The Renaissance mathematician who first published a solution to the cubic equation in “Ars Magna” was Gerolamo Cardano. Published in 1545, his book presented algebraic methods for solving cubic equations and also included Lodovico Ferrari’s solution of the quartic equation.
Cardano did not discover every ingredient himself. Scipione del Ferro had found a method for a particular class of cubics, and Niccolò Tartaglia later developed and communicated another version. Cardano learned Tartaglia’s method in 1539, promising not to publish it until Tartaglia had released his own work. After learning of del Ferro’s earlier discovery, Cardano published the results in “Ars Magna,” crediting both del Ferro and Tartaglia.
The book’s importance is therefore publication and systematic exposition, not exclusive invention. Cardano extended the methods to multiple forms of cubic equations and showed how general equations could be reduced to simpler ones. The formulas sometimes produced square roots of negative numbers, an issue later clarified through the development of complex-number mathematics. Tartaglia’s contribution was essential, but Cardano is the canonical answer to this wording.