1,068
个编辑
更改
跳到导航
跳到搜索
第27行：
第27行： − + 第155行：
第155行： − + 第193行：
第193行： − + 第200行：
第200行： − + − + 第230行：
第230行： − + − +
无编辑摘要
|doi = 10.1007/BF03025416
|doi = 10.1007/BF03025416
|issue = 3
|issue = 3
|journal = [[The Mathematical Intelligencer]]
|journal = The Mathematical Intelligencer
|pages = 51–63
|pages = 51–63
|title = Famous trails to Paul Erdős
|title = Famous trails to Paul Erdős
=== 物理领域 ===
=== 物理领域 ===
在诺贝尔物理学奖获得者中，爱因斯坦Albert Einstein和谢尔登·李·格拉肖Sheldon Lee Glashow的埃尔德什数为2。诺贝尔奖获得者中埃尔德什数为3的有: 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。获得菲尔兹奖的物理学家Ed Witten的埃尔德什数为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]] |access-date = 4 April 2014 }}</ref>
在诺贝尔物理学奖获得者中，爱因斯坦Albert Einstein和谢尔登·李·格拉肖Sheldon Lee Glashow的埃尔德什数为2。诺贝尔奖获得者中埃尔德什数为3的有: 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。获得菲尔兹奖的物理学家Ed Witten的埃尔德什数为3。<ref name="paths">{{Cite web |title = Some Famous People with Finite Erdős Numbers |url = http://www.oakland.edu/enp/erdpaths/ |publisher =oakland.edu |access-date = 4 April 2014 }}</ref>
=== 语言学领域 ===
=== 语言学领域 ===
罗马尼亚数学家和计算语言学家Solomon Marcus在1957年与埃尔德什合作了《 Acta Mathematica Hungarica》中的一篇论文，因此他的埃尔德什数为1。<ref>{{cite journal|first1=Paul|last1= Erdős |first2= Solomon|last2= Marcus| year=1957|title= Sur la décomposition de l'espace euclidien en ensembles homogènes |trans-title= On the decomposition of the Euclidean space into homogeneous sets|journal=[[Acta Mathematica Hungarica]]|volume=8|issue= 3–4 |pages=443–452|doi=10.1007/BF02020326 }}</ref>
罗马尼亚数学家和计算语言学家Solomon Marcus在1957年与埃尔德什合作了《 Acta Mathematica Hungarica》中的一篇论文，因此他的埃尔德什数为1。<ref>{{cite journal|first1=Paul|last1= Erdős |first2= Solomon|last2= Marcus| year=1957|title= Sur la décomposition de l'espace euclidien en ensembles homogènes |trans-title= On the decomposition of the Euclidean space into homogeneous sets|journal=Acta Mathematica Hungarica|volume=8|issue= 3–4 |pages=443–452|doi=10.1007/BF02020326 }}</ref>
[[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年获得菲尔兹奖，并于2007年当选为皇家学会会员。他的埃尔德什数为2。]]
[[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年获得菲尔兹奖，并于2007年当选为皇家学会会员。他的埃尔德什数为2。]]
多年以来，埃尔德什数在数学家之间一直盛行。在千年之交的所有在职数学家中，都伴随着一个有限埃尔德什数，数字范围最大为15，中位数为5，平均值为4.65。<ref name="Erdős Number Project"/>几乎每个具有有限埃尔德什数的人其数字都小于8。由于当今科学领域跨学科合作的频率很高，因此许多其他科学领域的大量非数学家也具有有限的埃尔德什数。<ref>{{cite web |url=http://www.oakland.edu/enp/erdpaths/ |title=Some Famous People with Finite Erdős Numbers | first=Jerry | last=Grossman |access-date=1 February 2011}}</ref>例如，政治学家Steven Brams的埃尔德什数为2。在生物医学研究中，统计学家通常是出版物的作者，许多统计学家可以通过John Tukey（其埃尔德什数为2）与埃尔德什链接。同样，著名的遗传学家Eric Lander和数学家Daniel Kleitman在论文上进行了合作，<ref>{{cite journal | pmid = 10582576 | doi=10.1089/106652799318364 | volume=6 | title=A dictionary-based approach for gene annotation | year=1999 | journal=J Comput Biol | pages=419–30 | last1 = Pachter | first1 = L | last2 = Batzoglou | first2 = S | last3 = Spitkovsky | first3 = VI | last4 = Banks | first4 = E | last5 = Lander | first5 = ES | last6 = Kleitman | first6 = DJ | last7 = Berger | first7 = B| issue=3–4 }}</ref><ref>{{cite web|url=http://www-math.mit.edu/~djk/list.html|title=Publications Since 1980 more or less|first=Daniel|last=Kleitman|publisher=[[Massachusetts Institute of Technology]]}}</ref>由于Kleitman的埃尔德什数为1，<ref>
