Editing Erdős number (section)

==Impact==
[[File:Paul Erdos with Terence Tao.jpg|thumb|Paul Erdős in 1985 at the [[University of Adelaide]] teaching [[Terence Tao]], who was then 10 years old. Tao became a math professor at [[University of California, Los Angeles]], received the [[Fields Medal]] in 2006, and was elected a [[Fellow of the Royal Society]] in 2007. His Erdős number is 2.]]
Erdős numbers have been a part of the [[folklore]] of mathematicians throughout the world for many years. Among all working mathematicians at the turn of the millennium who have a finite Erdős number, the numbers range up to 15, the median is 5, and the mean is 4.65;<ref name="Erdős Number Project"/> almost everyone with a finite Erdős number has a number less than 8.

Due to the very high frequency of interdisciplinary collaboration in science today, very large numbers of non-mathematicians in many other fields of science also have finite Erdős numbers.<ref>{{cite web |url=http://www.oakland.edu/enp/erdpaths/ |title=Some Famous People with Finite Erdős Numbers | first=Jerry | last=Grossman |access-date=1 February 2011}}</ref> For example, political scientist [[Steven Brams]] has an Erdős number of 2. In biomedical research, it is common for statisticians to be among the authors of publications, and many statisticians can be linked to Erdős via [[Persi Diaconis]] or [[Paul Deheuvels]], who have Erdős numbers of 1, or [[John Tukey]], who has an Erdős number of 2. Similarly, the prominent geneticist [[Eric Lander]] and the mathematician [[Daniel Kleitman]] have collaborated on papers,<ref>{{cite journal | pmid = 10582576 | doi=10.1089/106652799318364 | volume=6 | title=A dictionary-based approach for gene annotation | year=1999 | journal=J Comput Biol | pages=419–30 | last1 = Pachter | first1 = L | last2 = Batzoglou | first2 = S | last3 = Spitkovsky | first3 = VI | last4 = Banks | first4 = E | last5 = Lander | first5 = ES | last6 = Kleitman | first6 = DJ | last7 = Berger | first7 = B| issue=3–4 }}</ref><ref>{{cite web|url=http://www-math.mit.edu/~djk/list.html|title=Publications Since 1980 more or less|first=Daniel|last=Kleitman|author-link=Daniel Kleitman|publisher=[[Massachusetts Institute of Technology]]}}</ref> and since Kleitman has an Erdős number of 1,<ref>
{{cite journal | last1 = Erdős | first1 = Paul | author1-link = Paul Erdős |author2-link=Daniel Kleitman|last2=Kleitman|first2=Daniel  | title = On Collections of Subsets Containing No 4-Member Boolean Algebra | journal = [[Proceedings of the American Mathematical Society]] | volume = 28 | issue = 1 | pages = 87–90 |date=April 1971 | doi = 10.2307/2037762 | jstor = 2037762|url=http://www.math-inst.hu/~p_erdos/1971-07.pdf}}</ref> a large fraction of the genetics and genomics community can be linked via Lander and his numerous collaborators. Similarly, collaboration with [[Gustavus Simmons]] opened the door for 
[[List of people by Erdős number|Erdős numbers]] within the [[cryptographic]] research community, and many [[linguistics|linguists]] have finite Erdős numbers, many due to chains of collaboration with such notable scholars as [[Noam Chomsky]] (Erdős number 4),<ref>{{cite web |last=von Fintel |first=Kai |title=My Erdös Number is 8 |url=http://semantics-online.org/2004/01/my-erds-number-is-8 |publisher=Semantics, Inc. |date=2004 |archive-url=https://web.archive.org/web/20060823085712/http://semantics-online.org/2004/01/my-erds-number-is-8 |archive-date=23 August 2006}}</ref> [[William Labov]] (3),<ref>{{cite web|url=http://www.ling.upenn.edu/~dinkin/ |title=Aaron Dinkin has a web site? |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref> [[Mark Liberman]] (3),<ref>{{cite web|url=http://www.ling.upenn.edu/~myl/ |title=Mark Liberman's Home Page |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref> [[Geoffrey Pullum]] (3),<ref>{{cite web|url=http://www.stanford.edu/~cgpotts/miscellany.html |title=Christopher Potts: Miscellany |publisher=Stanford.edu |access-date=2010-08-29}}</ref> or [[Ivan Sag]] (4).<ref>{{cite web |url=http://lingo.stanford.edu/sag/erdos.html |title=Bob's Erdős Number |publisher=Lingo.stanford.edu |access-date=2010-08-29 |archive-date=2016-04-05 |archive-url=https://web.archive.org/web/20160405131402/http://lingo.stanford.edu/sag/erdos.html |url-status=dead }}</ref> There are also connections with [[arts]] fields.<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | author-link1=Jonathan Bowen | last2=Wilson | first2=Robin J. | author-link2=Robin Wilson (mathematician) | editor1-first=Stuart|editor1-last=Dunn|editor2-first=Jonathan P.|editor2-last=Bowen|editor3-first= Kia|editor3-last=Ng | title=Visualising Virtual Communities: From Erdős to the Arts | url=http://ewic.bcs.org/content/ConWebDoc/46141 | book-title= EVA London 2012: Electronic Visualisation and the Arts | publisher=[[British Computer Society]] | series= Electronic Workshops in Computing | pages = 238–244 |date=10–12 July 2012}}</ref>

