Gian-Carlo Rota

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Gian-Carlo Rota

Gian-Carlo Rota (born April 27, 1932 in Vigevano , Italy ; † April 18, 1999 in Cambridge , Massachusetts, USA ) was an Italian-American mathematician who dealt with analysis, probability theory and especially combinatorics . He is considered the founder of modern combinatorics.

life and work

Rota's father was a civil engineer and architect and, as a staunch anti-fascist, had to hide in northern Italy from the Italian fascists, on whose death list he was at the end of World War II. One of his uncles was a screenwriter for Federico Fellini . Rota and his family first emigrated to Ecuador .

In 1950 Rota went to study in the USA . From 1950 to 1953 he studied at Princeton University (Bachelor's degree summa cum laude), in 1954 at Yale University (Master's degree in 1954), where he took part in the seminar from which the well-known textbook Linear Operators by Nelson Dunford and Jacob was taken T. Schwartz emerged . In 1956 he received his doctorate under Jacob T. Schwartz at Yale University on differential equations ( extension theory of differential operators ). In 1956/7 he was a post-doc at the Courant Institute of Mathematical Sciences of New York University and then Benjamin Pierce Instructor at Harvard University until 1959 .

From 1959 he was at the Massachusetts Institute of Technology , where he stayed for the rest of his career, except for two years from 1965 to 1967 at Rockefeller University . He was a professor of applied mathematics at MIT and, from 1972, also of philosophy. In 1962 he became a Sloan Research Fellow .

In addition, he worked for the Los Alamos National Laboratory (as a consultant from 1966 to 1971 and finally as a senior fellow of the laboratory where he lectured), where his friend Stanislaw Ulam also worked. From 1966 to 1971 he was a consultant at the Rand Corporation and from 1969 to 1973 at Brookhaven National Laboratory . He also worked for the National Security Agency (NSA), whose Medal of Distinguished Service he received in 1992.

In the 1970s he put the Umbral calculus with Steven Roman on a strict foundation.

He died unexpectedly of a heart attack at home while he was sleeping.

Rota first worked on functional analysis and differential equations and came to combinatorics via ergodic theory . In 1964 he published a work On the Foundations of Combinatorial Theory which completely renewed the field of combinatorics, previously viewed predominantly as a barely interconnected collection of mathematical tricks, and embed it in the mainstream of mathematics. Nine further works appeared under the same series title from 1970 to 1972 and 1992. In 1988 he received the Leroy P. Steele Prize from the American Mathematical Society . In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Recent progress in combinatorics ) and in 1970 in Nice ( Combinatorial theory-old and new ).

He was married to Teresa Rondón since 1956 (divorced in 1980). In addition to Italian and English, Rota also spoke fluent French and Spanish. He also had philosophical interests, wrote philosophical essays and was a member of several philosophical societies such as the Heidegger Circle and the Husserl Circle.

In 1982 he became a member of the National Academy of Sciences and was also a member of the American Academy of Arts and Sciences (1963), the Argentine Academy of Sciences, the Institute of Mathematical Statistics. From 1995 to 1997 he was Vice President of the American Mathematical Society . Rota has received several honorary doctorates (University of Strasbourg, L´Aquila, Bologna, Brooklyn Polytechnical University)

Richard P. Stanley is one of his PhD students .


