Law School Culture and the Lost Art of Collaboration: Why Don\u27t Law Professors Play Well with Others

I have an Erdős number. Specifically, I have an Erdős number of 5. For the uninitiated, the concept of an “Erdős number” was created by mathematicians to describe how many “degrees of separation” an author of an article is from the great mathematician Paul Erdős. If you coauthored a paper with Erdős, you have an Erdős number of 1. If you coauthor a paper with someone with an Erdős number of 1, you have earned an Erdős number of 2. Coauthoring a paper with someone with an Erdős number of 2 gives you an Erdős number of 3, and so on. In 2010, I wrote an article on law and statistics in 2010 with my son, William Meyerson. He had previously written an article with Scott T. Chapman, who had written one with Lara K. Puwell, who in turn had coauthored a piece with Zsolt Tuza, who had actually written an article with Paul Erdős. Thus, William has an Erdős number of 4, which garners me an Erdős number of 5. I quickly discovered that I was not alone in feeling a sense of pride for having an “Erdős number.” But as I thought about the path one must follow to earn a coveted Erdős number, I began to understand that the mathematical community views collaborative work in a vastly different manner than the legal academy where I have spent my career. In mathematics, it is expected that one will coauthor numerous pieces throughout one’s career. In the law school culture, by contrast, coauthorship, while not unknown, is not a significant part of the academic tradition. This Article grew out of that insight. I wanted to explore whether my intuitive sense of these different attitudes towards collaboration was reflected empirically by a differing amount of coauthorship in the two fields, and, if so, what might be the reasons for such a difference. Finally, I wanted to explore whether there are lessons legal academics can learn from their counterparts in mathematics in terms of creating a culture that not only accepts but encourages coauthorship. The second Part of this Article discusses how mathematicians produced a culture of collaboration. I focus on the extraordinary career of Paul Erdős, and show how he helped create a social academic environment in which coauthorship is valued. The third Part explores the very different culture in legal academe. I begin the Part by exploring the disconnect between the individualistic culture of law schools and the collaborative culture of the legal community at large. I then discuss my study of legal coauthorship, which demonstrates that law professors collaborate at a rate much lower than their mathematical colleagues. Next, I explore the benefits that law professors and their students could gain from collaboration. The Article concludes with a consideration of some proposals to help turn the law school culture into one where collaboration and coauthorship are respected and encouraged

Law School Culture and the Lost Art of Collaboration: Why Don\u27t Law Professors Play Well with Others

I have an Erdős number. Specifically, I have an Erdős number of 5. For the uninitiated, the concept of an “Erdős number” was created by mathematicians to describe how many “degrees of separation” an author of an article is from the great mathematician Paul Erdős. If you coauthored a paper with Erdős, you have an Erdős number of 1. If you coauthor a paper with someone with an Erdős number of 1, you have earned an Erdős number of 2. Coauthoring a paper with someone with an Erdős number of 2 gives you an Erdős number of 3, and so on. In 2010, I wrote an article on law and statistics in 2010 with my son, William Meyerson. He had previously written an article with Scott T. Chapman, who had written one with Lara K. Puwell, who in turn had coauthored a piece with Zsolt Tuza, who had actually written an article with Paul Erdős. Thus, William has an Erdős number of 4, which garners me an Erdős number of 5. I quickly discovered that I was not alone in feeling a sense of pride for having an “Erdős number.” But as I thought about the path one must follow to earn a coveted Erdős number, I began to understand that the mathematical community views collaborative work in a vastly different manner than the legal academy where I have spent my career. In mathematics, it is expected that one will coauthor numerous pieces throughout one’s career. In the law school culture, by contrast, coauthorship, while not unknown, is not a significant part of the academic tradition. This Article grew out of that insight. I wanted to explore whether my intuitive sense of these different attitudes towards collaboration was reflected empirically by a differing amount of coauthorship in the two fields, and, if so, what might be the reasons for such a difference. Finally, I wanted to explore whether there are lessons legal academics can learn from their counterparts in mathematics in terms of creating a culture that not only accepts but encourages coauthorship. The second Part of this Article discusses how mathematicians produced a culture of collaboration. I focus on the extraordinary career of Paul Erdős, and show how he helped create a social academic environment in which coauthorship is valued. The third Part explores the very different culture in legal academe. I begin the Part by exploring the disconnect between the individualistic culture of law schools and the collaborative culture of the legal community at large. I then discuss my study of legal coauthorship, which demonstrates that law professors collaborate at a rate much lower than their mathematical colleagues. Next, I explore the benefits that law professors and their students could gain from collaboration. The Article concludes with a consideration of some proposals to help turn the law school culture into one where collaboration and coauthorship are respected and encouraged

Random Graphs: From Paul Erdős to the Internet

Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of large real world networks which grow unpredictably, including the Internet, World Wide Web (WWW), peer-to-peer, social, neural and metabolic networks.https://egrove.olemiss.edu/math_dalrymple/1006/thumbnail.jp

Math Quiz on the Radio

What word, often spelled with an umlaut, is used to identify a point on a two-dimensional graph? Many of you probably already figured out the answer is coordinate. But that\u27s because you are sitting comfortably in your dorm room rather than being on a stage with bright lights in front of a few hundred people being recorded for national broadcast on public radio. [excerpt

Non-three-colorable common graphs exist

A graph H is called common if the total number of copies of H in every graph and its complement asymptotically minimizes for random graphs. A former conjecture of Burr and Rosta, extending a conjecture of Erdos asserted that every graph is common. Thomason disproved both conjectures by showing that the complete graph of order four is not common. It is now known that in fact the common graphs are very rare. Answering a question of Sidorenko and of Jagger, Stovicek and Thomason from 1996 we show that the 5-wheel is common. This provides the first example of a common graph that is not three-colorable.Comment: 9 page

Thresholds in Random Motif Graphs

We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding an instance of a fixed graph $H$ on each of the copies of $H$ in the complete graph on $n$ vertices, independently with probability $p$. We establish that every monotone property has a threshold in this model, and determine the thresholds for connectivity, Hamiltonicity, the existence of a perfect matching, and subgraph appearance. Moreover, in the first three cases we give the analogous hitting time results; with high probability, the first graph in the random motif graph process that has minimum degree one (or two) is connected and contains a perfect matching (or Hamiltonian respectively).Comment: 19 page

Topology of random simplicial complexes: a survey

This expository article is based on a lecture from the Stanford Symposium on Algebraic Topology: Application and New Directions, held in honor of Gunnar Carlsson, Ralph Cohen, and Ib Madsen.Comment: After revisions, now 21 pages, 5 figure