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第280行： − + − + − 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。+ − + 第296行：
第296行： − 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。+ − + − 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)。+ − + − 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。+ − + − + − 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。+ − + 第336行：
第336行： − + − + − 从2005年到现在的德国总理，她的 erd 数字最多不超过5。+ − + − + − 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。+ − + − + − 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。+ − + − + − 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。+ + +
无编辑摘要
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。
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。
===Biology===
=== Biology 生物学领域 ===
[[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 biology|Computational biologist]] [[Lior Pachter]] has an Erdős number of 2. [[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.
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.
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的埃尔德什数为2。进化生物学家Richard Lenski的埃尔德什数为3，与Lior Pachter和数学家Bernd Sturmfels共同撰写了出版物的每位作者埃尔德什数为2。
===Finance and economics===
=== Finance and economics 财经领域 ===
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 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.
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.
至少有两名诺贝尔经济学奖获得者的埃尔德什数为2：哈里·马可维兹Harry M. Markowitz，（1990）和列昂尼德·坎托罗维奇Leonid Kantorovich（1975）。埃尔德什数为2的其他金融数学家包括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).
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).
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的埃尔德什数为3，其中包括Kenneth J. Arrow（1972），Milton Friedman（1976），Herbert A. Simon（1978），Gerard Debreu（1983），John Forbes Nash，Jr.（1994），James Mirrlees（1996），Daniel McFadden（2000），Daniel Kahneman（2002），Robert J.Aumann（2005），Leonid Hurwicz（2007），Roger Myerson（2007），Alvin E.Roth（2012）和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 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.
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.
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.
一些埃尔德什数低的数学家创立了投资公司，其中包括Axcom Technologies的James B. Ax和Renaissance Technologies的James H. Simons，两者的埃尔德什数均为3。
===Philosophy===
=== Philosophy 哲学领域 ===
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.
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.
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.
由于哲学的本质与数学基础缘由互通，因此它们有很多重叠的地方，许多哲学家都可以使用埃尔德什数。哲学家John P. Burgess的埃尔德什数为2。Barwise和Joel David Hamkins埃尔德什数都为2，他们为哲学做出了大量贡献，但通常被称为数学家。
===Law===
=== Law 法律领域 ===
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]].
===Politics===
=== Politics 政治领域 ===
[[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.
Angela Merkel, Chancellor of Germany from 2005 to the present, has an Erdős number of at most 5.
Angela Merkel, Chancellor of Germany from 2005 to the present, has an Erdős number of at most 5.
从2005年至今的德国总理安格拉·默克尔（Angela Merkel）的埃尔德什数最多为5。
===Engineering===
=== Engineering 工程领域 ===
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 [[California Institute of Technology|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)|RSA]] cryptosystem, all have Erdős number 2.
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.
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.
工程的某些领域，尤其是通信理论和密码学，直接利用了埃尔德什数主要涉及的离散数学。因此，这些领域的从业人员的埃尔德什数低就不足为奇了。例如，加州理工学院电气工程学教授Robert McEliece与埃尔德什本人合作，其埃尔德什数为1。RSA密码系统的发明者，密码学家Ron Rivest，Adi Shamir和Leonard Adleman的埃尔德什数均为2。
===Social network analysis===
=== Social network analysis 社交网络分析领域 ===
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.
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.
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·怀特Douglas R. White通过与图论家弗兰克·哈拉里Frank Harary合作得到埃尔德什数为2。社会学家巴里·韦尔曼Barry Wellman通过与社交网络分析师和统计学家Ove Frank（Harve's的另一位合作者）合作得到了埃尔德什数为3。
===Linguistics===
=== Linguistics 语言学领域 ===
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.
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.
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。
==Impact==
==Impact==