Definition:Quintic Equation/Historical Note

Historical Note on Quintic Equation
published what he thought was a solution to the quintic equation in $1683$, but pointed out that it was fallacious.

tried and failed to solve it, but he did develop new methods for solving the quartic, as did.

consolidated everything that was known about solutions to equations of degree less than $5$ in his of $1770$.

He noted that the usual attempt to find a solution by permutation of roots fails for the quintic.

In $1799$ published his $2$-volume  in which he tried to prove its insolubility, but he appeared to be unsuccessful.

In $1810$ he had another unsuccessful go, and again in $1813$.

Despite his lack of success, he had in fact made significant progress, despite this not having been realised at the time.

In $1824$, finally succeeded, although his proof was needlessly lengthy and contained a small mistake.

This was finally patched up in $1879$ by, whose proof, while based on 's ideas, was simple and rigorous.

The problem still remained whether certain particular quintics could be solved by radicals.

The techniques for answering this question were cracked wide open by the work of.