"To me, "computing" implies an exact calculation" You are not thinking like a computer scientist: https://en.wikipedia.org/wiki/Computable_number https://en.w

"To me, "computing" implies an exact calculation" You are not thinking like a computer scientist: https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number "Computing" typically means finding an approximation up to an arbitrary degree of precision. As for whether or not that counts as "solving," it is a matter of whether or not you will allow lambda expressions in a solution. Think of this: does the quadratic formula count as a solution to quadratic equations? x^2-2=0 has +/-sqrt(2) as a solution, but only if you allow "sqrt" as part of a "solution." If you wanted a decimal representation of the roots you would have to accept an approximation and you would be using some square root finding algorithm. If you are OK with that situation, why not allow a quintic formula that involves lambda expressions? What makes radicals so special? Remember, all the Abel-Ruffini theorem says is that there is no quintic formula involving only arithmetic and radicals -- it leaves open the possibility of another kind of formula for the quintic.