Niels Henrik Abel

Norwegian mathematician who, still in his early twenties and working largely in poverty, proved that the general quintic equation (and every higher degree) cannot be solved by a formula using only radicals, the Abel-Ruffini theorem, settling a question open since the sixteenth century solution of the cubic and quartic. He also did foundational work on elliptic and elliptic-related functions, including an 1827 result on dividing the lemniscate, the figure-eight curve, into equal arcs by straightedge and compass alone, a construction problem in the same family as Gauss's heptadecagon result three decades earlier. Recognition came only after his death from tuberculosis at twenty six; a professorship offer from Berlin arrived days too late.