  • with Garrett Birkhoff : Ordinary Differential Equations. Ginn, Boston MA 1962 (4th edition. Wiley, New York NY et al. 1989, ISBN 0-471-50020-8 ).
  • with Henry H. Crapo: On the foundations of combinatorial theory. Combinatorial geometries. Preliminary edition. MIT Press, Cambridge MA et al. 1970, ISBN 0-262-53016-3 (Preliminary edition, 2nd printing. Ibid. 1976).
  • with Peter Doubilet and Joel Stein: On the foundations of combinatorial theory: IX Combinatorial methods in invariant theory. In: Studies in Applied Mathematics. Vol. 53, 1974, ISSN  0022-2526 , pp. 185-216, online (PDF; 1.52 MB) .
  • with Peter Doubilet and others: Finite operator calculus. Academic Press, New York NY et al. 1975, ISBN 0-12-596650-4 .
  • with Joseph PS Kung: The invariant theory of binary forms. In: Bulletin of the American Mathematical Society. NS Vol. 10, No. 1, January 1984, ISSN  0273-0979 , pp. 27-85, (PDF; 4.63 MB).
  • Mathematics, Philosophy and Artificial Intelligence. A dialogue with Gian-Carlo Rota and David Sharp. In: Los Alamos Science. No. 15, Spring / Summer 1985, ISSN  0273-7116 , pp. 94-104, online (PDF; 2.59 MB) .
  • with Mark Kac and Jacob T. Schwartz : Discrete Thoughts. Essays on mathematics, science and philosophy. Birkhäuser, Boston MA 1986, ISBN 0-8176-3285-9 (Revised and corrected edition. Ibid 1992, ISBN 3-7643-3636-6 ; Reprint of the 1992 2nd edition, revised and corrected edition. Ibid 2008, ISBN 978- 0-8176-4774-2 ).
  • as editor with Ira Gessel: Classic Papers in Combinatorics. Birkhäuser, Boston et al. 1987, ISBN 3-7643-3364-2 (some of Rota's own work are also reprinted here).
  • with Frank D. Grosshans and Joel A. Stein: Invariant theory and superalgebras (= Regional Conference Series in Mathematics. Vol. 69). American Mathematical Society, Providence RI 1987, ISBN 0-8218-0719-6 .
  • The Lost Café. In: Stanislaw Ulam 1909–1984 (= Los Alamos Science. No. 15 = Special Issue). Los Alamos National Laboratory, Los Alamos NM 1987, pp. 23-32, online (PDF; 1.51 MB) .
  • Joseph P. Kung (Ed.): Gian-Carlo Rota on combinatorics. Introductory papers and commentaries. Birkhäuser Verlag, Boston MA et al. 1995, ISBN 3-7643-3713-3 .
  • Light shadows: remembrances of yale in the early fifties. In: Mathematical Intelligencer. Vol. 18, No. 3, 1996, ISSN  0343-6993 , pp. 44-51, doi : 10.1007 / BF03024310 .
  • Indiscrete Thoughts. Birkhäuser, Boston et al. 1997, ISBN 3-7643-3866-0 (essays).
  • with Daniel A. Klain : Introduction to geometric probability. Cambridge University Press, Cambridge et al. 1997, ISBN 0-521-59362-X .
  • The Many Lives of Lattice Theory. In: Notices of the American Mathematical Society. Vol. 44, No. 11, December 1997, ISSN  0002-9920 , pp. 1440-1445, (PDF; 112 KB).
  • Jean G. Dhombres, Joseph PS Kung, Norton Starr (Eds.): Gian-Carlo Rota on analysis and probability. Selected papers with commentaries. Birkhäuser, Boston MA et al. 2003, ISBN 3-7643-4275-7 .
  • with Joseph PS Kung and Catherine H. Yan: Combinatorics. The Rota Way. Cambridge University Press, Cambridge et al. 2009, ISBN 978-0-521-88389-4 .


Web links

Notes and individual references

  1. His sister Ester Rota Gasperoni reports on the family's escape in two books: Orage sur le lac. École des Loisirs, Paris 1995, ISBN 2-211-03134-X and L'arbre de Capulies. ibid 1996, ISBN 2-211-03858-1 .
  2. Communications on Pure and Applied Mathematics. 1958.
  3. ^ On the foundations of combinatorial theory I. Theory of Möbius Functions. In: Journal of Probability Theory and Allied Areas. Vol. 2, No. 4, 1964, ISSN  0044-3719 , pp. 340-368, doi : 10.1007 / BF00531932 .