So-called Fundamental Theorem of Algebra

AI Thread Summary
The discussion centers on the evolving perception of the Fundamental Theorem of Algebra, with a reference to Bell's 1934 critique suggesting it is losing significance in favor of Kronecker's approach. Participants question the differences between the traditional understanding of the theorem and Kronecker's treatment, which emphasizes a more rigorous foundation. Bell's use of "so-called" implies skepticism about the theorem's status and relevance in contemporary mathematics. The conversation highlights a shift in mathematical focus, indicating a potential departure from classical interpretations. Overall, the dialogue reflects ongoing debates about the rigor and relevance of foundational mathematical concepts.
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This came up in one of my readings:

"Neither the so-called fundamental theorem [of algebra] itself nor its classical proof by the theory of functions of a complex variable is as highly esteemed as it was a generation ago, and the theorem seems to be on its way out of algebra to make room for something closer to what Kronecker imagined" (Bell, 1934, p. 605).

My schooling taught "the" fundamental theorem of algebra. What is different about Kronecker's treatment? What is Bell disputing when he says it is "so-called"?

Bell, E. T. (1934) The place of rigor in mathematics. The American Mathematical Monthly, 41(10), 599-607.
 
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