Titlebook: Riemann, Topology, and Physics; Michael Monastyrsky Book 1999Latest edition Springer Science+Business Media New York 1999 History of Mathe

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Posthumous Fatesidered perhaps his main contribution to science: the theory of Abelian integrals, Riemann surfaces, and Riemannian geometry. There are many objective and subjective reasons that explain this circumstance. His views on geometry were, of course, completely novel for a wide circle of mathematicians. O

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Systems with Spontaneous Symmetry Breakingenon that unifies such physically different systems as liquid crystals, magnetism, and superfluid helium, is called . It underlies many contemporary concepts in the theory of elementary particles, the theory of phase transitions, and a number of problems of cosmology.

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Topological Particlesills equation for the group SO(3) and additional scalar fields (the fields of Goldstone- Higgs).. These solutions had one topological charge which was interpreted as a “magnetic charge.” G.’t Hooft suggested calling them magnetic monopoles. The name was to symbolize the deep commonality of the newly

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Soliton Particlesry student who has taken a course in differential equations will remember that the only differential equations for which a general solution is given in closed form are linear differential equations with constant coefficients. As often occurs in life, however, exceptions to the rule are sometimes are

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Knots, Links, and Physics of topology, which flourished in the late 1920’s and early 1930’s, withered and faded away after the war. Such things happen to entire subjects as well as to people. It was not that there were no outstanding unsolved problems left in knot theory. For example, the following natural problem remained

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