Robert Hermann (mathematician)

For other people named Robert Herman, see Robert Herman (disambiguation).

Robert Hermann (born April 28, 1931 in Brooklyn) is an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between vector bundles on Riemannian manifolds and gauge theory in physics, before these interconnections became "common knowledge" among physicists in the 1970s.

Hermann studied in Paris and at Princeton University, where he attended lectures by Charles Ehresmann and where in 1955 under Donald Spencer he received his PhD with thesis The Differential geometry of homogeneous spaces. He taught at Rutgers University, which he left in 1975 and then did research primarily with financial support from the Ames Research Center of NASA.[1] In the academic year 1969/1970 he was at the Institute for Advanced Study.

Following the French school of Élie Cartan, Hermann published numerous books on differential geometry and Lie group theory and their applications to differential equations, integrable systems, control theory, and physics. Most of these books were published in Brookline, Massachusetts by the Mathematical Science Press, which Hermann himself founded. He also worked on the history of differential geometry and Lie group theory and edited, with extensive new commentary, the work of Sophus Lie,[2] Gregorio Ricci-Curbastro and Tullio Levi-Civita,[3] Felix Klein's Vorlesungen über Mathematikgeschichte,[4] Élie Cartan,[5] Georges Valiron[6] and the contributions to invariant theory by David Hilbert.[7]


In the Mathematical Science Press, Brookline, Massachusetts:


  1. Letters by Hermann published in "Cartanian geometry, nonlinear waves and control theory“ 1979
  2. Sophus Lie's 1884 differential invariant paper, 1976; Sophus Lie's 1880 transformation group paper, 1975
  3. Ricci and Levi-Civita's tensor analysis paper, 1975
  4. The Development of mathematics in the 19th Century, 1979
  5. Geometry of Riemannian Spaces, 1983
  6. The geometric theory of ordinary differential equations, 1984; Classical differential geometry of curves and surfaces, 1986
  7. Hilbert's Invariant Theory Papers, 1978
  8. 1 2 Chernoff, P. R.; Marsden, J. E. (1973). "Review: Lie Algebras and Quantum Mechanics and Vector Bundles in Mathematical Physics and their relationship to the other works of Robert Hermann". Bull. Amer. Math. Soc. 79 (6): 1150–1162. doi:10.1090/s0002-9904-1973-13356-7.
  9. Givens, Clark R.; Millman, Richard S. (1982). "Review: Cartanian geometry, nonlinear waves, and control theory". Bull. Amer. Math. Soc. (N.S.). 6 (3): 467–478. doi:10.1090/s0273-0979-1982-15019-4.
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