the quintic…

has been solved. since 1858.

I suspect some of you out there are going to say “there’s no solution to the quintic”, and while you are trying in vain to repeat the Abel-Ruffini theorem.

As it says on “Finally, Ruffini (1799) and Abel (1826) showed that the solution of the general quintic cannot be written as a finite formula involving only the four arithmetic operations and the extraction of roots. By 1832 Galois had developed the theory of Galois groups and described exactly when a polynomial equation is solvable.”

In week201 of Baez’s TWF, he says “Of course, you can solve the quintic if you strengthen your methods.”

Like the Bring radical?

It is a *lie* to say to students “there is no solution to the quintic” without qualifying the statement in regards to the basic operations and radicals. Regrettably, there are no good references for Hiroshi Umemura’s discovery