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We discuss Abel’s theorem, that says a general quintic equation cannot be solved by radicals. We do this by showing that if a polynomial can be solved by radicals over a field of characteristic 0 then its roots lie in a solvable Galois extension. We give some examples of degree 5 polynoimals whose roots do not generate a solvable extension.
This video is part of a lecture course by Richard Borcherds from 2020-21.