1,592
个编辑
更改
跳到导航
跳到搜索
Moved page from wikipedia:en:Erdős number (history)
此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。
{{Short description|Closeness of someone's association with mathematician Paul Erdős}}
[[File:Erdos budapest fall 1992.jpg|thumb|upright|[[Paul Erdős]] in 1992]]
[[Paul Erdős in 1992]]
[保罗 · 爱德1992]
The '''Erdős number''' ({{IPA-hu|ˈɛrdøːʃ|lang}}) describes the "collaborative distance" between mathematician {{nobr|[[Paul Erdős]]}} and another person, as measured by authorship of [[List of important publications in mathematics|mathematical papers]]. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
The Erdős number () describes the "collaborative distance" between mathematician and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
Erd 的数字()描述了数学家和另一个人之间的“协作距离” ，这是通过数学论文的作者来衡量的。同样的原则也适用于其他领域，在这些领域中，某个特定的个人与众多的同龄人进行了合作。
== Overview ==
Paul Erdős (1913–1996) was an influential [[Hungarian people|Hungarian]] mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems.<ref name="newman2001">{{cite journal|last=Newman|first=Mark E. J.|authorlink=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}}</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 |accessdate=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 a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world.
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, working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least 1,525) than any other mathematician in history. Erdős spent a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world.
保罗 · 厄德(1913-1996)是一位颇有影响力的匈牙利数学家，他晚年花了大量时间与许多同事一起撰写论文，致力于解决杰出的数学问题。他一生发表的论文(至少1525篇)比历史上任何一位数学家都多。尔德晚年的大部分时间都生活在一个手提箱里，拜访了他在世界各地的500多名合作者。
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|url=http://www.oakland.edu/enp|title=Erdös Number Project|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>
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.
厄尔德数的概念最初是由这位数学家的朋友为了向他的巨大成就致敬而创立的。后来，它作为研究数学家如何合作找到未解决问题的答案的工具而获得了突出地位。几个项目致力于研究研究人员之间的连通性，使用 erd 数字作为一个代理。例如，erd 的协作图可以告诉我们作者是如何聚类的，每篇论文的协作作者数量是如何随时间演变的，或者新的理论是如何传播的。
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers.<ref name="trails">{{cite journal
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers.<ref name="trails">{{cite journal
一些研究表明，一流的数学家的 erd 数字往往特别低
|last1 = De Castro
|last1 = De Castro
1 = De Castro
|first1 = Rodrigo
|first1 = Rodrigo
1 = Rodrigo
|last2 = Grossman
|last2 = Grossman
2 = Grossman
|first2 = Jerrold W.
|first2 = Jerrold W.
2 = Jerrold w.
|doi = 10.1007/BF03025416
|doi = 10.1007/BF03025416
| doi = 10.1007/BF03025416
|issue = 3
|issue = 3
第三期
|journal = [[The Mathematical Intelligencer]]
|journal = The Mathematical Intelligencer
2012年3月24日 | 日志 = 数学通讯者
|mr = 1709679
|mr = 1709679
1709679先生
|pages = 51–63
|pages = 51–63
| 页数 = 51-63
|title = Famous trails to Paul Erdős
|title = Famous trails to Paul Erdős
保罗 · 厄德斯著名的小径
|url = http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
|url = http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
Http://www.oakland.edu/upload/docs/erdos%20number%20project/trails.pdf
|volume = 21
|volume = 21
21
|year = 1999
|year = 1999
1999年
|url-status = dead
|url-status = dead
地位 = 死亡
|archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
|archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
2012年3月24日 | archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/erdos%20number%20project/trails.pdf
|archivedate = 2015-09-24
|archivedate = 2015-09-24
| archivedate = 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 Medalists]] 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 smallest 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=":0" />
}} Original Spanish version in Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. 23 (89) 563–582, 1999, .</ref> The median Erdős number of Fields Medalists is 3. Only 7,097 (about 5% of mathematicians with a collaboration path) have an Erdős number of 2 or lower. As time passes, the smallest 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.
最初的西班牙语版本。Acad.哥伦比亚科伦坡。没错。Fís.女名女子名。23(89)563-582,1999.只有7,097人(大约5% 的数学家拥有协作路径)的 erd 数为2或更少。随着时间的推移，最小的 erd 数量仍然可以达到必然会增加，因为低 erd 数量的数学家死亡，变得无法进行合作。尽管如此，历史人物的 erd 值可能会比较低。例如，著名的印度数学家拉马努金的 erd 数值只有3(通过 g. h. Hardy 的 erd 数值2) ，尽管当 Ramanujan 去世时 Paul erd s 只有7岁。
==Definition and application in mathematics==
[[File:Erdosnumber.png|thumb|If [[Alice and Bob|Alice]] collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Alice is given an Erdős number of 1 and Bob is given an Erdős number of 2, as he is two steps from Erdős.]]
Alice collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Alice is given an Erdős number of 1 and Bob is given an Erdős number of 2, as he is two steps from Erdős.]]
爱丽丝和保罗在一篇论文上合作，鲍勃在另一篇论文上合作，但是鲍勃从来没有和厄尔德本人合作过，然后爱丽丝得到厄尔德数的1，鲍勃得到厄尔德数的2，因为他离 Erdős 只有两步
To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is {{math|''k'' + 1}} where {{math|''k''}} is the lowest Erdős number of any coauthor. The [[American Mathematical Society]] provides a free online tool to determine the Erdős number of every mathematical author listed in the ''[[Mathematical Reviews]]'' catalogue.<ref name=":0">{{cite web|url=http://www.ams.org/mathscinet/collaborationDistance.html|title=
To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is where is the lowest Erdős number of any coauthor. The American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.<ref name=":0">{{cite web|url=http://www.ams.org/mathscinet/collaborationDistance.html|title=
为了得到 erd 的编号，某人必须是一篇研究论文的合著者，而另一个人的 erd 编号是有限的。Paul erd s 的 erd 数为零。任何其他人的 erd 数是任何合著者的最小 erd 数。美国数学学会提供了一个免费的在线工具，用来确定《数学评论》目录中列出的每一位数学作者的 erd 编号。{ cite web | url = http://www.ams.org/mathscinet/collaborationdistance.html|title=
Collaboration Distance|work=[[MathSciNet]]|publisher=American Mathematical Society}}</ref>
Collaboration Distance|work=MathSciNet|publisher=American Mathematical Society}}</ref>
协作距离 | work = MathSciNet | publisher = American Mathematical Society } </ref >
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators;<ref name="Erdős Number Project"/> these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (11,009 people as of 2015<ref name="Erdős Number Project File Erdos2">[https://files.oakland.edu/users/grossman/enp/Erdos2.html Erdos2], Version 2015, July 14, 2015.</ref>), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of [[infinity]] (or an [[defined and undefined|undefined]] one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators;), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.
尔德在他的一生中写了大约1500篇数学文章，大部分是合著的。他有511个直接合作者;) ，那些与 erd 数为2的人(但不是 erd 数为1的人)合作的 erd 数为3，等等。如果一个人没有连接到 Erdős 的这样的合著者链，那么 erd 的数量就是无穷(或者一个未定义的无穷)。自从 Paul erd 死后，一个新的研究者所能得到的最低 erd 数是2。
There is room for ambiguity over what constitutes a link between two authors. The American Mathematical Society collaboration distance calculator uses data from ''Mathematical Reviews'', which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications{{citation needed|date=August 2015}}. The Erdős Number Project web site says:
There is room for ambiguity over what constitutes a link between two authors. The American Mathematical Society collaboration distance calculator uses data from Mathematical Reviews, which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications. The Erdős Number Project web site says:
关于两位作者之间的联系，还有模棱两可的余地。美国数学学会(American Mathematical Society)协作距离计算器使用的数据来自《数学评论》(Mathematical Reviews) ，该杂志包括大多数数学期刊，但仅以有限的方式涵盖其他学科，还包括一些非研究性出版物。爱德华的数字项目网站上说:
{{quote|... Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted,...}}
but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.<ref>Grossman ''et al.'' "[http://www.oakland.edu/?id=9569&sid=243#en2k Erdős numbers of the second kind]," in ''Facts about Erdős Numbers and the Collaboration Graph''. [http://www.oakland.edu/enp The Erdős Number Project], [[Oakland University]], USA. Retrieved July 25, 2009.</ref>
but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.
但不包括基础教科书、联合编辑、讣告等非研究性出版物。“第二类 erd 数”将 erd 数的分配限制在只有两个合作者的论文上。
The Erdős number was most likely first defined in print by Casper Goffman, an [[Mathematical analysis|analyst]] whose own Erdős number is 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> See also some comments in an obituary by Michael Golomb.<ref>{{cite web|url=http://www.math.purdue.edu/about/purview/fall96/paul-erdos.html|title= Erdős'obituary by Michael Golomb}}</ref>
The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 2. See also some comments in an obituary by Michael Golomb.
Erd 的数字很可能是由 Casper Goffman 首先在印刷品中定义的，他自己的 erd 数字是2。参见 Michael Golomb 的讣告中的一些评论。
The median Erdős number among [[Fields medal]]ists is as low as 3.<ref name="paths"/> Fields medalists with Erdős number 2 include [[Atle Selberg]], [[Kunihiko Kodaira]], [[Klaus Roth]], [[Alan Baker (mathematician)|Alan Baker]], [[Enrico Bombieri]], [[David Mumford]], [[Charles Fefferman]], [[William Thurston]], [[Shing-Tung Yau]], [[Jean Bourgain]], [[Richard Borcherds]], [[Manjul Bhargava]], [[Jean-Pierre Serre]] and [[Terence Tao]]. There are no Fields medalists with Erdős number 1;<ref name="project">{{cite web|url=http://www.oakland.edu/enp/erdpaths/|title=Paths to Erdös|work=The Erdös Number Project|publisher=Oakland University}}</ref> however, [[Endre Szemerédi]] is an [[Abel Prize]] Laureate with Erdős number 1.<ref name="trails"/>
The median Erdős number among Fields medalists is as low as 3. however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.