多年以来，埃尔德什数在数学家之间一直盛行。在千年之交的所有在职数学家中，都伴随着一个有限埃尔德什数，数字范围最大为15，中位数为5，平均值为4.65。<ref name="Erdős Number Project"/>几乎每个具有有限埃尔德什数的人其数字都小于8。由于当今科学领域跨学科合作的频率很高，因此许多其他科学领域的大量非数学家也具有有限的埃尔德什数。<ref>{{cite web |url=http://www.oakland.edu/enp/erdpaths/ |title=Some Famous People with Finite Erdős Numbers | first=Jerry | last=Grossman |access-date=1 February 2011}}</ref>例如，政治学家Steven Brams的埃尔德什数为2。在生物医学研究中，统计学家通常是出版物的作者，许多统计学家可以通过John Tukey（其埃尔德什数为2）与埃尔德什链接。同样，著名的遗传学家Eric Lander和数学家Daniel Kleitman在论文上进行了合作，<ref>{{cite journal | pmid = 10582576 | doi=10.1089/106652799318364 | volume=6 | title=A dictionary-based approach for gene annotation | year=1999 | journal=J Comput Biol | pages=419–30 | last1 = Pachter | first1 = L | last2 = Batzoglou | first2 = S | last3 = Spitkovsky | first3 = VI | last4 = Banks | first4 = E | last5 = Lander | first5 = ES | last6 = Kleitman | first6 = DJ | last7 = Berger | first7 = B| issue=3–4 }}</ref><ref>{{cite web|url=http://www-math.mit.edu/~djk/list.html|title=Publications Since 1980 more or less|first=Daniel|last=Kleitman|publisher=Massachusetts Institute of Technology}}</ref>由于Kleitman的埃尔德什数为1，<ref>
{{cite journal | last1 = Erdős | first1 = Paul | author1-link = Paul Erdős |last2=Kleitman|first2=Daniel | title = On Collections of Subsets Containing No 4-Member Boolean Algebra | journal = [[Proceedings of the American Mathematical Society]] | volume = 28 | issue = 1 | pages = 87–90 |date=April 1971 | doi = 10.2307/2037762|url=http://www.math-inst.hu/~p_erdos/1971-07.pdf}}</ref>因此可以通过Lander及其众多合作者将遗传学和基因组学领域的大部分联系起来。另外，与Gustavus Simmons的合作为密码研究界内的埃尔德什数打开了大门，许多语言学家拥有有限的埃尔德什数，这许多是由于与Noam Chomsky（埃尔德什数为4），<ref>{{cite web |last=von Fintel |first=Kai |title=My Erdös Number is 8 |url=http://semantics-online.org/2004/01/my-erds-number-is-8 |publisher=Semantics, Inc. |date=2004 |archive-url=https://web.archive.org/web/20060823085712/http://semantics-online.org/2004/01/my-erds-number-is-8 |archive-date=23 August 2006}}</ref>William Labov（埃尔德什数为3）等著名学者的合作产生，<ref>{{cite web|url=http://www.ling.upenn.edu/~dinkin/ |title=Aaron Dinkin has a web site? |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref>类似有Mark Liberman（3）<ref>{{cite web|url=http://www.ling.upenn.edu/~myl/ |title=Mark Liberman's Home Page |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref> ，Geoffrey Pullum（3）<ref>{{cite web|url=http://www.stanford.edu/~cgpotts/miscellany.html |title=Christopher Potts: Miscellany |publisher=Stanford.edu |access-date=2010-08-29}}</ref>或Ivan Sag（4）<ref>{{cite web|url=http://lingo.stanford.edu/sag/erdos.html |title=Bob's Erdős Number |publisher=Lingo.stanford.edu |access-date=2010-08-29}}</ref>。同时与艺术领域也有联系。<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | last2=Wilson | first2=Robin J. | editor1-first=Stuart|editor1-last=Dunn|editor2-first=Jonathan P.|editor2-last=Bowen|editor3-first= Kia|editor3-last=Ng | title=Visualising Virtual Communities: From Erdős to the Arts | url=http://ewic.bcs.org/content/ConWebDoc/46141 | book-title= EVA London 2012: Electronic Visualisation and the Arts | publisher=[[British Computer Society]] | series= Electronic Workshops in Computing | pages = 238–244 |date=10–12 July 2012}}</ref>
