"One question that the Cardano-Ferrari work left unanswered was the algebraic solution of the quintic... as was well known, any fifth-degree equation must have at least one real solution. ...because the graphs of odd-degree equations ...rise ever higher as we move in one direction on the x-axis and fall ever lower as we move in the other direction ...the continuous graph must somewhere cross the x-axis. A similar argument guarantees that any odd-degree polynomial equation has at least one real solution. ...It was the precise formula... that the algebraists who followed Ferrari were seeking. ...A century passed, and another, yet no one could provide a "solution by radicals" ...in spite of the fact that later mathematicians found a transformation to reduce the general quintic to...z5 + pz = qThen... Niels Abel shocked the mathematical world by showing that no "solution by radicals" was possible for fifth- or higher-degree equations. ...Abel's proof ...stands as a landmark in mathematics history."