菲尔兹奖获得者的中位数 erd 只有3。然而，恩德雷 · 塞梅雷迪却是艾伯尔奖的获奖者，而艾伯尔奖则排在第一位。
==Most frequent Erdős collaborators==
While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).<ref>Grossman, Jerry, [https://files.oakland.edu/users/grossman/enp/Erdos0p.html Erdos0p], Version 2010, ''[http://www.oakland.edu/enp The Erdős Number Project]'', [[Oakland University]], US, October 20, 2010.</ref>
While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).
虽然 erd 与数百名合著者合作，但也有一些人与他合著了几十篇论文。以下是与 erd s 合著最频繁的十位人士及他们与 erd s 合著的论文数目(即。他们的合作次数)。
{| class="wikitable sortable"
{| class="wikitable sortable"
{ | class = “ wikitable sortable”
|-
|-
|-
! Co-author !! Number of <br>collaborations
! Co-author !! Number of <br>collaborations
!合著者! ！合作次数
|-
|-
|-
| [[András Sárközy]] || 62
| András Sárközy || 62
| András Sárközy || 62
|-
|-
|-
| [[András Hajnal]] || 56
| András Hajnal || 56
| András Hajnal || 56
|-
|-
|-
| [[Ralph Faudree]] || 50
| Ralph Faudree || 50
拉尔夫 · 法德里 | 50
|-
|-
|-
| [[Richard Schelp]] || 42
| Richard Schelp || 42
| Richard Schelp | | 42
|-
|-
|-
| [[Cecil C. Rousseau]] || 35
| Cecil C. Rousseau || 35
塞西尔 · c · 卢梭 | 35
|-
|-
|-
| [[Vera T. Sós]] || 35
| Vera T. Sós || 35
| Vera T. Sós || 35
|-
|-
|-
| [[Alfréd Rényi]] || 32
| Alfréd Rényi || 32
| Alfréd Rényi || 32
|-
|-
|-
| [[Pál Turán]] || 30
| Pál Turán || 30
| Pál Turán || 30
|-
|-
|-
| [[Endre Szemerédi]] || 29
| Endre Szemerédi || 29
| Endre Szemerédi || 29
|-
|-
|-
| [[Ronald Graham]] || 28
| Ronald Graham || 28
罗纳德 · 格雷厄姆28
|}
|}
|}
==Related fields==
{{As of|2016}}, all [[Fields Medal]]ists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13.<ref>{{Cite web|url=http://wwwp.oakland.edu/enp/trivia/|title=Facts about Erdös Numbers and the Collaboration Graph - The Erdös Number Project- Oakland University|website=wwwp.oakland.edu|access-date=2016-10-27}}</ref> The table below summarizes the Erdős number statistics for [[Nobel Prize|Nobel prize]] laureates in Physics, Chemistry, Medicine and Economics.<ref>{{Cite journal|last=López de Prado|first=Marcos|title=Mathematics and Economics: A reality check|url=http://www.iijournals.com/doi/pdfplus/10.3905/jpm.2016.43.1.005|journal=The Journal of Portfolio Management|volume=43|issue=1|pages=5–8|doi=10.3905/jpm.2016.43.1.005|year=2016}}</ref> The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average and median Erdős numbers among those laureates.
, all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13. The table below summarizes the Erdős number statistics for Nobel prize laureates in Physics, Chemistry, Medicine and Economics. The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average and median Erdős numbers among those laureates.
所有田径奖获得者都有一个有限的 erd s 数，数值范围在2到6之间，中位数为3。相比之下，所有数学家的 erd 数的中位数(有限 erd 数)是5，极值是13。下表总结了 erd 的数字统计诺贝尔奖获得者在物理，化学，医学和经济学。第一栏计算获奖者的数量。第二列用有限的 erd 数计算赢家的数目。第三列是有限 erd 数目的获胜者的百分比。剩下的柱子报告的最低，最高，平均和中位数 erd 的数字在这些获奖者。
{| class="wikitable sortable"
{| class="wikitable sortable"
{ | class = “ wikitable sortable”
|+ Statistics on Mathematical Collaboration, 1903-2016
|+ Statistics on Mathematical Collaboration, 1903-2016
| + 数学合作统计，1903-2016
!
!
!
! #Laureates
! #Laureates
!* 获奖者
! #Erdős
! #Erdős
!#Erdős
! %Erdős
! %Erdős
!%Erdős
! Min
! Min
!最小
! Max
! Max
!麦克斯
! Average
! Average
!平均数
! Median
! Median
!中位数
|-
|-
|-
|Fields Medal
|Fields Medal
菲尔兹奖
|56
|56
|56
|56
|56
|56
|100.0%
|100.0%
|100.0%
|2
|2
|2
|6
|6
|6
|3.36
|3.36
|3.36
|3
|3
|3
|-
|-
|-
|Nobel Economics
|Nobel Economics
诺贝尔经济学奖
|76
|76
|76
|47
|47
|47
|61.84%
|61.84%
|61.84%
|2
|2
|2
|8
|8
|8
|4.11
|4.11
|4.11
|4
|4
|4
|-
|-
|-
|Nobel Chemistry
|Nobel Chemistry
| 诺贝尔化学奖
|172
|172
|172
|42
|42
|42
|24.42%
|24.42%
|24.42%
|3
|3
|3
|10
|10
|10
|5.48
|5.48
|5.48
|5
|5
|5
|-
|-
|-
|Nobel Medicine
|Nobel Medicine
诺贝尔医学奖
|210
|210
|210
|58
|58
|58
|27.62%
|27.62%
|27.62%
|3
|3
|3
|12
|12
|12
|5.50
|5.50
|5.50
|5
|5
|5
|-
|-
|-
|Nobel Physics
|Nobel Physics
诺贝尔物理学奖
|200
|200
|200
|159
|159
|159
|79.50%
|79.50%
|79.50%
|2
|2
|2
|12
|12
|12
|5.63
|5.63
|5.63
|5
|5
|5
|}
|}
|}
===Physics===
Among the Nobel Prize laureates in Physics, [[Albert Einstein]] and [[Sheldon Lee Glashow]] have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include [[Enrico Fermi]], [[Otto Stern]], [[Wolfgang Pauli]], [[Max Born]], [[Willis E. Lamb]], [[Eugene Wigner]], [[Richard P. Feynman]], [[Hans A. Bethe]], [[Murray Gell-Mann]], [[Abdus Salam]], [[Steven Weinberg]], [[Norman F. Ramsey]], [[Frank Wilczek]], and [[David Wineland]]. Fields Medal-winning physicist [[Ed Witten]] has an Erdős number of 3.<ref name="paths">{{Cite web |title = Some Famous People with Finite Erdős Numbers |url = http://www.oakland.edu/enp/erdpaths/ |publisher = [[Oakland University|oakland.edu]] |accessdate = 4 April 2014 }}</ref>
Among the Nobel Prize laureates in Physics, Albert Einstein and Sheldon Lee Glashow have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include Enrico Fermi, Otto Stern, Wolfgang Pauli, Max Born, Willis E. Lamb, Eugene Wigner, Richard P. Feynman, Hans A. Bethe, Murray Gell-Mann, Abdus Salam, Steven Weinberg, Norman F. Ramsey, Frank Wilczek, and David Wineland. Fields Medal-winning physicist Ed Witten has an Erdős number of 3.
在诺贝尔物理学奖获得者中，阿尔伯特 · 爱因斯坦和谢尔登·格拉肖的 erd 数是2。诺贝尔奖获得者包括 Enrico Fermi，Otto Stern，Wolfgang Pauli，Max Born，Willis e. Lamb，Eugene Wigner，理查德·费曼，Hans a. Bethe，默里·盖尔曼，Abdus Salam，Steven Weinberg，Norman f. Ramsey，Frank Wilczek，and David Wineland。菲尔兹奖获得者，物理学家爱德 · 威滕的爱德华数为3。
===Biology===
[[computational biology|Computational biologist]] [[Lior Pachter]] has an Erdős number of 2.<ref name="erdos2">{{cite web |title=List of all people with Erdos number less than or equal to 2 |url=https://files.oakland.edu/users/grossman/enp/ErdosA.html |work=The Erdös Number Project |publisher=Oakland University |date=14 July 2015 |accessdate=25 August 2015}}</ref> [[Evolutionary biology|Evolutionary biologist]] [[Richard Lenski]] has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician [[Bernd Sturmfels]], each of whom has an Erdős number of 2.<ref>{{cite web|url=http://telliamedrevisited.wordpress.com/2015/05/28/erdos-with-a-non-kosher-side-of-bacon|title=Erdös with a non-kosher side of Bacon|author=Richard Lenski|date=May 28, 2015}}</ref>
Computational biologist Lior Pachter has an Erdős number of 2. Evolutionary biologist Richard Lenski has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician Bernd Sturmfels, each of whom has an Erdős number of 2.
计算生物学家 Lior Pachter 的 erd 数为2。进化生物学家理查德 · 伦斯基的爱因斯坦数为3，他曾与莱尔 · 帕切特和数学家贝恩德 · 斯图尔斯合著了一本出版物，每本书的爱因斯坦数为2。
===Finance and economics===
There are at least two winners of the [[Nobel Memorial Prize in Economic Sciences|Nobel Prize in Economics]] with an Erdős number of 2: [[Harry M. Markowitz]] (1990) and [[Leonid Kantorovich]] (1975). Other financial mathematicians with Erdős number of 2 include [[David Donoho]], [[Marc Yor]], [[Henry McKean]], [[Daniel Stroock]], and [[Joseph Keller]].
There are at least two winners of the Nobel Prize in Economics with an Erdős number of 2: Harry M. Markowitz (1990) and Leonid Kantorovich (1975). Other financial mathematicians with Erdős number of 2 include David Donoho, Marc Yor, Henry McKean, Daniel Stroock, and Joseph Keller.
