Messy: The Power of Disorder to Transform Our Lives
by Tim Harford · 3 Oct 2016 · 349pp · 95,972 words
the world and across the twentieth century spreads so far it is measured in an honorific unit: the “Erdős number.” People who wrote articles jointly with Erdős himself are said by mathematicians to have an Erdős number of one. Over five hundred people enjoy this distinction. If you wrote a paper with one of
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them, your Erdős number is two. Over forty thousand people have Erdős numbers of three or less, all spinning in intellectual orbit around this astonishing man. Erdős’s achievement as the linchpin of so many mathematical partnerships is
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, My Brain Is Open: The Mathematical Journeys of Paul Erdős (Oxford: Oxford University Press, 1998), p. 182. Also see the Erdős Number Project at Oakland University: http://wwwp.oakland.edu/enp/. The Erdős number graph continues to evolve because mathematicians continue to publish research based on their collaborations with Erdős, crediting him as a
Enshittification: Why Everything Suddenly Got Worse and What to Do About It
by Cory Doctorow · 6 Oct 2025 · 313pp · 94,415 words
, this whole esoteric business was the exclusive province of academics, who made something of a game of it. For example, mathematicians like to calculate their “Erdős numbers,” a measure of their proximity to Paul Erdős, a legendary and fantastically prolific mathematician. Erdős was an itinerant, driven, brilliant weirdo who would show up
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.) If you collaborated with Erdős on a publication, you have an Erdős number of 1 (Erdős’s own Erdős number is 0, of course). If you collaborated with one of Erdős’s coauthors, you have an Erdős number of 2. Those academics’ collaborators have an Erdős number of 3, and so on. The PageRank paper proceeded from the
The Simpsons and Their Mathematical Secrets
by Simon Singh · 29 Oct 2013 · 262pp · 65,959 words
are made via co-authored articles, typically mathematical research papers. Anybody who has co-authored a paper directly with Erdős is said to have an Erdős number of 1. Similarly, mathematicians who have co-authored a paper with someone who has co-authored a paper with Erdős are said to have an
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Erdős number of 2, and so on. Via one chain or another, Erdős can be connected to almost any mathematician in the world, regardless of their field
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, Hopper’s hardheaded, applied, technology-driven, industrial, military mode of mathematics was utterly different from Erdős’s purist devotion to numbers, yet Hopper has an Erdős number of just 4. This is because she published papers with her doctoral supervisor Øystein Ore, whose other students included the eminent group theorist Marshall Hall
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a paper with the distinguished British mathematician Harold R. Davenport, who had published with Erdős. So, how does Jeff Westbrook rank in terms of his Erdős number? He started publishing research papers while working on his PhD in computer science at Princeton University. As well as writing his 1989 thesis, titled “Algorithms
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papers with his supervisor Robert Tarjan. In turn, Tarjan has published with Maria Klawe, who collaborated with Paul Erdős. This gives Westbrook a very respectable Erdős number of just 3. However, this does not make him a clear winner among the writers on The Simpsons. David S. Cohen has published a paper
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has published a paper with Noga Alon at Tel Aviv University, who in turn published several papers with Erdős. Hence, Cohen can also claim an Erdős number of 3. In order to break the tie between Cohen and Westbrook, I decided to explore another facet of being a successful writer on The
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3, which puts him just behind Stallone. In short, he has impressive Hollywood credentials. Thus, Westbrook has both a Bacon number of 3 and an Erdős number of 3. It is possible to combine these numbers into a so-called Erdős-Bacon number of 6, which gives an indication of Westbrook’s
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Kevin Bacon, which means that Bayer has a Bacon number of 2. As a highly respected mathematician, it is no surprise that Bayer has an Erdős number of 2, which gives him a combined Erdős-Bacon number of just 4. When A Beautiful Mind was released in 2001, Bayer claimed to have
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even lower Erdős-Bacon number. He co-authored a paper with Erdős, titled “The Asymptotic Behavior of a Family of Sequences,” which gives him an Erdős number of 1. Equally impressive is the fact that he had a very minor role in Pretty Maids All in a Row, a 1971 film written
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as co-author on a paper titled “Political Orientations Are Correlated with Brain Structure in Young Adults.” Although Rees is a neuroscientist, he has an Erdős number of 5, because of convoluted collaborations that ultimately link him to the world of mathematics. Having published with Rees, Firth can claim an
