Erdős number
The median Erdős number among Fields medalists is as low as 3. 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. There are no Fields medalists with Erdős number 1; however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.