至少有两位诺贝尔经济学奖获得者的 erd 数量是2: Harry m. Markowitz (1990)和列昂尼德·坎托罗维奇 · 马科维茨(1975)。其他拥有 erd 数2的金融数学家包括 David Donoho，Marc Yor，Henry McKean，Daniel Stroock 和 Joseph Keller。
Nobel Prize laureates in Economics with an Erdős number of 3 include [[Kenneth J. Arrow]] (1972), [[Milton Friedman]] (1976), [[Herbert A. Simon]] (1978), [[Gerard Debreu]] (1983), [[John Forbes Nash, Jr.]] (1994), [[James Mirrlees]] (1996), [[Daniel McFadden]] (1996), [[Daniel Kahneman]] (2002), [[Robert J. Aumann]] (2005), [[Leonid Hurwicz]] (2007), [[Roger Myerson]] (2007), [[Alvin E. Roth]] (2012), and [[Lloyd S. Shapley]] (2012) and [[Jean Tirole]] (2014).<ref>Grossman, J. (2015): "The Erdős Number Project." http://wwwp.oakland.edu/enp/erdpaths/</ref>
Nobel Prize laureates in Economics with an Erdős number of 3 include Kenneth J. Arrow (1972), Milton Friedman (1976), Herbert A. Simon (1978), Gerard Debreu (1983), John Forbes Nash, Jr. (1994), James Mirrlees (1996), Daniel McFadden (1996), Daniel Kahneman (2002), Robert J. Aumann (2005), Leonid Hurwicz (2007), Roger Myerson (2007), Alvin E. Roth (2012), and Lloyd S. Shapley (2012) and Jean Tirole (2014).
诺贝尔经济学奖获得者包括肯尼斯·约瑟夫·阿罗(1972) ，米尔顿弗里德曼(1976) ，赫伯特·西蒙(1978) ，Gerard Debreu (1983) ，约翰·福布斯·纳什，jr. 。(1994)、 James Mirrlees (1996)、 Daniel McFadden (1996)、 Daniel Kahneman (2002)、 Robert j. Aumann (2005)、,leonid Hurwicz (2007) ，Roger Myerson (2007) ，Alvin e. Roth (2012) ，Lloyd s. Shapley (2012)和 Jean Tirole (2014)。
Some investment firms have been founded by mathematicians with low Erdős numbers, among them [[James Ax|James B. Ax]] of [[Renaissance Technologies#Medallion Fund|Axcom Technologies]], and [[James H. Simons]] of [[Renaissance Technologies]], both with an Erdős number of 3.<ref>{{Cite news|url=https://www.bloomberg.com/news/articles/2016-11-11/six-degrees-of-quant-kevin-bacon-and-the-erdos-number-mystery|title=Six Degrees of Quant: Kevin Bacon and the Erdős Number Mystery|last=Kishan|first=Saijel|date=2016-11-11|newspaper=Bloomberg.com|access-date=2016-11-12}}</ref><ref>{{Cite news|url=http://www.financial-math.org/blog/2016/11/erdos-numbers-in-finance/|title=Erdős Numbers: A True "Prince and the Pauper" story|last=Bailey|first=David H.|date=2016-11-06|work=|newspaper=The Mathematical Investor|language=en-US|access-date=2016-11-12|via=}}</ref>
Some investment firms have been founded by mathematicians with low Erdős numbers, among them James B. Ax of Axcom Technologies, and James H. Simons of Renaissance Technologies, both with an Erdős number of 3.
有些投资公司是由数量较少的数学家创立的，其中包括詹姆斯 · b。的 Ax 和文艺复兴科技的 James h. Simons，他们的 erd 数都是3。
===Philosophy===
Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers.<ref>{{cite web |url=http://home.iprimus.com.au/than/toby/erdos.html |title=Philosophy research networks |author=Toby Handfield }}</ref> Philosopher [[John P. Burgess]] has an Erdős number of 2.<ref name="erdos2"/> [[Jon Barwise]] and [[Joel David Hamkins]], both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers. Philosopher John P. Burgess has an Erdős number of 2. Jon Barwise and Joel David Hamkins, both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
由于更正式的哲学版本与数学基础共享推理，这些领域有相当大的重叠，而 erd 的数字对许多哲学家来说是可用的。哲学家约翰 · p · 伯吉斯的 erd 数为2。乔恩 · 巴韦斯和乔尔 · 大卫 · 汉姆金斯，都是厄尔德二号，也对哲学做出了广泛的贡献，但主要被描述为数学家。
===Law===
Judge [[Richard Posner]], having coauthored with [[Alvin E. Roth]], has an Erdős number of at most 4. [[Roberto Mangabeira Unger]], a politician, philosopher and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with [[Lee Smolin]].
Judge Richard Posner, having coauthored with Alvin E. Roth, has an Erdős number of at most 4. Roberto Mangabeira Unger, a politician, philosopher and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with Lee Smolin.
法官理查德 · 波斯纳与阿尔文 · e · 罗斯合著了本书，本书的爱尔兰数量最多不超过4本。是一位政治家、哲学家和法律理论家，在哈佛大学法学院任教，他与 Lee Smolin 合著的《昂格尔多达4本。
===Politics===
[[Angela Merkel]], [[Chancellor of Germany]] from 2005 to the present, has an Erdős number of at most 5.<ref name="project"/>
Angela Merkel, Chancellor of Germany from 2005 to the present, has an Erdős number of at most 5.
从2005年到现在的德国总理，她的 erd 数字最多不超过5。
===Engineering===
Some fields of engineering, in particular [[communication theory]] and [[cryptography]], make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, [[Robert McEliece]], a professor of [[electrical engineering]] at [[California Institute of Technology|Caltech]], had an Erdős number of 1, having collaborated with Erdős himself.<ref>{{cite journal |author=Erdős, Paul, Robert McEliece, and Herbert Taylor |title=Ramsey bounds for graph products |journal=[[Pacific Journal of Mathematics]] |volume=37 |issue=1 |date=1971 |pages=45–46 |url=https://msp.org/pjm/1971/37-1/pjm-v37-n1-p07-p.pdf |doi=10.2140/pjm.1971.37.45}}</ref> Cryptographers [[Ron Rivest]], [[Adi Shamir]], and [[Leonard Adleman]], inventors of the [[RSA (cryptosystem)|RSA]] cryptosystem, all have Erdős number 2.<ref name="erdos2"/>
Some fields of engineering, in particular communication theory and cryptography, make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, Robert McEliece, a professor of electrical engineering at Caltech, had an Erdős number of 1, having collaborated with Erdős himself. Cryptographers Ron Rivest, Adi Shamir, and Leonard Adleman, inventors of the RSA cryptosystem, all have Erdős number 2.
一些工程领域，特别是通信理论和密码学，直接利用 erd 所拥护的离散数学。因此，这些领域的从业人员的 erd 值偏低就不足为奇了。例如，加州理工学院的电气工程教授罗伯特 · 麦克里斯与爱尔德本人合作，得到了爱尔德数1。RSA 密码系统的发明者——密码学家罗恩 · 里维斯特、阿迪 · 沙米尔和伦纳德 · 阿德曼都有 erd 数2。
===Social network analysis===
Anthropologist Douglas R. White has an Erdős number of 2 via graph theorist [[Frank Harary]].<ref>{{cite journal | last1 = White | first1 = Douglas R. | last2 = Harary | first2 = Frank | year = 2001 | title = The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density | url = | journal = Sociological Methodology | volume = 31 | issue = | pages = 305–59 | doi = 10.1111/0081-1750.00098 }}</ref><ref>{{cite web |url=http://eclectic.ss.uci.edu/~drwhite/6wwwvita.html |title=VITA: Douglas R.White, Anthropology & Social Science Professor, UC-Irvine |accessdate=December 14, 2017}}</ref> Sociologist [[Barry Wellman]] has an Erdős number of 3 via [[social network]] analyst and statistician Ove Frank,<ref>Barry Wellman, Ove Frank, Vicente Espinoza, Staffan Lundquist and Craig Wilson. "Integrating Individual, Relational and Structural Analysis". 1991. ''Social Networks'' 13 (Sept.): 223-50.</ref> another collaborator of Harary's.<ref>Ove Frank; Frank Harary, "Cluster Inference by Using Transitivity Indices in Empirical Graphs." ''Journal of the American Statistical Association'', 77, 380. (Dec., 1982), pp. 835–840.</ref>
Anthropologist Douglas R. White has an Erdős number of 2 via graph theorist Frank Harary. Sociologist Barry Wellman has an Erdős number of 3 via social network analyst and statistician Ove Frank, another collaborator of Harary's.
人类学家道格拉斯 · r · 怀特通过图论家弗兰克 · 哈拉里给出了 erd 数2。社会学家巴里 · 韦尔曼通过社交网络分析师和统计学家奥夫 · 弗兰克得到了 erd 数字3，奥夫 · 弗兰克是哈拉里的另一个合作者。
===Linguistics===
The Romanian mathematician and computational linguist [[Solomon Marcus]] had an Erdős number of 1 for a paper in ''[[Acta Mathematica Hungarica]]'' that he co-authored with Erdős in 1957.<ref>{{cite journal|first1=Paul|last1= Erdős |author1-link=Paul Erdős|first2= Solomon|last2= Marcus|author2-link=Solomon Marcus| year=1957| url=https://akademiai.com/doi/abs/10.1007/BF02020326?journalCode=10473|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|pages=443–452|mr=0095456|doi=10.1007/BF02020326}}</ref>
The Romanian mathematician and computational linguist Solomon Marcus had an Erdős number of 1 for a paper in Acta Mathematica Hungarica that he co-authored with Erdős in 1957.
