Which mathematician proposed the idea that a polynomial equation of degree n has exactly n roots?

The assertion that a polynomial equation of degree n has exactly n roots is rooted in the Fundamental Theorem of Algebra, which was significantly developed by Carl Friedrich Gauss. Gauss's work demonstrated that every non-constant polynomial function with complex coefficients has as many roots (counting multiplicities) as its degree. This means that for a polynomial of degree n, one can expect to find precisely n roots in the set of complex numbers, which encapsulates real and imaginary solutions.

This theorem is critical because it implies that not only do the roots exist, but one also can expect a complete set of solutions within the complex number system. Gauss’s contributions laid the groundwork for many developments in algebra and complex analysis, establishing a foundational understanding of polynomials.

The other mathematicians listed contributed to various fields of mathematics but did not specifically articulate or prove the concept of polynomial roots in the manner that Gauss did.