 1977 and 1981, almost all of which are percolation problems (so I won’t list them all here). You can see that Weiss actually comes in after this collaboration. Weiss and Stanley’s first paper is on percolation in 1984. The topics then branch off from there (pun intended!) Most of these papers had 3 or 4 authors total.
5: Me! I’ve published 7 papers with Bill, two as his graduate student. All of these papers have had at least one additional coauthor. We (me and Bill’s other graduate students) all worked relatively closely with Bill, in contrast to Gene’s sprawling group.
As a teacher at a liberal arts college, I’ve published with a philosopher, and I hope to be a critical link between Paul Erdos and some more humanities types!
It turns out that even without the critical Gene link, I would still have an Erdős number of 6 through a different route, but still through Bill. The MathSciNet automatically found the following path between Erdős and me:
0: Paul Erdős
1: Daniel J. Kleitman through the article Asymptotic enumeration of Kn-free graphs, 1976. Note that B. L. Rothschild is also a collaborator, so this link isn’t valid for the Erdős number of the second kind. Kleitman is an applied mathematician at MIT. I’m sure he’s awesome! But I’ve never heard of him. And I do not know what Kn-free graphs are.
2: Sidney Coleman through Mass formulas and mass inequalities for reducible unitary multiplets, 1964. The third author on this paper is Nobel laureate Shelly Glashow, who was also in the BU physics department when I was there. I have definitely heard of these guys! The also both worked with Murray Gell-Mann, who I met in Santa Fe in the summer of 2008
3: Howard J. Schnitzer through Departures from the eightfold way. II. Baryon electromagnetic masses, 1964.
4: Richard C. Brower via Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture, 2009.
5: William Klein via Single-cluster Monte Carlo dynamics for the Ising model, 1990.
6: Rachele Dominguez. Me, again! Via any of my seven publications with Bill. The one listed in MathSciNet is Early time kinetics of systems with spatial symmetry breaking, 2009.
And this.