The Erdös Number Project

Mathematics and Science Center, Room 346
146 Library Drive
Rochester, MI 48309-4479
(location map)

Computing Your Erdös Number

The first step in computing your Erdös number should be to search the Erdos1 file to see whether you or your coauthors are listed. If you are a coauthor of Paul Erdös, then presumably you know it. If you are a coauthor of a coauthor (i.e., you have Erdös number 2), then you will find your name listed in that file under the Erdös coauthor with whom you have written; do a search with your browser. If that doesn’t work, then search for your coauthors in that file; if you find one, then your Erdös number is 3 and you have the path. If this fails, then read on:

If you would like help in determining your Erdös numberwrite us and we’ll do our best to find a short path of coauthorships (no guarantees, but we have pretty good data and automated search methods). If you have published a paper reviewed in Mathematical Reviews  (MathSciNet), we should be able to find you (send us a complete name and cite a publication or two). If not, you’ll need to send the full names (and cite a publication or two, if possible) of your mathematical coauthors. Much applied mathematics, operations research, theoretical physics, mathematical economics, and computer science is included in MR, as well as pure mathematics.

It’s probably much more fun, however, for you to try to find the links yourself, using MathSciNet if your institution has access. (If it doesn’t, then bug them to subscribe!)

Actually Mathematical Reviews provides an even easier method. MathSciNet will automatically find a path in their database from you to Paul Erdös, or between any two people you wish (there is a special button for selecting Paul Erdös as one end of the path). Both the names of the authors on the path and the (clickable) Mathematical Review numbers of the joint papers are displayed. You can access this collaboration distance calculator even if you do not have access to MathSciNet. See their help page about this for more information. The enhanced facilities of MathSciNet now also allow you to find all the coauthors of any given author. One drawback of the MR system is that it considers all jointly authored works as providing legitimate links, even articles such as obituaries, which are not really joint research. If the path MR gives you contains a suspect link like this, you might try doing the search in the other direction — the algorithm is not symmetric. Other workarounds are possible, and you can also contact us for help. (If you want to give the MathSciNet path-finder a workout, ask for the path from Arturo Robles to Karen L. Thompson, or vice versa. Most paths will be shorter than this.)

Other websites with catalogs of papers and authors have similar pathfinders, such as one from

Once you know your Erdös number, you can use it in various ways, such as your license plate number.

Remember, the distribution of Erdös numbers is such that almost every mathematician with a finite Erdös number has a number of less than 8—only about 2% are higher, and none is more than 15. See our “Facts about Erdös Numbers and the Collaboration Graph” page for more details. People in other sciences or even social sciences may also have small Erdös numbers. My brother (a physician with only one publication) has an Erdös number of at most 9. An author in the MathSciNet database, Mutt, is a computer with an Erdös number of 2. We’ve even heard about a horse who claimed to have an Erdös number of 3. And by all means, check out this cartoon. On a related note, in the spring of 2004, a consultant in Ann Arbor, Michigan, who has an Erdös number of 4 auctioned off his services on eBay, advertising that the winner would obtain Erdös number 5 upon successful completion of work leading to a publication. For further information on this, see William Tozier’s article in Science News.

Finally, there is the issue of which kind of Erdös number to use. Our data are for Erdös numbers of the first kind, where a paper with k authors gives rise to C(k,2) edges. (For example, if Tom, Dick, and Harry wrote a joint paper, then there are edges between Tom and Dick, between Dick and Harry, and between Harry and Tom.) Purists would insist that only papers with two authors should count. It might be a bit harder to compute these Erdös numbers of the second kind by hand.

This page was last updated on June 6, 2020.