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The algebra theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

The calculus theorem states that an indefinite integration can be reversed by a differentiation and that a definite integral of a function can be computed by using any one of its infinitely many anti-derivatives.

According to Wikipedia, the Fundamental Theorem of Algebra is not fundamental for modern algebra; its name was given at a time in which algebra was basically about solving polynomial equations with real or complex coefficients. In any case, what's is fundamental about these theorems? This is a word useage question more than a math question.