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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.

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。

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

}} 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.

 

==Definition and application in mathematics==

==Definition and application in mathematics==