{{cite journal | last1 = Erdős | first1 = Paul | author1-link = Paul Erdős |last2=Kleitman|first2=Daniel | title = On Collections of Subsets Containing No 4-Member Boolean Algebra | journal = Proceedings of the American Mathematical Society | volume = 28 | issue = 1 | pages = 87–90 |date=April 1971 | doi = 10.2307/2037762|url=http://www.math-inst.hu/~p_erdos/1971-07.pdf}}</ref>因此可以通过Lander及其众多合作者将遗传学和基因组学领域的大部分联系起来。另外，与Gustavus Simmons的合作为密码研究界内的埃尔德什数打开了大门，许多语言学家拥有有限的埃尔德什数，这许多是由于与Noam Chomsky（埃尔德什数为4），<ref>{{cite web |last=von Fintel |first=Kai |title=My Erdös Number is 8 |url=http://semantics-online.org/2004/01/my-erds-number-is-8 |publisher=Semantics, Inc. |date=2004 |archive-url=https://web.archive.org/web/20060823085712/http://semantics-online.org/2004/01/my-erds-number-is-8 |archive-date=23 August 2006}}</ref>William Labov（埃尔德什数为3）等著名学者的合作产生，<ref>{{cite web|url=http://www.ling.upenn.edu/~dinkin/ |title=Aaron Dinkin has a web site? |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref>类似有Mark Liberman（3）<ref>{{cite web|url=http://www.ling.upenn.edu/~myl/ |title=Mark Liberman's Home Page |publisher=Ling.upenn.edu |access-date=2010-08-29}}</ref> ，Geoffrey Pullum（3）<ref>{{cite web|url=http://www.stanford.edu/~cgpotts/miscellany.html |title=Christopher Potts: Miscellany |publisher=Stanford.edu |access-date=2010-08-29}}</ref>或Ivan Sag（4）<ref>{{cite web|url=http://lingo.stanford.edu/sag/erdos.html |title=Bob's Erdős Number |publisher=Lingo.stanford.edu |access-date=2010-08-29}}</ref>。同时与艺术领域也有联系。<ref>{{cite conference | last1=Bowen | first1=Jonathan P. | last2=Wilson | first2=Robin J. | editor1-first=Stuart|editor1-last=Dunn|editor2-first=Jonathan P.|editor2-last=Bowen|editor3-first= Kia|editor3-last=Ng | title=Visualising Virtual Communities: From Erdős to the Arts | url=http://ewic.bcs.org/content/ConWebDoc/46141 | book-title= EVA London 2012: Electronic Visualisation and the Arts | publisher=British Computer Society | series= Electronic Workshops in Computing | pages = 238–244 |date=10–12 July 2012}}</ref>
很少一部分人同时与埃尔德什和培根相连，因此有一个埃尔德什-培根数，该数通过求和将两个数相加。一个例子是女演员兼数学家丹妮卡·麦凯拉Danica McKellar，她在电视连续剧《纯真年代》中扮演温妮·库珀而闻名。她的埃尔德什数是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>她的培根数是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>
很少一部分人同时与埃尔德什和培根相连，因此有一个埃尔德什-培根数，该数通过求和将两个数相加。一个例子是女演员兼数学家丹妮卡·麦凯拉Danica McKellar，她在电视连续剧《纯真年代》中扮演温妮·库珀而闻名。她的埃尔德什数是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>她的培根数是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>
以此类推可以进一步扩展，例如，“埃尔德什-培根–萨巴什数”是“埃尔德什-培根数”在大众音乐领域与黑色安息日Black Sabbath乐队的协作距离总和。物理学家斯蒂芬·霍金Stephen Hawking的埃尔德什–培根–萨巴什数为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> 女演员娜塔莉·波特曼Natalie Portman的埃德斯–培根–萨巴什数为11（她的埃尔德什数为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>
以此类推可以进一步扩展，例如，“埃尔德什-培根–萨巴什数”是“埃尔德什-培根数”在大众音乐领域与黑色安息日Black Sabbath乐队的协作距离总和。物理学家斯蒂芬·霍金Stephen Hawking的埃尔德什–培根–萨巴什数为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> 女演员娜塔莉·波特曼Natalie Portman的埃德斯–培根–萨巴什数为11（她的埃尔德什数为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>