Israel Gelfand - Work

Work

Gelfand is known for many developments including:

  • the book Calculus of Variations (1963), which he co-authored with Sergei Fomin
  • the Gelfand representation in Banach algebra theory;
  • the Gelfand–Mazur theorem in Banach algebra theory;
  • the Gelfand–Naimark theorem;
  • the Gelfand–Naimark–Segal construction;
  • Gelfand–Shilov spaces
  • the Gelfand–Pettis integral;
  • the representation theory of the complex classical Lie groups;
  • contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I.N. Bernstein and S.I. Gelfand);
  • contributions to distribution theory and measures on infinite-dimensional spaces;
  • the first observation of the connection of automorphic forms with representations (with Sergei Fomin);
  • conjectures about the Atiyah–Singer index theorem;
  • Ordinary differential equations (Gelfand–Levitan theory);
  • work on calculus of variations and soliton theory (Gelfand–Dikii equations);
  • contributions to the philosophy of cusp forms;
  • Gelfand–Fuks cohomology of foliations;
  • Gelfand–Kirillov dimension;
  • integral geometry;
  • combinatorial definition of the Pontryagin class;
  • Coxeter functors;
  • general hypergeometric functions;
  • Gelfand - Tsetlin patterns;
  • and many other results, particularly in the representation theory for the classical groups.

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    “Do not put off your work until tomorrow and the day after. For the sluggish worker does not fill his barn, nor the one who puts off his work; industry aids work, but the man who puts off work always wrestles with disaster.”
    —Hesiod (c. 8th century B.C.)

    “I am from time to time congratulating myself on my general want of success as a lecturer; apparent want of success, but is it not a real triumph? I do my work clean as I go along, and they will not be likely to want me anywhere again. So there is no danger of my repeating myself, and getting to a barrel of sermons, which you must upset, and begin again with.”
    —Henry David Thoreau (1817–1862)

    “In the beginning, I wanted to enter what was essentially a man’s field. I wanted to prove I could do it. Then I found that when I did as well as the men in the field I got more credit for my work because I am a woman, which seems unfair.”
    —Eugenie Clark (b. 1922)