罗马尼亚数学家、计算语言学家所罗门 · 马库斯在1957年与厄尔德合著的《数学学报》上的一篇论文中，给出了厄尔德数1。
==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 [[UCLA]], received the [[Fields Medal]] in 2006, and was elected a [[Fellow of the Royal Society]] in 2007. His Erdős number is 2]]
Paul Erdős in 1985 at the [[University of Adelaide teaching Terence Tao, who was then 10 years old. Tao became a math professor at UCLA, received the Fields Medal in 2006, and was elected a Fellow of the Royal Society in 2007. His Erdős number is 2]]
1985年，Paul erd 在阿德莱德大学教导10岁的 Terence Tao。陶成为加州大学洛杉矶分校的数学教授，2006年获得菲尔兹奖，2007年被选为皇家学会会员。他的 erd 数字是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 |accessdate=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 [[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}}</ref><ref>{{cite web|url=http://www-math.mit.edu/~djk/list.html|title=Publications Since 1980 more or less|first=Daniel|last=Kleitman|authorlink=Daniel Kleitman|publisher=[[Massachusetts Institute of Technology]]}}</ref> and since Kleitman has an Erdős number of 1,<ref>
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; 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 John Tukey, who has an Erdős number of 2. Similarly, the prominent geneticist Eric Lander and the mathematician Daniel Kleitman have collaborated on papers, and since Kleitman has an Erdős number of 1,<ref>
多年来，厄尔德数字一直是世界各地数学家的民间传说。在千禧年之交所有有限 erd 数字的数学工作者中，这个数字最高可达15，中位数是5，平均数是4.65; 例如，政治学家史蒂文 · 布拉姆斯的 erd 数是2。在21生物医学研究，统计学家通常是出版物的作者之一，许多统计学家可以通过 John Tukey 链接到 erd s，他的 erd 数为2。同样，杰出的遗传学家埃里克 · 兰德尔和数学家丹尼尔 · 克莱特曼合作撰写论文，自从克莱特曼有一个 erd 数字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
</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
大部分的遗传学和基因组学社区可以通过 Lander 和他的众多合作者联系起来。同样的，与古斯塔夫斯·希门斯的合作也打开了一扇大门
[[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 |archiveurl=https://web.archive.org/web/20060823085712/http://semantics-online.org/2004/01/my-erds-number-is-8 |archivedate=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 |accessdate=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 |accessdate=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 |accessdate=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 |accessdate=2010-08-29}}</ref> There are also connections with [[arts]] fields.<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | authorlink1=Jonathan Bowen | last2=Wilson | first2=Robin J. | authorlink2=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 | booktitle= 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>
Erdős numbers within the cryptographic research community, and many linguists have finite Erdős numbers, many due to chains of collaboration with such notable scholars as Noam Chomsky (Erdős number 4), William Labov (3), Mark Liberman (3), Geoffrey Pullum (3), or Ivan Sag (4). There are also connections with arts fields.
Erd 的数字在密码学研究领域，许多语言学家都有有限的 erd 数字，许多是由于与著名学者 Noam Chomsky (erd 数字4) ，William Labov (3) ，Mark Liberman (3) ，Geoffrey Pullum (3) ，或 Ivan Sag (4)的合作链。与艺术领域也有联系。
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.
According to Alex Lopez-Ortiz, all the Fields and Nevanlinna prize winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.
根据 Alex Lopez-Ortiz 的说法，在1986年到1994年的3个赛季中，所有的费尔德斯和奈望林纳奖冠军的 erd 数量最多不超过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>
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.
早期数学家发表的论文比现代数学家少，联合发表的论文也更少。根据出版资格标准的不同，已知最早拥有有限 erd 数目的人要么是安托万-洛朗·德·拉瓦锡(出生于1743年，erd 数目13) ，要么是理查德·戴德金(出生于1831年，erd 数目7) ，要么是费迪南德·格奥尔格·弗罗贝尼乌斯(出生于1849年，erd 数目3)。
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}} {{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}}</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.
Martin Tompa 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.
Martin Tompa 提出了 erd 数问题的一个有向图版本，通过定向协作图的边，从字母顺序的前作者到字母顺序的后作者，并定义单调的作者 erd 数为从 Erdős 到作者的最长路径的长度。他找到了一条长度为12的路径。
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. 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.
Also, 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. 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.
此外，迈克尔 · 巴尔还提出了“合理的 erd 数字” ，概括了这样一个观点，即一个与 erd s 共同撰写了 p 篇论文的人应该被赋予 erd s 1/p。从第二种合作多重图(虽然他也有办法处理第一种情况)ーー两个数学家为他们生产的每一张合作论文画一条边ーー形成一个电网络，每条边上有一个一欧姆电阻器。两个节点之间的总电阻表示这两个节点的“关闭”程度。
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]'', IBM Research Report R109002, February 2009; also appeared as {{Cite journal | doi = 10.1145/1871437.1871470| pmc = | pmid = | 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>
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 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."
有人认为，”对于单个研究人员来说，erd 数字这样的衡量标准反映了网络的结构特性，而 h-index 则反映了出版物的引用影响” ，”人们很容易相信，在合作网络中的排名应该考虑到这两项措施，以产生一个现实的和可接受的排名
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 however did not intend to pay but just 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 | jstor=4015267}}</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 however did not intend to pay but just placed the bid to stop what he considered a mockery.
2004年，数学家威廉 · 托齐尔(William Tozier)在 eBay 上拍卖了一幅共同作者的作品，给买家提供了厄德数为5的作品。一位西班牙数学家以1031美元的价格成交，但是这位数学家并不打算出价，只是为了阻止这个他认为是嘲弄的东西。
==Variations==
A number of variations on the concept have been proposed to apply to other fields.
A number of variations on the concept have been proposed to apply to other fields.
对这一概念提出了若干变通办法，以适用于其他领域。
The best known is the [[Bacon number]] (as in the game [[Six Degrees of Kevin Bacon]]), connecting actors that appeared in a film together to the actor [[Kevin Bacon]]. It was created in 1994, 25 years after Goffman's article on the Erdős number.
The best known is the Bacon number (as in the game Six Degrees of Kevin Bacon), connecting actors that appeared in a film together to the actor Kevin Bacon. It was created in 1994, 25 years after Goffman's article on the Erdős number.
最著名的是“培根号码”(就像在游戏《凯文 · 培根的六度》中一样) ，它把一起出现在电影中的演员和演员凯文 · 培根联系在一起。它创建于1994年，比戈夫曼关于厄尔德数字的文章晚了25年。
A small number of people are connected to both Erdős and Bacon and thus have an [[Erdős–Bacon number]], which combines the two numbers by taking their sum. One example is the actress-mathematician [[Danica McKellar]], best known for playing Winnie Cooper on the TV series ''[[The Wonder Years]]''.
A small number of people are connected to both Erdős and Bacon and thus have an Erdős–Bacon number, which combines the two numbers by taking their sum. One example is the actress-mathematician Danica McKellar, best known for playing Winnie Cooper on the TV series The Wonder Years.
一小部分人同时连接到 erd 和 Bacon，因此有一个 erd s-Bacon 数，它通过求和来组合这两个数。一个例子是女演员兼数学家丹妮卡 · 麦凯勒，她因在电视连续剧《奇迹年代》中扮演温妮 · 库珀而闻名。
Her Erdős number is 4,<ref>McKellar's co-author Lincoln Chayes published [https://projecteuclid.org/euclid.cmp/1103940982 a paper] with [[Elliott H. Lieb]], who in turn co-authored [https://doi.org/10.1016/0012-365X(71)90004-5 a paper] with [[Daniel Kleitman]], a co-author of Paul Erdős.</ref> and her Bacon number is 2.<ref>Danica McKellar was in ''[[The Year That Trembled]]'' (2002) with James Kisicki, who was in ''[[Telling Lies in America]]'' (1997) with Kevin Bacon.</ref>
Her Erdős number is 4, and her Bacon number is 2.
她的 erd 数字是4，而她的 Bacon 数字是2。
Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band [[Black Sabbath]] in terms of singing in public. Physicist [[Stephen Hawking]] had an Erdős–Bacon–Sabbath number of 8,<ref>{{cite web|url=https://www.timeshighereducation.com/blog/whats-your-erdos-bacon-sabbath-number |title=What's your Erdős–Bacon–Sabbath number? |website=[[Times Higher Education]] |date=2016-02-17 |access-date=2018-07-29 |last=Fisher |first=Len}}</ref> and actress [[Natalie Portman]] has one of 11 (her Erdős number is 5).<ref>{{cite web|url=http://blogs.surrey.ac.uk/physics/2012/09/15/erdos-bacon-sabbath-numbers/comment-page-1/ |title=Erdős–Bacon–Sabbath numbers |date=2012-09-15 |access-date=2018-07-29 |last=Sear |first=Richard |website=Department of Physics, [[University of Surrey]]}}</ref>
Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band Black Sabbath in terms of singing in public. Physicist Stephen Hawking had an Erdős–Bacon–Sabbath number of 8, and actress Natalie Portman has one of 11 (her Erdős number is 5).
进一步延长是可能的。例如，“ erd s-Bacon-Sabbath 数”是 erd s-Bacon 数和黑色 Sabbath 乐队在公共场合演唱时的合作距离之和。物理学家斯蒂芬 · 霍金的 erd-Bacon-Sabbath 数字是8，女演员娜塔莉 · 波特曼的 erd 数字是11(她的 erd 数字是5)。
== See also ==
* {{annotated link|Scientometrics}}
* {{annotated link|Small-world experiment}}
* {{annotated link|Small-world network}}
* {{annotated link|Six degrees of separation}}
* {{annotated link|Sociology of scientific knowledge}}
* {{annotated link|List of people by Erdős number}}
* {{annotated link|List of things named after Paul Erdős}}
* {{annotated link|Collaboration graph}}
== References ==
{{Reflist|30em}}
== External links ==
* Jerry Grossman, [http://www.oakland.edu/enp The Erdős Number Project]. Contains statistics and a complete list of all mathematicians with an Erdős number less than or equal to 2.
* [http://www4.oakland.edu/upload/docs/Erdos%20Number%20Project/collab.pdf "On a Portion of the Well-Known Collaboration Graph"], Jerrold W. Grossman and Patrick D. F. Ion.
* [http://vlado.fmf.uni-lj.si/pub/networks/doc/erdos/erdos.pdf "Some Analyses of Erdős Collaboration Graph"], Vladimir Batagelj and Andrej Mrvar.
* American Mathematical Society, [http://www.ams.org/mathscinet/freeTools.html?version=2]. A search engine for Erdős numbers and collaboration distance between other authors. As of 18 November 2011 no special access is required.
* [https://www.youtube.com/watch?v=izdZPx89ph4 Numberphile video]. Ron Graham on imaginary Erdős numbers.
{{DEFAULTSORT:Erdos Number}}
[[Category:Paul Erdős|Number]]
Number
数目
[[Category:Social networks]]
Category:Social networks
分类: 社交网络
[[Category:Mathematics literature]]
Category:Mathematics literature
类别: 数学文献
[[Category:Separation numbers]]
Category:Separation numbers
分类: 离职号码
[[Category:Bibliometrics]]
Category:Bibliometrics
分类: 文献计量学
<noinclude>
<small>This page was moved from [[wikipedia:en:Erdős number]]. Its edit history can be viewed at [[埃尔德什数理论/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{Short description|Closeness of someone's association with mathematician Paul Erdős}}
[[File:Erdos budapest fall 1992.jpg|thumb|upright|[[Paul Erdős]] in 1992]]
[[Paul Erdős in 1992]]
[保罗 · 爱德1992]
The '''Erdős number''' ({{IPA-hu|ˈɛrdøːʃ|lang}}) describes the "collaborative distance" between mathematician {{nobr|[[Paul Erdős]]}} and another person, as measured by authorship of [[List of important publications in mathematics|mathematical papers]]. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
The Erdős number () describes the "collaborative distance" between mathematician and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.
