Abel-Ruffini theorem

《代数学引论》 · 第 266 页 · 定理 15（阿贝尔–鲁菲尼）

$n\geq 5$ 时一般方程 $f(x)=x^n+t_1x^{n-1}+\cdots+t_n$ 在 $F(t_1,\dots,t_n)$ 上是不能用根式解的。

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《The foundations of geometry》 · 第 364 页 · Section 15.5「Solving Polynomial Equations by Radicals」，Corollary 15.48 及命名说明

There are no formulas in radicals for the solutions of a general polynomial equation of degree $\geq 5$. […] It took another 250+ years before it was proved that there are no formulas in radicals for the solutions of equations of degree $5$ or higher (that is, Corollary 15.48): this is known as the Abel–Ruffini theorem.