The Fundamental Theorem of Algebra

John W. Dawson
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John W. Dawson: Penn State York

Chapter Chapter 8 in Why Prove it Again?, 2015, pp 59-91 from Springer

Abstract: Abstract The Fundamental Theorem of Algebra (stated below) provides an ideal case study for illustrating the roles of alternative proofs in mathematical practice. Like the Pythagorean Theorem, the Fundamental Theorem of Algebra has been proved in many different ways since its enunciation by Euler in 1739. Unlike the Pythagorean Theorem, however, early attempts to prove the Fundamental Theorem of Algebra are not shrouded in the mists of antiquity, so we know how the adequacy of those attempts was evaluated by mathematicians of the time. We can see how criticisms of earlier efforts to prove the theorem led to alternative proof strategies, and we can analyze why the proof given by Gauss in his 1799 inaugural dissertation was the first to be accorded general acceptance, though it too would later be deemed not fully rigorous.

Keywords: Fundamental Theorem; Complex Root; Symmetric Polynomial; Real Coefficient; Complex Coefficient (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-17368-9_8

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