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第23行： − + − 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。+ − + − + − 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。
→Overview
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 graph]]s can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.
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.
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.
埃尔德什数的概念最初是由数学家的朋友们提出来的，以赞扬保罗·埃尔德什的巨大成就。后来，它演变为研究数学家如何通过合作来解决问题的的工具而受到重视。有几个项目专门通过使用埃尔德什数作为代理来研究人员之间的连通性。例如，埃尔德什合作图可以告诉我们作者是如何聚集在一起的，每篇论文的共同作者数量随时间变化或新理论的产生又是如何传播的。
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. 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.
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. 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.
多项研究表明，领先的数学家往往具有极低的埃尔德什数。费尔兹奖Fields Medalists的埃尔德什中位数是3。只有7,097名（拥有合作经历的数学家中约5％）的埃尔德什数为2或更低。随着时间的流逝，低埃尔德什数的数学家因死亡而无法进行协作，最小埃尔德什数（仍然存在）必然会增加。即使历史人物仍可能一直具有较低的埃尔德什数。例如，印度著名数学家Srinivasa Ramanujan的埃尔德什数仅为3（通过G. H. Hardy，Erdős数为2），尽管Ramanujan去世时保罗·埃尔德什只有7岁。
==Definition and application in mathematics==
==Definition and application in mathematics==