D'Alembert's proof of the fundamental theorem of algebra
Copyright policy )D'Alembert's proof of the fundamental theorem of algebra
This paper examines d'Alembert's original 1746 publication that attempts to prove the Fundamental Theorem of Algebra, as well as a somewhat different version of the proof that appeared in~1754. Both d'Alembert's work and the views of several commentators are discussed. On the one hand, the author considers the basic soundness of d'Alembert's proof to have been underrated by many. On the other hand, he considers several other, more favorable, commentators (1)~to underestimate what is needed to install proper rigor into the proof and/or (2)~to deviate too far from d'Alembert's line of thought in patching up the proof. The article outlines a rigorous argument that the author feels adheres more closely to d'Alembert's ideas.
- Purchase College United States
- SUNY College at Oswego United States
Algebraic functions, History, Mathematics(all), fundamental theorem of algebra, Fundamental theorem of algebra, d'Alembert, Algebraic equations, algebraic functions, D'Alembert, Algebraic functions and function fields in algebraic geometry, algebraic equations, History of mathematics in the 18th century, History of field theory
Algebraic functions, History, Mathematics(all), fundamental theorem of algebra, Fundamental theorem of algebra, d'Alembert, Algebraic equations, algebraic functions, D'Alembert, Algebraic functions and function fields in algebraic geometry, algebraic equations, History of mathematics in the 18th century, History of field theory
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