Mathematical challenges for a better living
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Tartaglia was an abacus master in Verona in the early sixteenth century. This profession involved teaching mathematics, but also giving expert advice in various fields such as accounting and architecture, or carrying out topographical surveys. Aware of his skill, many people turned to him for answers to mathematical problems, whether for self-interested reasons or simply out of intellectual curiosity.
Some, highly skilled in the art of calculation, delighted in challenging him, and Tartaglia took pleasure in responding to these requests. This kind of mathematical challenge was very much in vogue in the early Italian Renaissance; its rules were modeled on those of chivalric tournaments. One of the protagonists would send several problems to his rival, who then had to answer them within a set period of time. It was then his turn to propose problems to his opponent. The winner, besides glory and prestige, could charge high fees for his lessons or advice.
During a challenge in Bologna, a certain Zuanne de Tonini da Coi set Tartaglia problems that reduced to cubic equations. At the time, the solution to this type of equation was not known, and answers were sought by trial and error. Tartaglia was the only one who knew the method for solving them, but he was careful not to reveal it, so as to keep this advantage for as long as possible. He of course had no difficulty answering and won by a wide margin.
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