Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in geometry and graph theory.
[1][2][3] He spent the rest of the war years serving in the United States Air Force as a First Lieutenant, before returning to academia with a teaching appointment at the University of Southern California in 1946.
[1][2] At UCSB, his students included Brian Alspach (through whom he has nearly 30 academic descendants) and Phyllis Chinn.
[1][2] Kelly is known for posing the reconstruction conjecture with his advisor Ulam, which states that every graph is uniquely determined by the ensemble of subgraphs formed by deleting one vertex in each possible way.
[5] He is the coauthor of three textbooks: Projective geometry and projective metrics (1953, with Herbert Busemann),[6] Geometry and convexity: A study in mathematical methods (1979, with Max L. Weiss),[7] and The non-Euclidean, hyperbolic plane: Its structure and consistency (1981, with Gordon Matthews).