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第376行： − + − + − 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。 第449行：
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→Impact
==Impact==
== Impact 影响 ==
[[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]]
[[文件:Paul Erdos with Terence Tao.jpg|缩略图|右|1985年，保罗·埃尔德什在阿德莱德大学任教，他的学生陶哲轩（Terence Tao）当时只有10岁。陶后来成为加州大学洛杉矶分校的数学教授，于2006年获得费尔兹奖，并于2007年当选为皇家学会会员。他的埃尔德什数为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; 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. 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, a large fraction of the genetics and genomics community can be linked via Lander and his numerous collaborators. Similarly, collaboration with Gustavus Simmons opened the door for [[List of people by Erdős number|Erdős numbers]] within the [[cryptographic]] research community, and many [[linguistics|linguists]] have finite Erdős numbers, many due to chains of collaboration with such notable scholars as [[Noam Chomsky]] (Erdős number 4), [[William Labov]] (3), [[Mark Liberman]] (3), [[Geoffrey Pullum]] (3), or [[Ivan Sag]] (4). There are also connections with [[arts]] fields.
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, 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 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.
多年以来，埃尔德什数在数学家之间一直盛行。在千年之交的所有在职数学家中，都伴随着一个有限埃尔德什数，数字范围最大为15，中位数为5，平均值为4.65。几乎每个具有有限埃尔德什数的人其数字都小于8。由于当今科学领域跨学科合作的频率很高，因此许多其他科学领域的大量非数学家也具有有限的埃尔德什数。例如，政治学家Steven Brams的埃尔德什数为2。在生物医学研究中，统计学家通常是出版物的作者，许多统计学家可以通过John Tukey（其埃尔德什数为2）与埃尔德什链接。同样，著名的遗传学家Eric Lander和数学家Daniel Kleitman在论文上进行了合作，由于Kleitman的埃尔德什数为1，因此可以通过Lander及其众多合作者将遗传学和基因组学领域的大部分联系起来。另外，与Gustavus Simmons的合作为密码研究界内的埃尔德什数打开了大门，许多语言学家拥有有限的埃尔德什数，这许多是由于与Noam Chomsky（埃尔德什数为4），William Labov（3）等著名学者的合作产生，Mark Liberman（3），Geoffrey Pullum（3）或Ivan Sag（4）。同时与艺术领域也有联系。
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。
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==
==Variations==