Editing Erdős number (section)

== Overview ==
{{See also|Paul Erdős}}
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&nbsp;— more than 500&nbsp;— working on solutions to outstanding mathematical problems.<ref name="newman2001">{{cite journal|last=Newman|first=Mark E. J.|author-link=Mark Newman|title=The structure of scientific collaboration networks|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]| year=2001| doi=10.1073/pnas.021544898| volume=98|issue=2|pages=404–409|pmid=11149952|pmc=14598|doi-access=free}}</ref> He published more papers during his lifetime (at least 1,525<ref>{{cite web |url=http://www.oakland.edu/enp/pubinfo/ |title=Publications of Paul Erdős | first=Jerry | last=Grossman |access-date=1 Feb 2011}}</ref>) than any other mathematician in history.<ref name="newman2001"/> ([[Leonhard Euler]] published more total pages of mathematics but fewer separate papers: about 800.)<ref>{{cite web| url=https://www.math.dartmouth.edu/~euler/FAQ.html| work=The Euler Archive| title=Frequently Asked Questions| publisher=Dartmouth College}}</ref> 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 with whom he wanted to collaborate, often unexpectedly, and expect to stay with them.<ref>{{cite journal| last=Cofield | first=Calla | title=An Arbitrary Number of Years Since Mathematician Paul Erdős's Birth | journal=Scientific American | date=26 March 2013 | url=https://www.scientificamerican.com/article/an-arbitrary-number-of-years-since-mathematicians-birth/ }}</ref><ref>{{cite news| last=Krauthammer | first=Charles | title=Paul Erdos |newspaper=The Washington Post|format=[[PostScript]] file|url=http://theory.cs.uchicago.edu/erdos/wash-post2.ps|date=27 September 1996|page=A25}} [https://www.solipsys.co.uk/new/PaulErdos.html File available as HTML via Solipsys]</ref><ref>{{Cite book|title=Math and mathematicians: the history of math discoveries around the world|last=Bruno|first=Leonard C. |author-link1=Leonard C. Bruno |year=2003|orig-year=1999|publisher=U X L|others=Baker, Lawrence W.|isbn=978-0787638139|location=Detroit, Mich.|oclc=41497065|url=https://archive.org/details/mathmathematicia00brun|url-access=registration}}</ref>

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.<ref name="Erdős Number Project">{{cite web|title=Facts about Erdös Numbers and the Collaboration Graph|url=https://oakland.edu/enp/trivia/|publisher=Oakland University}}</ref> For example, Erdős [[collaboration graph]]s can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.<ref>{{cite web|url=http://www.oakland.edu/enp/trivia/|title=Facts about Erdös Numbers and the Collaboration Graph|work=Erdös Number Project|publisher=Oakland University}}</ref>

Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers, ''i.e.'', high proximity).<ref name="trails">{{cite journal
 |last1       = De Castro
 |first1      = Rodrigo
 |last2       = Grossman
 |first2      = Jerrold W.
 |doi         = 10.1007/BF03025416
 |issue       = 3
 |journal     = [[The Mathematical Intelligencer]]
 |mr          = 1709679
 |pages       = 51–63
 |title       = Famous trails to Paul Erdős
 |url         = http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
 |volume      = 21
 |year        = 1999
 |s2cid = 120046886
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
 |archive-date = 2015-09-24
}} Original Spanish version in ''Rev. Acad. Colombiana Cienc. Exact. Fís. Natur.'' '''23''' (89) 563–582, 1999, {{MR|1744115}}.</ref> The median Erdős number of [[Fields Medal]]ists is 3. Only 7,097 (about 5% of mathematicians with a collaboration path) have an Erdős number of 2 or lower.<ref name="paths"/> As time passes, the lowest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration. Still, historical figures can have low Erdős numbers. For example, renowned Indian mathematician [[Srinivasa Ramanujan]] has an Erdős number of only 3 (through [[G. H. Hardy]], Erdős number 2), even though Paul Erdős was only 7 years old when Ramanujan died.<ref name="Collaboration distance" />