Paul J. Kelly

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Paul Joseph Kelly (born June 26, 1915 in Riverside , California , † July 10, 1995 in Santa Barbara , California) was an American mathematician .

Life

Kelly studied at the University of California, Los Angeles (with a bachelor's and master's degree) and received her doctorate in 1942 from the University of Wisconsin under Ralph Langer ( On isometric transformations ). During the Second World War he was a lieutenant in the US Air Force for three years. In 1946 he became an instructor at the University of Southern California and from 1949 he was at the University of California, Santa Barbara (UCSB), where he became a professor and was the rest of his career until his retirement in 1982. From 1957 to 1962 he headed the mathematics faculty and was responsible for installing the graduate program in mathematics.

In 1955/56 he was at the Institute for Advanced Study .

plant

He dealt mainly with geometry, topology and graph theory . He also published with Paul Erdős .

In the theory of convex bodies, he proved a theorem, proven by Tommy Bonnesen and Werner Fenchel in the case of n-dimensional Euclidean space, about the equivalence of convex bodies of constant width with whole subsets (Entire Subsets) for the n-dimensional Minkowski space. In 1945 he proved a special case of a conjecture by Stanislaw Ulam about the question of when isometries of product sets of metric spaces E × E and F × F result in those of E and F.

He and Stanislaw Ulam originated Reconstruction conjecture for graphs (graph reconstruction conjecture). It says that a graph G with at least three nodes is uniquely determined by the subgraphs in which one node was removed from G. Kelly proved the guess for trees. In general, the guesswork is open.

He published a monograph on projective geometry (with Herbert Busemann ) and wrote school books on geometry. He also translated, with Lewis Walton, the book on convex figures by Vladimir Boltjanski and Isaak Jaglom from Russian.

Fonts

  • with Herbert Busemann Projective Geometry and Projective Metrics , Academic Press 1953, Dover 2006
  • with Max L. Weiss Geometry and Convexity: a study in mathematical methods , Wiley 1979, Dover 2009
  • with Gordon Matthews The non-Euclidean, hyperbolic plane: Its structure and consistency , Springer Verlag 1981
  • with Norman E. Ladd Geometry , Chicago: Scott, Foresman 1965
  • with Norman E. Ladd Analytic Geometry , Scott, Foresman 1968
  • with Ernst G. Strauss Elements of Analytic Geometry , Glenview: Scott, Foresman 1970
  • with Ernst G. Strauss Elements of analytic geometry and linear transformations , Scott, Foresman 1970

Web links

Individual evidence

  1. ↑ Notices of the American Mathematical Society, Volume 46 (1999), Issue 6, page 686
  2. ↑ Bonnesen, Fennel: Theory of the convex body 1934
  3. ↑ The addition of any point increases its diameter
  4. ↑ Kelly On Minkowski bodies of constant width , Bulletin AMS, Volume 55, 1949, pp. 1147-1150, online
  5. ↑ Formulated by this for homeomorphy
  6. ↑ Kelly On isometries of square sets , Bulletin AMS, Volume 51, 1945, pp. 960-963, online . Continued in On isometries of product sets , Bulletin AMS, Volume 54, 1948, pp. 723-727, online
  7. ↑ Kelly, A congruence theorem for trees, Pacific J. Math., Vol. 7, 1957, pp. 961-968.
personal data
SURNAME Kelly, Paul J.
ALTERNATIVE NAMES Kelly, Paul Joseph (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 26, 1915
PLACE OF BIRTH Riverside , California
DATE OF DEATH July 10, 1995
Place of death Santa Barbara , California