According to Alex Lopez-Ortiz, all the [[Fields Medal|Fields]] and [[Nevanlinna Prize|Nevanlinna prize]] winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.

Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either [[Antoine Lavoisier]] (born 1743, Erdős number 13), [[Richard Dedekind]] (born 1831, Erdős number 7), or [[Ferdinand Georg Frobenius]] (born 1849, Erdős number 3), depending on the standard of publication eligibility.<ref>{{cite web|url=http://www.oakland.edu/enp/erdpaths |title=Paths to Erdös - The Erdös Number Project- Oakland University|work=oakland.edu}}</ref>

Martin Tompa<ref>{{cite journal|last=Tompa|first=Martin|title=Figures of merit|journal=ACM SIGACT News|volume=20|issue=1|pages=62–71|year=1989|doi=10.1145/65780.65782|s2cid=34277380}} {{cite journal|last=Tompa|first= Martin|title=Figures of merit: the sequel|journal=ACM SIGACT News|volume=21|issue=4|pages=78–81|year=1990|doi=10.1145/101371.101376|s2cid= 14144008}}</ref> proposed a [[directed graph]] version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the ''monotone Erdős number'' of an author to be the length of a [[longest path]] from Erdős to the author in this directed graph. He finds a path of this type of length 12.

Also, [[Michael Barr (mathematician)|Michael Barr]] suggests "rational Erdős numbers", generalizing the idea that a person who has written ''p'' joint papers with Erdős should be assigned Erdős number 1/''p''.<ref>{{cite web|last=Barr|first=Michael|title=Rational Erdős numbers|url=https://drive.google.com/file/d/1F325pmlIvqOpp7PmAQK5lm7lZHWIBP-U/view}}</ref> From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind)—with one edge between two mathematicians for ''each'' joint paper they have produced—form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are.

It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the [[h-index|''h''-index]] captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."<ref name=Dixit>Kashyap Dixit, S Kameshwaran, Sameep Mehta, Vinayaka Pandit, N Viswanadham, ''[http://domino.research.ibm.com/library/cyberdig.nsf/papers/2B600A90C54E51B18525755800283D37/$File/RR_ranking.pdf Towards simultaneously exploiting structure and outcomes in interaction networks for node ranking] {{Webarchive|url=https://web.archive.org/web/20111110144241/http://domino.research.ibm.com/library/cyberdig.nsf/papers/2B600A90C54E51B18525755800283D37/$File/RR_ranking.pdf |date=2011-11-10 }}'', IBM Research Report R109002, February 2009; also appeared as {{Cite book | doi = 10.1145/1871437.1871470 | last1 = Kameshwaran | first1 = S. | last2 = Pandit | first2 = V. | last3 = Mehta | first3 = S. | last4 = Viswanadham | first4 = N. | last5 = Dixit | first5 = K. | title = Proceedings of the 19th ACM international conference on Information and knowledge management | chapter = Outcome aware ranking in interaction networks | pages = 229–238 | year = 2010 | isbn = 978-1-4503-0099-5 | s2cid = 16370569 | chapter-url = https://eprints.exchange.isb.edu//id/eprint/254/ }}</ref>

In 2004 William Tozier, a mathematician with an Erdős number of 4 auctioned off a co-authorship on [[eBay]], hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who refused to pay and only placed the bid to stop what he considered a mockery.<ref>Clifford A. Pickover: ''A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality''. Wiley, 2011, {{ISBN|9781118046074}}, S. 33 ({{Google books|03CVDsZSBIcC|excerpt|page=33}})</ref><ref>{{cite journal | last1 = Klarreich | first1 = Erica | year = 2004 | title = Theorem for Sale | journal = Science News | volume = 165 | issue = 24| pages = 376–377 | doi = 10.2307/4015267 | jstor=4015267}}</ref>