Geodesic
On solvability and unsolvability of equations in explicit form
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 4, pp. 661-736

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In this survey the classical results of Abel, Liouville, Galois, Picard, Vessiot, Kolchin, and others on the solvability and unsolvability of equations in explicit form are discussed. The one-dimensional topological version of Galois theory is presented in detail (this version describes topological obstructions to the representability of functions by quadratures). 
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     author = {A. G. Khovanskii},
     title = {On solvability and unsolvability of equations in explicit form},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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A. G. Khovanskii. On solvability and unsolvability of equations in explicit form. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 4, pp. 661-736. http://geodesic.mathdoc.fr/item/RM_2004_59_4_a2/