What is the Erdős number?

Paul Erdős (1913–1996) was a hugely influential mathematician who spent a large portion of his later life writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems.

The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output. If person A collaborated directly with Erdős, then A would have the Erdős number 1; if B collaborated with A (but not directly with Erdős), then B would have the Erdős number 2; if C collaborated with B (but not directly with Erdős or anyone with Erdős number 1), then C would have the Erdős number 3... and so on. The higher the number, the greater the separation between the person and Erdős himself.

What started as a very specific idea in relation to just one mathematician has become much more general, not only in the world of mathematics and but also in other fields of research. The Erdős-number idea has gained prominence as a tool to study how individuals cooperate in order to find the answers to unsolved problems. Several projects are devoted to studying connectivity among researchers, using the Erdős-number approach. For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per scientific paper evolves over time, or how new theories propagate.