Paul Erdös (1913-1996) was a phenomenally prolific mathematician, who combined extraordinary talent with near-total devotion to mathematical research. For most of his career he did not have a conventional position; he was a mathematical nomad who disdained property, power, and even family life as distractions from what he really wanted to do: prove theorems.
Erdös was known as a problem-solver rather than a theory-builder. He solved hard problems in many areas of mathematics, and posed even more. Most of his work was in number theory, set theory, various kinds of combinatorics (including graph theory), analysis, and probability theory. His publication list (still growing with posthumous items) stood at 1525 items in February 2007. Erdös was famous for having many collaborators (511 at last count). This has given rise to the notion of an "Erdös number". All those mathematicians who co-authored a paper or book with Erdös are said to have Erdös number 1; those who have co-authored with someone of Erdös number 1 (but not with Erdös himself) have Erdös number 2; and so on. The Erdös Number Project has various data on the subject; in particular, there are known to be 9779 people with Erdös number at most 2.
Figuring out one's Erdös number used to be a popular pastime with mathematicians, but now it can be done with a few clicks of the mouse; the online version of Mathematical Reviews has a feature called "Collaboration Distance" that produces a path of collaborators, if it exists, between any two authors in the Mathematical Reviews database. While there are no current members of USNA Math Department faculty with Erdös number 1, one former member (Allen Schwenk) has that distinction. Only two current members of the faculty, Prof. Craig Bailey and Assoc. Prof. Vrej Zarikian, have Erdös number 2. On the other hand, many math faculty members have Erdös number 3, and hardly any who have written joint papers have an Erdös number greater than 5.
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