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Erdős number of 6. He also has a Bacon number of just 1, because he worked with Bacon on Where the Truth Lies (2005). This gives Firth
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the other co-authors was Abigail A. Baird, who has a link into mathematical research, which results in her having an Erdős number of 4. This means Portman has an Erdős number of 5. Her Bacon number relies on a directorial credit for one of the segments in the anthology film New York, I
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Mill and the Cross (2011) with Rutger Hauer, who was in Wedlock (1991) with Preston Maybank, who was in Novocaine (2001) with Kevin Bacon. His Erdős number, for obvious reasons, is 0, so Erdős has a combined Erdős-Bacon number of 4—not quite enough to match Reznick. And, finally, what about
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Kevin Bacon’s Erdős-Bacon number? Bacon, being Bacon, has a Bacon number of 0. As yet, he does not have an Erdős number. In theory, he might develop a passion for number theory and collaborate on a research paper with someone who already has an
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Erdős number of 1. This would give him an unbeatably low Erdős-Bacon number of 2. CHAPTER 6 Lisa Simpson, Queen of Stats and Bats When the
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well known as having co-authored more than two dozen papers with Paul Erdős, and he was the foremost figure in popularizing the notion of Erdős numbers. One of Graham’s other claims to fame is Graham’s number, which set a record in 1977 for the largest number ever used in
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been lost in the mists of time (or the writers have understandably sought anonymity). 8. I have, of course, looked at my own credentials. My Erdős number is 4 and my Bacon number is 2, which puts me on a par with Jeff Westbrook. Moreover, I also appear to have a Sabbath
The Music of the Primes
by Marcus Du Sautoy · 26 Apr 2004 · 434pp · 135,226 words
, with the Indian mathematician Saravadam Chowla, and that somewhat against his will. The other took collaboration to such an extreme that mathematicians talk of their Erdos number, the number of co-authors that link them to a paper with Erdos. Mine is 3, which means I’ve written a paper with someone
Six Degrees: The Science of a Connected Age
by Duncan J. Watts · 1 Feb 2003 · 379pp · 113,656 words
that Bacon was for the world of movie actors. As a result, if you have published a paper with Erdos, you get to have an Erdos number of one. If you haven’t published a paper with Erdos but you have written one with someone who has, then you have an
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
by Jordan Ellenberg · 14 May 2021 · 665pp · 159,350 words
has been a party game ever since Casper Goffman wrote a half-page note in the American Mathematical Monthly, “And What Is Your Erdős Number?,” in 1969. Your Erdős number is your distance from the mathematician Paul Erdős, who’s considered central to the network thanks to his immense number of collaborators—511 at
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a group of mathematicians for a post-lunch coffee, explaining, “I have something much better than coffee.”) Your Erdős number is the length of the shortest chain of links connecting you to Erdős. If you are Erdős, your Erdős number is 0; if you are not Erdős but wrote a paper with Erdős, your
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Erdős number is 1, if you didn’t write a paper with Erdős but you wrote one with someone whose Erdős number is 1, your Erdős number is 2, and so on. Erdős is connected to just about every mathematician who ever wrote
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a collaborative paper, which is to say that just about every mathematician has an Erdős number. Marion Tinsley, the master of checkers, had an
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Erdős number of 3. So do I; I wrote a paper in 200sd1 about modular forms with Chris Skinner, who as a Bell
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Ukraine. Every single mathematician in the big component is connected to Erdős by a chain of no greater than thirteen links; if you have an Erdős number at all, it’s at most 13. It may seem weird that there’s such a big gap between the one giant glob and the
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globs of various sizes. But it’s actually the general way of things, a fact we know thanks to Erdős himself. The notion of the Erdős number doesn’t just honor Erdős’s sociability; it’s a shout-out to the pioneer work that Erdős, together with Alfréd Rényi,* did on the
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define a movie star’s Bacon number to be the distance, in the costar geometry, from Kevin Bacon. Just as almost every mathematician has an Erdős number, almost every actor has a Bacon number. I happen to have both. My Bacon number is 2, thanks to being in Gifted with Octavia Spencer