Erd 的数字()描述了数学家和另一个人之间的“协作距离” ，这是通过数学论文的作者来衡量的。同样的原则也适用于其他领域，在这些领域中，某个特定的个人与众多的同龄人进行了合作。
== Overview ==
Paul Erdős (1913–1996) was an influential [[Hungarian people|Hungarian]] mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems.<ref name="newman2001">{{cite journal|last=Newman|first=Mark E. J.|authorlink=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}}</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 |accessdate=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 a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world.
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, working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least 1,525) than any other mathematician in history. Erdős spent a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world.
保罗 · 厄德(1913-1996)是一位颇有影响力的匈牙利数学家，他晚年花了大量时间与许多同事一起撰写论文，致力于解决杰出的数学问题。他一生发表的论文(至少1525篇)比历史上任何一位数学家都多。尔德晚年的大部分时间都生活在一个手提箱里，拜访了他在世界各地的500多名合作者。
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|url=http://www.oakland.edu/enp|title=Erdös Number Project|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>
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.
厄尔德数的概念最初是由这位数学家的朋友为了向他的巨大成就致敬而创立的。后来，它作为研究数学家如何合作找到未解决问题的答案的工具而获得了突出地位。几个项目致力于研究研究人员之间的连通性，使用 erd 数字作为一个代理。例如，erd 的协作图可以告诉我们作者是如何聚类的，每篇论文的协作作者数量是如何随时间演变的，或者新的理论是如何传播的。
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers.<ref name="trails">{{cite journal
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers.<ref name="trails">{{cite journal
一些研究表明，一流的数学家的 erd 数字往往特别低
|last1 = De Castro
|last1 = De Castro
1 = De Castro
|first1 = Rodrigo
|first1 = Rodrigo
1 = Rodrigo
|last2 = Grossman
|last2 = Grossman
2 = Grossman
|first2 = Jerrold W.
|first2 = Jerrold W.
2 = Jerrold w.
|doi = 10.1007/BF03025416
|doi = 10.1007/BF03025416
| doi = 10.1007/BF03025416
|issue = 3
|issue = 3
第三期
|journal = [[The Mathematical Intelligencer]]
|journal = The Mathematical Intelligencer
2012年3月24日 | 日志 = 数学通讯者
|mr = 1709679
|mr = 1709679
1709679先生
|pages = 51–63
|pages = 51–63
| 页数 = 51-63
|title = Famous trails to Paul Erdős
|title = Famous trails to Paul Erdős
保罗 · 厄德斯著名的小径
|url = http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
|url = http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
Http://www.oakland.edu/upload/docs/erdos%20number%20project/trails.pdf
|volume = 21
|volume = 21
21
|year = 1999
|year = 1999
1999年
|url-status = dead
|url-status = dead
地位 = 死亡
|archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
|archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/Erdos%20Number%20Project/trails.pdf
2012年3月24日 | archiveurl = https://web.archive.org/web/20150924054224/http://www.oakland.edu/upload/docs/erdos%20number%20project/trails.pdf
|archivedate = 2015-09-24
|archivedate = 2015-09-24
| archivedate = 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 Medalists]] 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 smallest 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=":0" />
}} Original Spanish version in Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. 23 (89) 563–582, 1999, .</ref> The median Erdős number of Fields Medalists is 3. Only 7,097 (about 5% of mathematicians with a collaboration path) have an Erdős number of 2 or lower. As time passes, the smallest 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.
最初的西班牙语版本。Acad.哥伦比亚科伦坡。没错。Fís.女名女子名。23(89)563-582,1999.只有7,097人(大约5% 的数学家拥有协作路径)的 erd 数为2或更少。随着时间的推移，最小的 erd 数量仍然可以达到必然会增加，因为低 erd 数量的数学家死亡，变得无法进行合作。尽管如此，历史人物的 erd 值可能会比较低。例如，著名的印度数学家拉马努金的 erd 数值只有3(通过 g. h. Hardy 的 erd 数值2) ，尽管当 Ramanujan 去世时 Paul erd s 只有7岁。
==Definition and application in mathematics==
[[File:Erdosnumber.png|thumb|If [[Alice and Bob|Alice]] collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Alice is given an Erdős number of 1 and Bob is given an Erdős number of 2, as he is two steps from Erdős.]]
Alice collaborates with Paul Erdős on one paper, and with Bob on another, but Bob never collaborates with Erdős himself, then Alice is given an Erdős number of 1 and Bob is given an Erdős number of 2, as he is two steps from Erdős.]]
爱丽丝和保罗在一篇论文上合作，鲍勃在另一篇论文上合作，但是鲍勃从来没有和厄尔德本人合作过，然后爱丽丝得到厄尔德数的1，鲍勃得到厄尔德数的2，因为他离 Erdős 只有两步
To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is {{math|''k'' + 1}} where {{math|''k''}} is the lowest Erdős number of any coauthor. The [[American Mathematical Society]] provides a free online tool to determine the Erdős number of every mathematical author listed in the ''[[Mathematical Reviews]]'' catalogue.<ref name=":0">{{cite web|url=http://www.ams.org/mathscinet/collaborationDistance.html|title=
To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is where is the lowest Erdős number of any coauthor. The American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.<ref name=":0">{{cite web|url=http://www.ams.org/mathscinet/collaborationDistance.html|title=
为了得到 erd 的编号，某人必须是一篇研究论文的合著者，而另一个人的 erd 编号是有限的。Paul erd s 的 erd 数为零。任何其他人的 erd 数是任何合著者的最小 erd 数。美国数学学会提供了一个免费的在线工具，用来确定《数学评论》目录中列出的每一位数学作者的 erd 编号。{ cite web | url = http://www.ams.org/mathscinet/collaborationdistance.html|title=
Collaboration Distance|work=[[MathSciNet]]|publisher=American Mathematical Society}}</ref>
Collaboration Distance|work=MathSciNet|publisher=American Mathematical Society}}</ref>
协作距离 | work = MathSciNet | publisher = American Mathematical Society } </ref >
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators;<ref name="Erdős Number Project"/> these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (11,009 people as of 2015<ref name="Erdős Number Project File Erdos2">[https://files.oakland.edu/users/grossman/enp/Erdos2.html Erdos2], Version 2015, July 14, 2015.</ref>), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of [[infinity]] (or an [[defined and undefined|undefined]] one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators;), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.
尔德在他的一生中写了大约1500篇数学文章，大部分是合著的。他有511个直接合作者;) ，那些与 erd 数为2的人(但不是 erd 数为1的人)合作的 erd 数为3，等等。如果一个人没有连接到 Erdős 的这样的合著者链，那么 erd 的数量就是无穷(或者一个未定义的无穷)。自从 Paul erd 死后，一个新的研究者所能得到的最低 erd 数是2。
There is room for ambiguity over what constitutes a link between two authors. The American Mathematical Society collaboration distance calculator uses data from ''Mathematical Reviews'', which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications{{citation needed|date=August 2015}}. The Erdős Number Project web site says:
There is room for ambiguity over what constitutes a link between two authors. The American Mathematical Society collaboration distance calculator uses data from Mathematical Reviews, which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications. The Erdős Number Project web site says:
关于两位作者之间的联系，还有模棱两可的余地。美国数学学会(American Mathematical Society)协作距离计算器使用的数据来自《数学评论》(Mathematical Reviews) ，该杂志包括大多数数学期刊，但仅以有限的方式涵盖其他学科，还包括一些非研究性出版物。爱德华的数字项目网站上说:
{{quote|... Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional co-authors is permitted,...}}
but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.<ref>Grossman ''et al.'' "[http://www.oakland.edu/?id=9569&sid=243#en2k Erdős numbers of the second kind]," in ''Facts about Erdős Numbers and the Collaboration Graph''. [http://www.oakland.edu/enp The Erdős Number Project], [[Oakland University]], USA. Retrieved July 25, 2009.</ref>
but they do not include non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.
但不包括基础教科书、联合编辑、讣告等非研究性出版物。“第二类 erd 数”将 erd 数的分配限制在只有两个合作者的论文上。
The Erdős number was most likely first defined in print by Casper Goffman, an [[Mathematical analysis|analyst]] whose own Erdős number is 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> See also some comments in an obituary by Michael Golomb.<ref>{{cite web|url=http://www.math.purdue.edu/about/purview/fall96/paul-erdos.html|title= Erdős'obituary by Michael Golomb}}</ref>
The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 2. See also some comments in an obituary by Michael Golomb.
Erd 的数字很可能是由 Casper Goffman 首先在印刷品中定义的，他自己的 erd 数字是2。参见 Michael Golomb 的讣告中的一些评论。
The median Erdős number among [[Fields medal]]ists is as low as 3.<ref name="paths"/> Fields medalists with Erdős number 2 include [[Atle Selberg]], [[Kunihiko Kodaira]], [[Klaus Roth]], [[Alan Baker (mathematician)|Alan Baker]], [[Enrico Bombieri]], [[David Mumford]], [[Charles Fefferman]], [[William Thurston]], [[Shing-Tung Yau]], [[Jean Bourgain]], [[Richard Borcherds]], [[Manjul Bhargava]], [[Jean-Pierre Serre]] and [[Terence Tao]]. There are no Fields medalists with Erdős number 1;<ref name="project">{{cite web|url=http://www.oakland.edu/enp/erdpaths/|title=Paths to Erdös|work=The Erdös Number Project|publisher=Oakland University}}</ref> however, [[Endre Szemerédi]] is an [[Abel Prize]] Laureate with Erdős number 1.<ref name="trails"/>
The median Erdős number among Fields medalists is as low as 3. however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.
