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|issue = 3

|journal = [[The Mathematical Intelligencer]]

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~~|mr = 1709679~~

|pages = 51–63

|title = Famous trails to Paul Erdős

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|archive-url = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf

|archive-date = 2015-09-24

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}} Original Spanish version in ''Rev. Acad. Colombiana Cienc. Exact. Fís. Natur.'' '''23''' (89) 563–582, 1999~~, {{MR|1744115}}~~.</ref>菲尔兹奖得主Fields Medalists的埃尔德什中位数是3。只有7,097名（拥有合作经历的数学家中约5％）的埃尔德什数为2或更低。随着时间的流逝，低埃尔德什数的数学家因死亡而无法进行协作，所能达到的最小埃尔德什数必然会增加。历史人物仍可能一直具有较低的埃尔德什数。例如，印度著名数学家Srinivasa Ramanujan的埃尔德什数仅为3（通过与G. H. Hardy合作，其埃尔德什数为2），尽管Ramanujan去世时保罗·埃尔德什只有7岁。<ref name="paths"/> <ref name=":0" />

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}} Original Spanish version in ''Rev. Acad. Colombiana Cienc. Exact. Fís. Natur.'' '''23''' (89) 563–582, 1999.</ref>菲尔兹奖得主Fields Medalists的埃尔德什中位数是3。只有7,097名（拥有合作经历的数学家中约5％）的埃尔德什数为2或更低。随着时间的流逝，低埃尔德什数的数学家因死亡而无法进行协作，所能达到的最小埃尔德什数必然会增加。历史人物仍可能一直具有较低的埃尔德什数。例如，印度著名数学家Srinivasa Ramanujan的埃尔德什数仅为3（通过与G. H. Hardy合作，其埃尔德什数为2），尽管Ramanujan去世时保罗·埃尔德什只有7岁。<ref name="paths"/> <ref name=":0" />

== 数学的定义与应用 ==

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埃尔德什数很可能最早由卡斯珀·高夫曼Casper Goffman定义，他自己的埃尔德什数为2。<ref name="Erdős Number Project File Erdos2"/> Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled "''And what is your Erdős number?''"<ref>{{cite journal|last=Goffman|first=Casper|title=And what is your Erdős number?|journal=[[American Mathematical Monthly]]|volume=76|year=1969|doi=10.2307/2317868|page=791~~|jstor=2317868~~|issue=7}}</ref>高夫曼在1969年发表的一篇文章“您的埃尔德什数是多少”中表示了他对埃尔德什多产合作的看法，另请参阅迈克尔·哥伦布Michael Golomb在讣告中的一些评论。<ref>{{Cite web|url=https://www.math.purdue.edu/about/purview/fall96/paul-erdos.html|title=Paul Erdös at Purdue|website=www.math.purdue.edu}}</ref>

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埃尔德什数很可能最早由卡斯珀·高夫曼Casper Goffman定义，他自己的埃尔德什数为2。<ref name="Erdős Number Project File Erdos2"/> Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled "''And what is your Erdős number?''"<ref>{{cite journal|last=Goffman|first=Casper|title=And what is your Erdős number?|journal=[[American Mathematical Monthly]]|volume=76|year=1969|doi=10.2307/2317868|page=791|issue=7}}</ref>高夫曼在1969年发表的一篇文章“您的埃尔德什数是多少”中表示了他对埃尔德什多产合作的看法，另请参阅迈克尔·哥伦布Michael Golomb在讣告中的一些评论。<ref>{{Cite web|url=https://www.math.purdue.edu/about/purview/fall96/paul-erdos.html|title=Paul Erdös at Purdue|website=www.math.purdue.edu}}</ref>

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=== 语言学领域 ===

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罗马尼亚数学家和计算语言学家Solomon Marcus在1957年与埃尔德什合作了《 Acta Mathematica Hungarica》中的一篇论文，因此他的埃尔德什数为1。<ref>{{cite journal|first1=Paul|last1= Erdős |author1-link=Paul Erdős|first2= Solomon|last2= Marcus|author2-link=Solomon Marcus| year=1957|title= Sur la décomposition de l'espace euclidien en ensembles homogènes |trans-title= On the decomposition of the Euclidean space into homogeneous sets|journal=[[Acta Mathematica Hungarica]]|volume=8|issue= 3–4 |pages=443–452~~|mr=0095456~~|doi=10.1007/BF02020326 }}</ref>

