Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

Education and career

Kelly was born in

Riverside, California Riverside is a city in and the county seat of Riverside County, California, United States. It is named for its location beside the Santa Ana River. As of the 2020 census, the city has a population of 314,998. It is the most populous city in th ...

. He earned bachelor's and master's degrees from the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...

before moving to the

University of Wisconsin–Madison The University of Wisconsin–Madison (University of Wisconsin, Wisconsin, UW, UW–Madison, or simply Madison) is a public land-grant research university in Madison, Wisconsin, United States. It was founded in 1848 when Wisconsin achieved st ...

for doctoral studies; he earned his Ph.D. in 1942 with a dissertation concerning

geometric transformation In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such as preserving distances, angles, or ratios (scale). More specifically, it is a function wh ...

s under the supervision of

Stanislaw Ulam Stanislav and variants may refer to: People *Stanislav (given name), a Slavic given name with many spelling variations (Stanislaus, Stanislas, Stanisław, etc.) Places * Stanislav, Kherson Oblast, a coastal village in Ukraine * Stanislaus County, ...

. He spent the rest of the war years serving in the

United States Air Force The United States Air Force (USAF) is the Air force, air service branch of the United States Department of Defense. It is one of the six United States Armed Forces and one of the eight uniformed services of the United States. Tracing its ori ...

as a First Lieutenant, before returning to academia with a teaching appointment at the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

in 1946. He moved to the

University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, United States. Tracing its roots back to 1891 as an ...

in 1949, and was chair there from 1957 to 1962. At UCSB, his students included Brian Alspach (through whom he has nearly 30 academic descendants) and Phyllis Chinn. He retired in 1982.

Contributions

Kelly is known for posing the

reconstruction conjecture Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to KellyKelly, P. J.A congruence theorem for trees ''Pacific J. Math.'' 7 (1957), 961–968. and Ulam.Ulam, S. ...

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. He also proved a special case of this conjecture, for

trees In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only p ...

. He is the coauthor of three textbooks: ''Projective geometry and projective metrics'' (1953, with

Herbert Busemann Herbert Busemann (12 May 1905 – 3 February 1994) was a German-American mathematician specializing in convex and differential geometry. He is the author of Busemann's theorem in Euclidean geometry and geometric tomography. He was a member of ...

), ''Geometry and convexity: A study in mathematical methods'' (1979, with Max L. Weiss), and ''The non-Euclidean, hyperbolic plane: Its structure and consistency'' (1981, with Gordon Matthews).

Selected articles

*with David Merriell: *with E. G. Straus: * * *

References

{{DEFAULTSORT:Kelly, Paul Joseph 1915 births 1995 deaths 20th-century American mathematicians Graph theorists University of California, Los Angeles alumni University of Wisconsin–Madison alumni University of Southern California faculty University of California, Santa Barbara faculty Mathematicians from California