I first heard an economist talking about this fascinating concept at Al’s market design coffee. These days I found a student in my coauthor’s former PhD advisor’s group has Erdős number 3—and he’s a first-year PhD.
orz.
The Erdős number describes the “collaborative distance” between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers.
How it has started:
Paul Erdős (1913–1996) was an influential Hungarian mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues—over 500—working on solutions to outstanding mathematical problems.
Erdős spent most of his career with no permanent home or job. He traveled with everything he owned in two suitcases, and would visit mathematicians he wanted to collaborate with, often unexpectedly, and expect to stay with them.
And as many excellent ideas starts with a joke:
The idea of the Erdős number was originally created by the mathematician’s friends as a tribute to his enormous output. Later it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems.
Several projects are devoted to studying connectivity among researchers, using the Erdős number as a proxy. For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.
As of 2022, all Fields Medalists and Nobel Price laureates have a finite Erdős number. It seems that Erdős number is strongly correlated with success in academia.
However, notice that, the lowest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration.
Question at the end: as time goes by, does Erdős number converge to a certain finite distribution or simply everyone’s goes to infinity?
One more wonder, what the Erdős number dynamic appears for surgeons’ network—measured in terms of dinner banquet attended?
reference
Wikipedia contributors. (2024, August 30). Erdős number. In Wikipedia, The Free Encyclopedia. Retrieved 14:22, September 19, 2024, from https://en.wikipedia.org/w/index.php?title=Erd%C5%91s_number&oldid=1243138427