Sophus Lie and Harmony in Mathematical Physics, on the 150th Anniversary of His Birth

  • Nail H. Ibragimov


“The extraordinary significance of Lie’s work for the general development of geometry can not be overstated; I am convinced that in years to come it will grow still greater”—so wrote Felix Klein [13] in his nomination of the results of Sophus Lie on the group-theoretic foundations of geometry to receive the N. I. Lobachevskii prize. This prize was established by the Physical-Mathematical Society of the Imperial University of Kazan in 1895 and was to recognize works on geometry, especially non-Euclidean geometry, chosen by leading specialists. The first three prizes awarded were to the following:
  • 1897: S. Lie (Nominator: F. Klein)

  • 1900: W. Killing (Nominator: F. Engel)

  • 1904: D. Hilbert (Nominator: H. Poincaré).


Canonical Variable Invariance Principle Invariant Solution Kepler Problem Goursat Problem 
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  • Nail H. Ibragimov

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