The Fundamental Theorem of Algebra View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2015

AUTHORS

John W. Dawson

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. More... »

PAGES

59-91

Book

TITLE

Why Prove it Again?

ISBN

978-3-319-17367-2
978-3-319-17368-9

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-17368-9_8

DOI

http://dx.doi.org/10.1007/978-3-319-17368-9_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018888101


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