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第41行：
第41行： − 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 > − − − − − 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。+ 第71行：
第61行： − 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:+ − + + + − 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。+ − + − 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。+ − − + − + − 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。+
→Definition and application in mathematics 数学的定义与应用
[[文件:Erdosnumber.png|缩略图|右|如果爱丽丝在一张纸上与保罗·埃尔德什合作，在另一张纸上与鲍勃合作，但是鲍勃从未与埃尔德什本人合作，那么爱丽丝的埃尔德什数为1，而鲍勃的埃尔德什数为2，因为他离埃尔德什有两步。]]
[[文件:Erdosnumber.png|缩略图|右|如果爱丽丝在一张纸上与保罗·埃尔德什合作，在另一张纸上与鲍勃合作，但是鲍勃从未与埃尔德什本人合作，那么爱丽丝的埃尔德什数为1，而鲍勃的埃尔德什数为2，因为他离埃尔德什有两步。]]
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.
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.
要分配一个埃尔德什数，某人必须与另一个具有有限埃尔德什数的人共同撰写研究论文。保罗·埃尔德什的埃尔德什数为零。其他人的埃尔德什数为k+1，其中k是任何合著者中最低的埃尔德什数。美国数学学会提供免费的在线工具，可确定《数学评论》目录中列出的每个数学作者的埃尔德什数。
Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 511 direct collaborators; 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), 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;<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.
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.
埃尔德什一生撰写了约1500篇数学文章，其中大部分是合作的。他有511个直接合作者；这些是埃尔德什数为1的人。与这些人合作（但未与埃尔德什本人合作）的人所拥有的埃尔德什数为2（截至2020年8月7日为12,600人），而与埃尔德什数为2的人合作的人（但与埃尔德什或埃尔德什数为1的任何人无合作关系），其埃尔德什数为3，依此类推。没有此类共同作者链接能指向埃尔德什的人，其埃尔德什数为无穷大（或未定义）。自保罗·埃尔德什逝世以来，新研究员可获得的最低Erdős数为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. 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:
关于具体由什么构成两位作者之间的联系，众说纷纭。美国数学学会的“协作距离计算器”使用的是来自《数学评论》的数据，包括大多数数学期刊，但仅以有限的方式涵盖了其他主题，同时还包括一些非研究出版物。埃尔德什数项目官方网站Erdős Number Project表示：
{{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,...}}
{{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>
...我们在顶点u和v之间共有的包含边标准是，它们之间的某些研究合作导致了发表的作品。允许任何数量的其他共同作者，...
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.
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.
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.
但它们不包括非研究性出版物，例如教科书，联合编辑，讣告等。“第二种埃尔德什数”将其分配给只有两个合作者的论文。
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 [[Mathematical analysis|analyst]] whose own Erdős number is 2. Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled "''And what is your Erdős number?''" See also some comments in an obituary by Michael Golomb.
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.
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.
埃尔德什数很可能最早由卡斯珀·高夫曼Casper Goffman定义，他自己的埃尔德什数为2。高夫曼在1969年发表的一篇文章中表示了他对埃尔德什多产合作的看法，“您的埃尔德什数是多少？”另请参阅迈克尔·哥伦布Michael Golomb在讣告中的一些评论。
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 medal]]ists is as low as 3. 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; however, [[Endre Szemerédi]] is an [[Abel Prize]] Laureate with Erdős number 1.
The median Erdős number among Fields medalists is as low as 3. however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.
The median Erdős number among Fields medalists is as low as 3.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; however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.
Fields奖牌获得者的埃尔德什中位数低至3。埃尔德什排名第二的奖牌获得者包括Atle Selberg，Kunihiko Kodaira，Klaus Roth，Alan Baker，Enrico Bombieri，David Mumford，Charles Fefferman，William Thurston，Shing-Tung Tung，Jean Bourgain，Richard Borcherds，Manjul Bhargava，Jean-Pierre Serre和陶哲轩。Fields的获得者中没有人的Erdős为1。但是，恩德雷·塞梅雷迪（Endre Szemerédi）是阿贝尔奖获得者，其埃尔德什数为1。
==Most frequent Erdős collaborators==
==Most frequent Erdős collaborators==