The Erdős number describes the “collaborative distance” between a person and mathematician Paul Erdős, as measured by authorship of (mathematical) papers.
Paul Erdős (1913–1996) was an influential mathematician, who spent a large portion of his later life living out of a suitcase and writing papers with those of his colleagues willing to give him room and board. He published more papers during his life (at least 1,525) than any other mathematician in history.
The idea of the Erdős number was created by the mathematician's friends as a humorous tribute to his enormous output as one of the most prolific modern writers of mathematical papers. The Erdős number has become well known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.
Friedrich Aumayr, e.g. has an Erdős number of at least 6 because of the following sequence of papers:
1. L. Babai, P. Erdős, and S. Selkow
“Random graph isomorphism”
SIAM Journal on Computing 9 (1980) 628
http://dx.doi.org/10.1137/0209047
2. L. Babai, and W. Imrich
“On groups of polyhedral graphs”
Discrete Math. 5 (1973) 101
http://dx.doi.org/10.1016/0012-365X(73)90030-7
3. W. Imrich, and P. F. Stadler
“Minimum Cycle Bases of Product Graphs”
The Australasian Journal of Combinatorics 26 (2002) 233
http://ajc.maths.uq.edu.au/pdf/26/ajc_v26_p233.pdf
4. M. T. Wolfinger, W. A. Svrcek-Seiler, C. Flamm, I. L. Hofacker, and P. F. Stadler
“Efficient computation of RNA folding dynamics”
Journal of Physics A: Math. Gen. 37 (2004) 4731
http://dx.doi.org/10.1088/0305-4470/37/17/005
5. W. A. Svrcek-Seiler, I. C. Gebeshuber, F. Rattay, T. S. Biro, H. Markum
“Micromechanical models for the Brownian motion of hair cell stereocilia”
Journal of Theoretical Biology 193 (1998) 623
http://dx.doi.org/10.1006/jtbi.1998.0729
6. I. C. Gebeshuber, S. Cernusca, F. Aumayr, HP. Winter
“Nanoscopic surface modification by slow ion bombardment”
International Journal of Mass Spectrometry 229 (2003) 27
http://dx.doi.org/10.1016/S1387-3806(03)00252-5