Erdős Number

Erdős number is the collaborative distance between a mathematician and Paul Erdős, measured in co-authored papers. Erdős himself has number 0; his direct co-authors have number 1; their co-authors (excluding Erdős) have number 2; and so on. The concept, born from the obsessive folklore of 20th-century mathematics, has since been generalized to other fields — most famously the Bacon number in film acting — and has become a playful index of connectivity within intellectual communities.

The Erdős number is more than a curiosity. It is an early instance of using graph-theoretic distance to measure professional proximity, and it prefigures the network-science tools that would later analyze collaboration networks, citation graphs, and social media structures at scale. Barabási has noted that his own Erdős number is 2, a detail that simultaneously asserts his place within mathematical genealogy and suggests that his network-science work transcends pure mathematics. Whether this self-placement is accurate or self-serving is, like most matters of number, a matter of counting.