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” of this geometry, the greatest distance you can travel from the center before running out of room to run. Just as 13 is the biggest Erdős number any mathematician has, 6 is the maximum shuffle number any permutation of the cards has. (As you might expect, the ordering where the cards are
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Revolution, 48n amicability, 109, 109n amicus briefs, 384–85, 385n, 401 Analysis Situs (Poincaré), 46 Analytical Society, 253 Android phones, 99 “And What Is Your Erdős Number?” (Goffman), 311 animation, 55n Annalen der Physik, 82 annulus, 42 Antarctic distortion, 307 anti-averages, 72–74 anti-Semitism, 320–21, 322n apportionment, 351–52
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Crowe in all the blackboard scenes in the John Nash biopic A Beautiful Mind, has a Bacon number of 2 via Ed Harris, and an Erdős number of 2 via Diaconis, whose paper with Erdős on the greatest common divisor was published eight years after Erdős’s death. That paper, in turn
The Golden Ticket: P, NP, and the Search for the Impossible
by Lance Fortnow · 30 Mar 2013 · 236pp · 50,763 words
3-18. Icosian Solution. * I have written papers with three different co-authors of Paul Erdős, giving me an Erdős number of 2. With Erdős’s 1996 passing, my chances of reducing my Erdős number are slim. I have had no acting experience (or talent) and do not have a Bacon number. Chapter 4
Why Stock Markets Crash: Critical Events in Complex Financial Systems
by Didier Sornette · 18 Nov 2002 · 442pp · 39,064 words
the research reported in the paper. The idea of networks of coauthorship is not new. Most practicing mathematicians are familiar with the definition of the Erdös number [178]. Paul Erdös (1913–1996), the widely traveled and incredibly prolific Hungarian mathematician, wrote at least 1,400 mathematical research papers in many different areas
Machine Learning for Hackers
by Drew Conway and John Myles White · 10 Feb 2012 · 451pp · 103,606 words
networks is by no means news. In the mathematics community, an example of social network analysis at work is the calculation of a person’s Erdős number, which measures her distance from the prolific mathematician Paul Erdős. Erdős was arguably the most prolific mathematician of the 20th century and published over 1
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,500 papers during his career. Many of these papers were coauthored, and Erdős numbers measure a mathematician’s distance from the circle of coauthors that Erdős enlisted. If a mathematician coauthored with Erdős on a paper, then she would
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have an Erdős number of one, i.e., her distance to Erdős in the network of 20th-century mathematics is one. If another author collaborated with one of Erdős
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’ coauthors but not with Erdős directly, then that author would have an Erdős number of two, and so on. This metric has been used, though rarely seriously, as a crude measure of a person’s prominence in mathematics
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. Erdős numbers allow us to quickly summarize the massive network of mathematicians orbiting around Paul Erdős. Erving Goffman, one of the most celebrated intellectuals of the 20th
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directly during this chapter. Our project begins by building a local network, or ego-network, and snowballing from there in the same way that an Erdős number is calculated. For our first analysis, we will explore methods of community detection that attempt to partition social networks into cohesive subgroups. Within the context
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and analyze these Twitter networks. To build these graph objects, our strategy will be to use a single Twitter user as a seed (recall the Erdős number) and build out the network from that seed. We will use a method called snowball sampling, which begins with a single seed and then finds
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of Columns in Your Data, Inferring the Types of Columns in Your Data enumerations, compared to factors, Inferring the Types of Columns in Your Data Erdős number, Social Network Analysis error handling, Organizing location data Euclidean distance, A Brief Introduction to Distance Metrics and Multidirectional Scaling, The k-Nearest Neighbors Algorithm Euler
A Mathematician Plays the Stock Market
by John Allen Paulos · 1 Jan 2003 · 295pp · 66,824 words
areas during his long life. Many of these had co-authors, who are therefore said to have Erdös number 1. Mathematicians who have written a joint paper with someone with Erdös number 1 are said to have Erdos number 2, and so on. Ideas about such informal networks lead naturally to the network of all networks
Networks, Crowds, and Markets: Reasoning About a Highly Connected World
by David Easley and Jon Kleinberg · 15 Nov 2010 · 1,535pp · 337,071 words
A Man for All Markets
by Edward O. Thorp · 15 Nov 2016 · 505pp · 142,118 words
Rationality: What It Is, Why It Seems Scarce, Why It Matters
by Steven Pinker · 14 Oct 2021 · 533pp · 125,495 words
Algorithms in C++ Part 5: Graph Algorithms
by Robert Sedgewick · 2 Jan 1992
SQL Hacks
by Andrew Cumming and Gordon Russell · 28 Nov 2006 · 696pp · 111,976 words