菲尔兹奖获得者的中位数 erd 只有3。然而，恩德雷 · 塞梅雷迪却是艾伯尔奖的获奖者，而艾伯尔奖则排在第一位。
==Most frequent Erdős collaborators==
While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).<ref>Grossman, Jerry, [https://files.oakland.edu/users/grossman/enp/Erdos0p.html Erdos0p], Version 2010, ''[http://www.oakland.edu/enp The Erdős Number Project]'', [[Oakland University]], US, October 20, 2010.</ref>
While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).
虽然 erd 与数百名合著者合作，但也有一些人与他合著了几十篇论文。以下是与 erd s 合著最频繁的十位人士及他们与 erd s 合著的论文数目(即。他们的合作次数)。
{| class="wikitable sortable"
{| class="wikitable sortable"
{ | class = “ wikitable sortable”
|-
|-
|-
! Co-author !! Number of <br>collaborations
! Co-author !! Number of <br>collaborations
!合著者! ！合作次数
|-
|-
|-
| [[András Sárközy]] || 62
| András Sárközy || 62
| András Sárközy || 62
|-
|-
|-
| [[András Hajnal]] || 56
| András Hajnal || 56
| András Hajnal || 56
|-
|-
|-
| [[Ralph Faudree]] || 50
| Ralph Faudree || 50
拉尔夫 · 法德里 | 50
|-
|-
|-
| [[Richard Schelp]] || 42
| Richard Schelp || 42
| Richard Schelp | | 42
|-
|-
|-
| [[Cecil C. Rousseau]] || 35
| Cecil C. Rousseau || 35
塞西尔 · c · 卢梭 | 35
|-
|-
|-
| [[Vera T. Sós]] || 35
| Vera T. Sós || 35
| Vera T. Sós || 35
|-
|-
|-
| [[Alfréd Rényi]] || 32
| Alfréd Rényi || 32
| Alfréd Rényi || 32
|-
|-
|-
| [[Pál Turán]] || 30
| Pál Turán || 30
| Pál Turán || 30
|-
|-
|-
| [[Endre Szemerédi]] || 29
| Endre Szemerédi || 29
| Endre Szemerédi || 29
|-
|-
|-
| [[Ronald Graham]] || 28
| Ronald Graham || 28
罗纳德 · 格雷厄姆28
|}
|}
|}
==Related fields==
{{As of|2016}}, all [[Fields Medal]]ists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13.<ref>{{Cite web|url=http://wwwp.oakland.edu/enp/trivia/|title=Facts about Erdös Numbers and the Collaboration Graph - The Erdös Number Project- Oakland University|website=wwwp.oakland.edu|access-date=2016-10-27}}</ref> The table below summarizes the Erdős number statistics for [[Nobel Prize|Nobel prize]] laureates in Physics, Chemistry, Medicine and Economics.<ref>{{Cite journal|last=López de Prado|first=Marcos|title=Mathematics and Economics: A reality check|url=http://www.iijournals.com/doi/pdfplus/10.3905/jpm.2016.43.1.005|journal=The Journal of Portfolio Management|volume=43|issue=1|pages=5–8|doi=10.3905/jpm.2016.43.1.005|year=2016}}</ref> The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average and median Erdős numbers among those laureates.
, all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13. The table below summarizes the Erdős number statistics for Nobel prize laureates in Physics, Chemistry, Medicine and Economics. The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average and median Erdős numbers among those laureates.
所有田径奖获得者都有一个有限的 erd s 数，数值范围在2到6之间，中位数为3。相比之下，所有数学家的 erd 数的中位数(有限 erd 数)是5，极值是13。下表总结了 erd 的数字统计诺贝尔奖获得者在物理，化学，医学和经济学。第一栏计算获奖者的数量。第二列用有限的 erd 数计算赢家的数目。第三列是有限 erd 数目的获胜者的百分比。剩下的柱子报告的最低，最高，平均和中位数 erd 的数字在这些获奖者。
{| class="wikitable sortable"
{| class="wikitable sortable"
{ | class = “ wikitable sortable”
|+ Statistics on Mathematical Collaboration, 1903-2016
|+ Statistics on Mathematical Collaboration, 1903-2016
| + 数学合作统计，1903-2016
!
!
!
! #Laureates
! #Laureates
!* 获奖者
! #Erdős
! #Erdős
!#Erdős
! %Erdős
! %Erdős
!%Erdős
! Min
! Min
!最小
! Max
! Max
!麦克斯
! Average
! Average
!平均数
! Median
! Median
!中位数
|-
|-
|-
|Fields Medal
|Fields Medal
菲尔兹奖
|56
|56
|56
|56
|56
|56
|100.0%
|100.0%
|100.0%
|2
|2
|2
|6
|6
|6
|3.36
|3.36
|3.36
|3
|3
|3
|-
|-
|-
|Nobel Economics
|Nobel Economics
诺贝尔经济学奖
|76
|76
|76
|47
|47
|47
|61.84%
|61.84%
|61.84%
|2
|2
|2
|8
|8
|8
|4.11
|4.11
|4.11
|4
|4
|4
|-
|-
|-
|Nobel Chemistry
|Nobel Chemistry
| 诺贝尔化学奖
|172
|172
|172
|42
|42
|42
|24.42%
|24.42%
|24.42%
|3
|3
|3
|10
|10
|10
|5.48
|5.48
|5.48
|5
|5
|5
|-
|-
|-
|Nobel Medicine
|Nobel Medicine
诺贝尔医学奖
|210
|210
|210
|58
|58
|58
|27.62%
|27.62%
|27.62%
|3
|3
|3
|12
|12
|12
|5.50
|5.50
|5.50
|5
|5
|5
|-
|-
|-
|Nobel Physics
|Nobel Physics
诺贝尔物理学奖
|200
|200
|200
|159
|159
|159
|79.50%
|79.50%
|79.50%
|2
|2
|2
|12
|12
|12
|5.63
|5.63
|5.63
|5
|5
|5
|}
|}
|}
===Physics===
Among the Nobel Prize laureates in Physics, [[Albert Einstein]] and [[Sheldon Lee Glashow]] have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include [[Enrico Fermi]], [[Otto Stern]], [[Wolfgang Pauli]], [[Max Born]], [[Willis E. Lamb]], [[Eugene Wigner]], [[Richard P. Feynman]], [[Hans A. Bethe]], [[Murray Gell-Mann]], [[Abdus Salam]], [[Steven Weinberg]], [[Norman F. Ramsey]], [[Frank Wilczek]], and [[David Wineland]]. Fields Medal-winning physicist [[Ed Witten]] has an Erdős number of 3.<ref name="paths">{{Cite web |title = Some Famous People with Finite Erdős Numbers |url = http://www.oakland.edu/enp/erdpaths/ |publisher = [[Oakland University|oakland.edu]] |accessdate = 4 April 2014 }}</ref>
Among the Nobel Prize laureates in Physics, Albert Einstein and Sheldon Lee Glashow have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include Enrico Fermi, Otto Stern, Wolfgang Pauli, Max Born, Willis E. Lamb, Eugene Wigner, Richard P. Feynman, Hans A. Bethe, Murray Gell-Mann, Abdus Salam, Steven Weinberg, Norman F. Ramsey, Frank Wilczek, and David Wineland. Fields Medal-winning physicist Ed Witten has an Erdős number of 3.
在诺贝尔物理学奖获得者中，阿尔伯特 · 爱因斯坦和谢尔登·格拉肖的 erd 数是2。诺贝尔奖获得者包括 Enrico Fermi，Otto Stern，Wolfgang Pauli，Max Born，Willis e. Lamb，Eugene Wigner，理查德·费曼，Hans a. Bethe，默里·盖尔曼，Abdus Salam，Steven Weinberg，Norman f. Ramsey，Frank Wilczek，and David Wineland。菲尔兹奖获得者，物理学家爱德 · 威滕的爱德华数为3。
===Biology===
[[computational biology|Computational biologist]] [[Lior Pachter]] has an Erdős number of 2.<ref name="erdos2">{{cite web |title=List of all people with Erdos number less than or equal to 2 |url=https://files.oakland.edu/users/grossman/enp/ErdosA.html |work=The Erdös Number Project |publisher=Oakland University |date=14 July 2015 |accessdate=25 August 2015}}</ref> [[Evolutionary biology|Evolutionary biologist]] [[Richard Lenski]] has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician [[Bernd Sturmfels]], each of whom has an Erdős number of 2.<ref>{{cite web|url=http://telliamedrevisited.wordpress.com/2015/05/28/erdos-with-a-non-kosher-side-of-bacon|title=Erdös with a non-kosher side of Bacon|author=Richard Lenski|date=May 28, 2015}}</ref>
Computational biologist Lior Pachter has an Erdős number of 2. Evolutionary biologist Richard Lenski has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician Bernd Sturmfels, each of whom has an Erdős number of 2.
计算生物学家 Lior Pachter 的 erd 数为2。进化生物学家理查德 · 伦斯基的爱因斯坦数为3，他曾与莱尔 · 帕切特和数学家贝恩德 · 斯图尔斯合著了一本出版物，每本书的爱因斯坦数为2。
===Finance and economics===
There are at least two winners of the [[Nobel Memorial Prize in Economic Sciences|Nobel Prize in Economics]] with an Erdős number of 2: [[Harry M. Markowitz]] (1990) and [[Leonid Kantorovich]] (1975). Other financial mathematicians with Erdős number of 2 include [[David Donoho]], [[Marc Yor]], [[Henry McKean]], [[Daniel Stroock]], and [[Joseph Keller]].
There are at least two winners of the Nobel Prize in Economics with an Erdős number of 2: Harry M. Markowitz (1990) and Leonid Kantorovich (1975). Other financial mathematicians with Erdős number of 2 include David Donoho, Marc Yor, Henry McKean, Daniel Stroock, and Joseph Keller.
