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

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

Education and career

Kelly was born in

Riverside, California Riverside is a city in and the county seat of Riverside County, California, United States, in the Inland Empire metropolitan area. It is named for its location beside the Santa Ana River. It is the most populous city in the Inland Empire an ...

. 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 land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

before moving to the

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

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. More specifically, it is a function whose domain and range are sets of points — most often ...

s under the supervision of

Stanislaw Ulam Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...

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

United States Air Force The United States Air Force (USAF) is the air service branch of the United States Armed Forces, and is one of the eight uniformed services of the United States. Originally created on 1 August 1907, as a part of the United States Army Signal ...

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 C ...

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, Santa Barbara, California with 23,196 undergraduate ...

in 1949, and was chair there from 1957 to 1962. At UCSB, his students included

Brian Alspach Brian Roger Alspach is a mathematician whose main research interest is in graph theory. Alspach has also studied the mathematics behind poker, and writes for ''Poker Digest ''and ''Canadian Poker Player'' magazines. Biography Brian Alspach was bo ...

(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. M. ...

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, including only woody plants with secondary growth, plants that are u ...

. 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