History — Tartaglia, Cardano and the cube formula
Quadratic equations were already solved by the Babylonians (around 1800 BC), but for cubic ones one had to wait for the sixteenth-century Italy. Around 1535, Niccolò Fontana known as Tartaglia (“the stammerer”, after a wound suffered as a child) found a method for solving cubics of the type . He communicated it under an oath of secrecy to Gerolamo Cardano, who nevertheless published it in his Ars Magna (1545). This gave rise to one of the most famous controversies in the history of mathematics.
The Ars Magna is a revolutionary book for several reasons: it not only contained the resolving formula for cubics and (thanks to his pupil Ludovico Ferrari) also for quartics, but — above all — it forced one to reckon with certain “roots of negative numbers” that appeared in the calculations. It is in these pages that, for the first time, algebra meets the imaginary numbers (Boyer, ch. 13). A beautiful account of the whole affair can be found in Dunham (ch. 6).
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Topics: Quadratic equations
Concepts: Cubic equation · Imaginary numbers
People: Gerolamo Cardano · Lodovico Ferrari · Niccolò Tartaglia