至少有两位诺贝尔经济学奖获得者的 erd 数量是2: Harry m. Markowitz (1990)和列昂尼德·坎托罗维奇 · 马科维茨(1975)。其他拥有 erd 数2的金融数学家包括 David Donoho，Marc Yor，Henry McKean，Daniel Stroock 和 Joseph Keller。
Nobel Prize laureates in Economics with an Erdős number of 3 include [[Kenneth J. Arrow]] (1972), [[Milton Friedman]] (1976), [[Herbert A. Simon]] (1978), [[Gerard Debreu]] (1983), [[John Forbes Nash, Jr.]] (1994), [[James Mirrlees]] (1996), [[Daniel McFadden]] (1996), [[Daniel Kahneman]] (2002), [[Robert J. Aumann]] (2005), [[Leonid Hurwicz]] (2007), [[Roger Myerson]] (2007), [[Alvin E. Roth]] (2012), and [[Lloyd S. Shapley]] (2012) and [[Jean Tirole]] (2014).<ref>Grossman, J. (2015): "The Erdős Number Project." http://wwwp.oakland.edu/enp/erdpaths/</ref>
Nobel Prize laureates in Economics with an Erdős number of 3 include Kenneth J. Arrow (1972), Milton Friedman (1976), Herbert A. Simon (1978), Gerard Debreu (1983), John Forbes Nash, Jr. (1994), James Mirrlees (1996), Daniel McFadden (1996), Daniel Kahneman (2002), Robert J. Aumann (2005), Leonid Hurwicz (2007), Roger Myerson (2007), Alvin E. Roth (2012), and Lloyd S. Shapley (2012) and Jean Tirole (2014).
诺贝尔经济学奖获得者包括肯尼斯·约瑟夫·阿罗(1972) ，米尔顿弗里德曼(1976) ，赫伯特·西蒙(1978) ，Gerard Debreu (1983) ，约翰·福布斯·纳什，jr. 。(1994)、 James Mirrlees (1996)、 Daniel McFadden (1996)、 Daniel Kahneman (2002)、 Robert j. Aumann (2005)、,leonid Hurwicz (2007) ，Roger Myerson (2007) ，Alvin e. Roth (2012) ，Lloyd s. Shapley (2012)和 Jean Tirole (2014)。
Some investment firms have been founded by mathematicians with low Erdős numbers, among them [[James Ax|James B. Ax]] of [[Renaissance Technologies#Medallion Fund|Axcom Technologies]], and [[James H. Simons]] of [[Renaissance Technologies]], both with an Erdős number of 3.<ref>{{Cite news|url=https://www.bloomberg.com/news/articles/2016-11-11/six-degrees-of-quant-kevin-bacon-and-the-erdos-number-mystery|title=Six Degrees of Quant: Kevin Bacon and the Erdős Number Mystery|last=Kishan|first=Saijel|date=2016-11-11|newspaper=Bloomberg.com|access-date=2016-11-12}}</ref><ref>{{Cite news|url=http://www.financial-math.org/blog/2016/11/erdos-numbers-in-finance/|title=Erdős Numbers: A True "Prince and the Pauper" story|last=Bailey|first=David H.|date=2016-11-06|work=|newspaper=The Mathematical Investor|language=en-US|access-date=2016-11-12|via=}}</ref>
Some investment firms have been founded by mathematicians with low Erdős numbers, among them James B. Ax of Axcom Technologies, and James H. Simons of Renaissance Technologies, both with an Erdős number of 3.
有些投资公司是由数量较少的数学家创立的，其中包括詹姆斯 · b。的 Ax 和文艺复兴科技的 James h. Simons，他们的 erd 数都是3。
===Philosophy===
Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers.<ref>{{cite web |url=http://home.iprimus.com.au/than/toby/erdos.html |title=Philosophy research networks |author=Toby Handfield }}</ref> Philosopher [[John P. Burgess]] has an Erdős number of 2.<ref name="erdos2"/> [[Jon Barwise]] and [[Joel David Hamkins]], both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers. Philosopher John P. Burgess has an Erdős number of 2. Jon Barwise and Joel David Hamkins, both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
由于更正式的哲学版本与数学基础共享推理，这些领域有相当大的重叠，而 erd 的数字对许多哲学家来说是可用的。哲学家约翰 · p · 伯吉斯的 erd 数为2。乔恩 · 巴韦斯和乔尔 · 大卫 · 汉姆金斯，都是厄尔德二号，也对哲学做出了广泛的贡献，但主要被描述为数学家。
===Law===
Judge [[Richard Posner]], having coauthored with [[Alvin E. Roth]], has an Erdős number of at most 4. [[Roberto Mangabeira Unger]], a politician, philosopher and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with [[Lee Smolin]].
Judge Richard Posner, having coauthored with Alvin E. Roth, has an Erdős number of at most 4. Roberto Mangabeira Unger, a politician, philosopher and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with Lee Smolin.
法官理查德 · 波斯纳与阿尔文 · e · 罗斯合著了本书，本书的爱尔兰数量最多不超过4本。是一位政治家、哲学家和法律理论家，在哈佛大学法学院任教，他与 Lee Smolin 合著的《昂格尔多达4本。
===Politics===
[[Angela Merkel]], [[Chancellor of Germany]] from 2005 to the present, has an Erdős number of at most 5.<ref name="project"/>
Angela Merkel, Chancellor of Germany from 2005 to the present, has an Erdős number of at most 5.
从2005年到现在的德国总理，她的 erd 数字最多不超过5。
===Engineering===
Some fields of engineering, in particular [[communication theory]] and [[cryptography]], make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, [[Robert McEliece]], a professor of [[electrical engineering]] at [[California Institute of Technology|Caltech]], had an Erdős number of 1, having collaborated with Erdős himself.<ref>{{cite journal |author=Erdős, Paul, Robert McEliece, and Herbert Taylor |title=Ramsey bounds for graph products |journal=[[Pacific Journal of Mathematics]] |volume=37 |issue=1 |date=1971 |pages=45–46 |url=https://msp.org/pjm/1971/37-1/pjm-v37-n1-p07-p.pdf |doi=10.2140/pjm.1971.37.45}}</ref> Cryptographers [[Ron Rivest]], [[Adi Shamir]], and [[Leonard Adleman]], inventors of the [[RSA (cryptosystem)|RSA]] cryptosystem, all have Erdős number 2.<ref name="erdos2"/>
Some fields of engineering, in particular communication theory and cryptography, make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, Robert McEliece, a professor of electrical engineering at Caltech, had an Erdős number of 1, having collaborated with Erdős himself. Cryptographers Ron Rivest, Adi Shamir, and Leonard Adleman, inventors of the RSA cryptosystem, all have Erdős number 2.
一些工程领域，特别是通信理论和密码学，直接利用 erd 所拥护的离散数学。因此，这些领域的从业人员的 erd 值偏低就不足为奇了。例如，加州理工学院的电气工程教授罗伯特 · 麦克里斯与爱尔德本人合作，得到了爱尔德数1。RSA 密码系统的发明者——密码学家罗恩 · 里维斯特、阿迪 · 沙米尔和伦纳德 · 阿德曼都有 erd 数2。
===Social network analysis===
Anthropologist Douglas R. White has an Erdős number of 2 via graph theorist [[Frank Harary]].<ref>{{cite journal | last1 = White | first1 = Douglas R. | last2 = Harary | first2 = Frank | year = 2001 | title = The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density | url = | journal = Sociological Methodology | volume = 31 | issue = | pages = 305–59 | doi = 10.1111/0081-1750.00098 }}</ref><ref>{{cite web |url=http://eclectic.ss.uci.edu/~drwhite/6wwwvita.html |title=VITA: Douglas R.White, Anthropology & Social Science Professor, UC-Irvine |accessdate=December 14, 2017}}</ref> Sociologist [[Barry Wellman]] has an Erdős number of 3 via [[social network]] analyst and statistician Ove Frank,<ref>Barry Wellman, Ove Frank, Vicente Espinoza, Staffan Lundquist and Craig Wilson. "Integrating Individual, Relational and Structural Analysis". 1991. ''Social Networks'' 13 (Sept.): 223-50.</ref> another collaborator of Harary's.<ref>Ove Frank; Frank Harary, "Cluster Inference by Using Transitivity Indices in Empirical Graphs." ''Journal of the American Statistical Association'', 77, 380. (Dec., 1982), pp. 835–840.</ref>
Anthropologist Douglas R. White has an Erdős number of 2 via graph theorist Frank Harary. Sociologist Barry Wellman has an Erdős number of 3 via social network analyst and statistician Ove Frank, another collaborator of Harary's.
人类学家道格拉斯 · r · 怀特通过图论家弗兰克 · 哈拉里给出了 erd 数2。社会学家巴里 · 韦尔曼通过社交网络分析师和统计学家奥夫 · 弗兰克得到了 erd 数字3，奥夫 · 弗兰克是哈拉里的另一个合作者。
===Linguistics===
The Romanian mathematician and computational linguist [[Solomon Marcus]] had an Erdős number of 1 for a paper in ''[[Acta Mathematica Hungarica]]'' that he co-authored with Erdős in 1957.<ref>{{cite journal|first1=Paul|last1= Erdős |author1-link=Paul Erdős|first2= Solomon|last2= Marcus|author2-link=Solomon Marcus| year=1957| url=https://akademiai.com/doi/abs/10.1007/BF02020326?journalCode=10473|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|pages=443–452|mr=0095456|doi=10.1007/BF02020326}}</ref>
The Romanian mathematician and computational linguist Solomon Marcus had an Erdős number of 1 for a paper in Acta Mathematica Hungarica that he co-authored with Erdős in 1957.
