The Unsolvability of the Quintic

J. J. P. Veerman ()
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J. J. P. Veerman: Portland State University

Chapter Chapter 15 in Numbers from all Angles, 2026, pp 321-345 from Springer

Abstract: Abstract The roots of polynomials of degree less than 5 can be determined exactly by using only multiplication, addition, and their inverses, and the nth root operation $$z\rightarrow z^{1/n}$$z→z1/n. This is called solving by radicals. For degree 5 polynomials, the situation unexpectedly changes: the Abel-Ruffini theorem says that no such general solution is possible! The traditional proofs of this type of theorem use Galois theory. Excellent references are [61, 111].

Date: 2026
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DOI: 10.1007/978-3-032-10000-9_15

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