Paul Erdos has (or rather had) an Erdos Number of zero. Everyone else has an Erdos Number equal to one plus the lowest Erdos Number of anyone they have written a mathematical paper with. Consequently, Erdos' co-authors have a number of 1, their co-authors have a number of 2, etc.
Erdos Numbers are amusing because Paul Erdos published papers with so many people - he was the most prolific mathematician of our time - and because mathematicians collaborate so much, hence every mathematician has an Erdos Number. The idea wouldn't work for other fields where people don't connect as much (such as history, perhaps). It does work for similarly promiscuous fields - for example, the Bacon Number in cinema acting.
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