Erdős number
Paul Erdős (1913–1996) was an influential Hungarian mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues—over 500—working on solutions to outstanding mathematical problems.
He traveled with everything he owned in two suitcases, and would visit mathematicians he wanted to collaborate with, often unexpectedly, and expect to stay with them.
[4][5][6] The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output.
Later it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems.
[7] For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.
[8] Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers (i.e. high proximity).
Any number of additional co-authors is permitted,...but excludes non-research publications such as elementary textbooks, joint editorships, obituaries, and the like.
[10] Fields medalists with Erdős number 2 include Atle Selberg, Kunihiko Kodaira, Klaus Roth, Alan Baker, Enrico Bombieri, David Mumford, Charles Fefferman, William Thurston, Shing-Tung Yau, Jean Bourgain, Richard Borcherds, Manjul Bhargava, Jean-Pierre Serre and Terence Tao.
[19] The table below summarizes the Erdős number statistics for Nobel prize laureates in Physics, Chemistry, Medicine, and Economics.
The remaining columns report the minimum, maximum, average, and median Erdős numbers among those laureates.
Nobel Laureates with an Erdős number of 3 include Enrico Fermi, Otto Stern, Wolfgang Pauli, Max Born, Willis E. Lamb, Eugene Wigner, Richard P. Feynman, Hans A. Bethe, Murray Gell-Mann, Abdus Salam, Steven Weinberg, Norman F. Ramsey, Frank Wilczek, David Wineland, and Giorgio Parisi.
Other financial mathematicians with Erdős number of 2 include David Donoho, Marc Yor, Henry McKean, Daniel Stroock, and Joseph Keller.
Nobel Prize laureates in Economics with an Erdős number of 3 include Kenneth J. Arrow (1972), Milton Friedman (1976), Herbert A. Simon (1978), Gerard Debreu (1983), John Forbes Nash, Jr. (1994), James Mirrlees (1996), Daniel McFadden (2000), Daniel Kahneman (2002), Robert J. Aumann (2005), Leonid Hurwicz (2007), Roger Myerson (2007), Alvin E. Roth (2012), and Lloyd S. Shapley (2012) and Jean Tirole (2014).
[24][25] Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers.
[12] Jon Barwise and Joel David Hamkins, both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.
Roberto Mangabeira Unger, a politician, philosopher, and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with Lee Smolin.
[17] Some fields of engineering, in particular communication theory and cryptography, make direct use of the discrete mathematics championed by Erdős.
[27] Cryptographers Ron Rivest, Adi Shamir, and Leonard Adleman, inventors of the RSA cryptosystem, all have Erdős number 2.
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the h-index captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking.