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罗马尼亚数学家和计算语言学家Solomon Marcus在1957年与埃尔德什合作了《 Acta Mathematica Hungarica》中的一篇论文，因此他的埃尔德什数为1。<ref>{{cite journal|first1=Paul|last1= Erdős |author1-link=Paul Erdős|first2= Solomon|last2= Marcus|author2-link=Solomon Marcus| year=1957|title= Sur la décomposition de l'espace euclidien en ensembles homogènes |trans-title= On the decomposition of the Euclidean space into homogeneous sets|journal=[[Acta Mathematica Hungarica]]|volume=8|issue= 3–4 |pages=443–452|doi=10.1007/BF02020326 }}</ref>

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多年以来，埃尔德什数在数学家之间一直盛行。在千年之交的所有在职数学家中，都伴随着一个有限埃尔德什数，数字范围最大为15，中位数为5，平均值为4.65。<ref name="Erdős Number Project"/>几乎每个具有有限埃尔德什数的人其数字都小于8。由于当今科学领域跨学科合作的频率很高，因此许多其他科学领域的大量非数学家也具有有限的埃尔德什数。<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>例如，政治学家Steven Brams的埃尔德什数为2。在生物医学研究中，统计学家通常是出版物的作者，许多统计学家可以通过John Tukey（其埃尔德什数为2）与埃尔德什链接。同样，著名的遗传学家Eric Lander和数学家Daniel Kleitman在论文上进行了合作，<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|publisher=[[Massachusetts Institute of Technology]]}}</ref>由于Kleitman的埃尔德什数为1，<ref>

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{{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>因此可以通过Lander及其众多合作者将遗传学和基因组学领域的大部分联系起来。另外，与Gustavus Simmons的合作为密码研究界内的埃尔德什数打开了大门，许多语言学家拥有有限的埃尔德什数，这许多是由于与Noam Chomsky（埃尔德什数为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（埃尔德什数为3）等著名学者的合作产生，<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>类似有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>或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}}</ref>。同时与艺术领域也有联系。<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | last2=Wilson | first2=Robin J. | 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>

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{{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|url=http://www.math-inst.hu/~p_erdos/1971-07.pdf}}</ref>因此可以通过Lander及其众多合作者将遗传学和基因组学领域的大部分联系起来。另外，与Gustavus Simmons的合作为密码研究界内的埃尔德什数打开了大门，许多语言学家拥有有限的埃尔德什数，这许多是由于与Noam Chomsky（埃尔德什数为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（埃尔德什数为3）等著名学者的合作产生，<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>类似有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>或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}}</ref>。同时与艺术领域也有联系。<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | last2=Wilson | first2=Robin J. | 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>

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有人提出：“对于独立研究人员而言，诸如埃尔德什数之类的量度可以捕获网络的结构特性，而''h''指数则可以捕获出版物的引文影响。” 并且“可以很容易地使人相信，共同作者网络中的排名应该同时考虑到两种方法，以产生现实且可接受的排名。”<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]'', IBM Research Report R109002, February 2009; also appeared as {{Cite journal | 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 = Outcome aware ranking in interaction networks | pages = 229–238| year = 2010 ~~| isbn = 978-1-4503-0099-5~~| journal = Proceedings of the 19th ACM International Conference on Information and Knowledge Management (CIKM '10)| url = http://www.cse.iitd.ernet.in/%7Epandit/cikm_camera_ready.pdf}}</ref>

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有人提出：“对于独立研究人员而言，诸如埃尔德什数之类的量度可以捕获网络的结构特性，而''h''指数则可以捕获出版物的引文影响。” 并且“可以很容易地使人相信，共同作者网络中的排名应该同时考虑到两种方法，以产生现实且可接受的排名。”<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]'', IBM Research Report R109002, February 2009; also appeared as {{Cite journal | 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 = Outcome aware ranking in interaction networks | pages = 229–238| year = 2010 | journal = Proceedings of the 19th ACM International Conference on Information and Knowledge Management (CIKM '10)| url = http://www.cse.iitd.ernet.in/%7Epandit/cikm_camera_ready.pdf}}</ref>

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2004年，数学家埃尔德什数为4的William Tozier在eBay上拍卖了合著者，因此为买家提供了埃尔德什数为5的机会。一位西班牙数学家发布了1031美元的中标价格。不过他并不打算付款，而只是进行出价以阻止他认为是嘲弄的行为。<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>

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2004年，数学家埃尔德什数为4的William Tozier在eBay上拍卖了合著者，因此为买家提供了埃尔德什数为5的机会。一位西班牙数学家发布了1031美元的中标价格。不过他并不打算付款，而只是进行出价以阻止他认为是嘲弄的行为。<ref>Clifford A. Pickover: ''A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality''. Wiley, 2011, S. 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 }}</ref>

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