via Quanta Magazine
Galois’ edict emerged from a mathematical predicament. In the 1500s, mathematicians had studied polynomials like x2 − 2 and x4 − 10×2 + 22. They had tried to find simple formulas that would allow them to calculate the roots of those polynomials — the values of x that make the equation equal zero — but could only find them when the highest exponent was no greater than 4.
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It is unfortunate formatting for the polynomials is lost in the blockquote. Would unicode characters make it more readable?
𝘹² − 𝟤 and 𝘹⁴ − 𝟣𝟢𝘹² + 𝟤𝟤