罗马尼亚数学家、计算语言学家所罗门 · 马库斯在1957年与厄尔德合著的《数学学报》上的一篇论文中，给出了厄尔德数1。
==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 [[UCLA]], received the [[Fields Medal]] in 2006, and was elected a [[Fellow of the Royal Society]] in 2007. His Erdős number is 2]]
Paul Erdős in 1985 at the [[University of Adelaide teaching Terence Tao, who was then 10 years old. Tao became a math professor at UCLA, received the Fields Medal in 2006, and was elected a Fellow of the Royal Society in 2007. His Erdős number is 2]]
1985年，Paul erd 在阿德莱德大学教导10岁的 Terence Tao。陶成为加州大学洛杉矶分校的数学教授，2006年获得菲尔兹奖，2007年被选为皇家学会会员。他的 erd 数字是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 |accessdate=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 [[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}}</ref><ref>{{cite web|url=http://www-math.mit.edu/~djk/list.html|title=Publications Since 1980 more or less|first=Daniel|last=Kleitman|authorlink=Daniel Kleitman|publisher=[[Massachusetts Institute of Technology]]}}</ref> and since Kleitman has an Erdős number of 1,<ref>
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; 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 John Tukey, who has an Erdős number of 2. Similarly, the prominent geneticist Eric Lander and the mathematician Daniel Kleitman have collaborated on papers, and since Kleitman has an Erdős number of 1,<ref>
多年来，厄尔德数字一直是世界各地数学家的民间传说。在千禧年之交所有有限 erd 数字的数学工作者中，这个数字最高可达15，中位数是5，平均数是4.65; 例如，政治学家史蒂文 · 布拉姆斯的 erd 数是2。在21生物医学研究，统计学家通常是出版物的作者之一，许多统计学家可以通过 John Tukey 链接到 erd s，他的 erd 数为2。同样，杰出的遗传学家埃里克 · 兰德尔和数学家丹尼尔 · 克莱特曼合作撰写论文，自从克莱特曼有一个 erd 数字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
</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
大部分的遗传学和基因组学社区可以通过 Lander 和他的众多合作者联系起来。同样的，与古斯塔夫斯·希门斯的合作也打开了一扇大门
[[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 |archiveurl=https://web.archive.org/web/20060823085712/http://semantics-online.org/2004/01/my-erds-number-is-8 |archivedate=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 |accessdate=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 |accessdate=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 |accessdate=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 |accessdate=2010-08-29}}</ref> There are also connections with [[arts]] fields.<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | authorlink1=Jonathan Bowen | last2=Wilson | first2=Robin J. | authorlink2=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 | booktitle= 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>
Erdős numbers within the cryptographic research community, and many linguists have finite Erdős numbers, many due to chains of collaboration with such notable scholars as Noam Chomsky (Erdős number 4), William Labov (3), Mark Liberman (3), Geoffrey Pullum (3), or Ivan Sag (4). There are also connections with arts fields.
Erd 的数字在密码学研究领域，许多语言学家都有有限的 erd 数字，许多是由于与著名学者 Noam Chomsky (erd 数字4) ，William Labov (3) ，Mark Liberman (3) ，Geoffrey Pullum (3) ，或 Ivan Sag (4)的合作链。与艺术领域也有联系。
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.
According to Alex Lopez-Ortiz, all the Fields and Nevanlinna prize winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.
根据 Alex Lopez-Ortiz 的说法，在1986年到1994年的3个赛季中，所有的费尔德斯和奈望林纳奖冠军的 erd 数量最多不超过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>
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.
早期数学家发表的论文比现代数学家少，联合发表的论文也更少。根据出版资格标准的不同，已知最早拥有有限 erd 数目的人要么是安托万-洛朗·德·拉瓦锡(出生于1743年，erd 数目13) ，要么是理查德·戴德金(出生于1831年，erd 数目7) ，要么是费迪南德·格奥尔格·弗罗贝尼乌斯(出生于1849年，erd 数目3)。
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}} {{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}}</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.
Martin Tompa 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.
Martin Tompa 提出了 erd 数问题的一个有向图版本，通过定向协作图的边，从字母顺序的前作者到字母顺序的后作者，并定义单调的作者 erd 数为从 Erdős 到作者的最长路径的长度。他找到了一条长度为12的路径。
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. 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.
Also, 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. 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.
此外，迈克尔 · 巴尔还提出了“合理的 erd 数字” ，概括了这样一个观点，即一个与 erd s 共同撰写了 p 篇论文的人应该被赋予 erd s 1/p。从第二种合作多重图(虽然他也有办法处理第一种情况)ーー两个数学家为他们生产的每一张合作论文画一条边ーー形成一个电网络，每条边上有一个一欧姆电阻器。两个节点之间的总电阻表示这两个节点的“关闭”程度。
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]'', IBM Research Report R109002, February 2009; also appeared as {{Cite journal | doi = 10.1145/1871437.1871470| pmc = | pmid = | 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>
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 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."
有人认为，”对于单个研究人员来说，erd 数字这样的衡量标准反映了网络的结构特性，而 h-index 则反映了出版物的引用影响” ，”人们很容易相信，在合作网络中的排名应该考虑到这两项措施，以产生一个现实的和可接受的排名
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 however did not intend to pay but just 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 | jstor=4015267}}</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 however did not intend to pay but just placed the bid to stop what he considered a mockery.
2004年，数学家威廉 · 托齐尔(William Tozier)在 eBay 上拍卖了一幅共同作者的作品，给买家提供了厄德数为5的作品。一位西班牙数学家以1031美元的价格成交，但是这位数学家并不打算出价，只是为了阻止这个他认为是嘲弄的东西。
==Variations==
A number of variations on the concept have been proposed to apply to other fields.
A number of variations on the concept have been proposed to apply to other fields.
对这一概念提出了若干变通办法，以适用于其他领域。
The best known is the [[Bacon number]] (as in the game [[Six Degrees of Kevin Bacon]]), connecting actors that appeared in a film together to the actor [[Kevin Bacon]]. It was created in 1994, 25 years after Goffman's article on the Erdős number.
The best known is the Bacon number (as in the game Six Degrees of Kevin Bacon), connecting actors that appeared in a film together to the actor Kevin Bacon. It was created in 1994, 25 years after Goffman's article on the Erdős number.
最著名的是“培根号码”(就像在游戏《凯文 · 培根的六度》中一样) ，它把一起出现在电影中的演员和演员凯文 · 培根联系在一起。它创建于1994年，比戈夫曼关于厄尔德数字的文章晚了25年。
A small number of people are connected to both Erdős and Bacon and thus have an [[Erdős–Bacon number]], which combines the two numbers by taking their sum. One example is the actress-mathematician [[Danica McKellar]], best known for playing Winnie Cooper on the TV series ''[[The Wonder Years]]''.
A small number of people are connected to both Erdős and Bacon and thus have an Erdős–Bacon number, which combines the two numbers by taking their sum. One example is the actress-mathematician Danica McKellar, best known for playing Winnie Cooper on the TV series The Wonder Years.
一小部分人同时连接到 erd 和 Bacon，因此有一个 erd s-Bacon 数，它通过求和来组合这两个数。一个例子是女演员兼数学家丹妮卡 · 麦凯勒，她因在电视连续剧《奇迹年代》中扮演温妮 · 库珀而闻名。
Her Erdős number is 4,<ref>McKellar's co-author Lincoln Chayes published [https://projecteuclid.org/euclid.cmp/1103940982 a paper] with [[Elliott H. Lieb]], who in turn co-authored [https://doi.org/10.1016/0012-365X(71)90004-5 a paper] with [[Daniel Kleitman]], a co-author of Paul Erdős.</ref> and her Bacon number is 2.<ref>Danica McKellar was in ''[[The Year That Trembled]]'' (2002) with James Kisicki, who was in ''[[Telling Lies in America]]'' (1997) with Kevin Bacon.</ref>
Her Erdős number is 4, and her Bacon number is 2.
她的 erd 数字是4，而她的 Bacon 数字是2。
Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band [[Black Sabbath]] in terms of singing in public. Physicist [[Stephen Hawking]] had an Erdős–Bacon–Sabbath number of 8,<ref>{{cite web|url=https://www.timeshighereducation.com/blog/whats-your-erdos-bacon-sabbath-number |title=What's your Erdős–Bacon–Sabbath number? |website=[[Times Higher Education]] |date=2016-02-17 |access-date=2018-07-29 |last=Fisher |first=Len}}</ref> and actress [[Natalie Portman]] has one of 11 (her Erdős number is 5).<ref>{{cite web|url=http://blogs.surrey.ac.uk/physics/2012/09/15/erdos-bacon-sabbath-numbers/comment-page-1/ |title=Erdős–Bacon–Sabbath numbers |date=2012-09-15 |access-date=2018-07-29 |last=Sear |first=Richard |website=Department of Physics, [[University of Surrey]]}}</ref>
Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band Black Sabbath in terms of singing in public. Physicist Stephen Hawking had an Erdős–Bacon–Sabbath number of 8, and actress Natalie Portman has one of 11 (her Erdős number is 5).
进一步延长是可能的。例如，“ erd s-Bacon-Sabbath 数”是 erd s-Bacon 数和黑色 Sabbath 乐队在公共场合演唱时的合作距离之和。物理学家斯蒂芬 · 霍金的 erd-Bacon-Sabbath 数字是8，女演员娜塔莉 · 波特曼的 erd 数字是11(她的 erd 数字是5)。
== See also ==
* {{annotated link|Scientometrics}}
* {{annotated link|Small-world experiment}}
* {{annotated link|Small-world network}}
* {{annotated link|Six degrees of separation}}
* {{annotated link|Sociology of scientific knowledge}}
* {{annotated link|List of people by Erdős number}}
* {{annotated link|List of things named after Paul Erdős}}
* {{annotated link|Collaboration graph}}
== References ==
{{Reflist|30em}}
== External links ==
* Jerry Grossman, [http://www.oakland.edu/enp The Erdős Number Project]. Contains statistics and a complete list of all mathematicians with an Erdős number less than or equal to 2.
* [http://www4.oakland.edu/upload/docs/Erdos%20Number%20Project/collab.pdf "On a Portion of the Well-Known Collaboration Graph"], Jerrold W. Grossman and Patrick D. F. Ion.
* [http://vlado.fmf.uni-lj.si/pub/networks/doc/erdos/erdos.pdf "Some Analyses of Erdős Collaboration Graph"], Vladimir Batagelj and Andrej Mrvar.
* American Mathematical Society, [http://www.ams.org/mathscinet/freeTools.html?version=2]. A search engine for Erdős numbers and collaboration distance between other authors. As of 18 November 2011 no special access is required.
* [https://www.youtube.com/watch?v=izdZPx89ph4 Numberphile video]. Ron Graham on imaginary Erdős numbers.
{{DEFAULTSORT:Erdos Number}}
[[Category:Paul Erdős|Number]]
Number
数目
[[Category:Social networks]]
Category:Social networks
分类: 社交网络
[[Category:Mathematics literature]]
Category:Mathematics literature
类别: 数学文献
[[Category:Separation numbers]]
Category:Separation numbers
分类: 离职号码
[[Category:Bibliometrics]]
Category:Bibliometrics
分类: 文献计量学
<noinclude>
<small>This page was moved from [[wikipedia:en:Erdős number]]. Its edit history can be viewed at [[埃尔德什数理论/edithistory]]</small></noinclude>
[[Category:待整理页面]]