In the second half of the 1530s, Girolamo Cardano learned that a certain Niccolò Tartaglia, from the city of Brescia, would have discovered the solution of some cubic equations. Using tricks, insults, praise and promises, he managed to convince the other mathematician to visit him in Milan in 1539.
During the visit, Tartaglia revealed the secret of the equations x3+px=qex3+q=px, with a promise to be the first to publish. But in 1542 Cardano discovered that Scipione del Ferro, from the University of Bologna, already knew how to solve x3+px=q decades ago. He then considered himself released from the promise, and included the solution of this equation in his book “Artis Magnae”, published in 1545, attributing it to del Ferro and Tartaglia.
The latter was understandably furious, going on to attack Cardano in his writings. Cardano did not respond, but his young disciple Ludovico Ferrari took on this role, attacking Tartaglia and challenging him to a mathematical duel. He himself had made a great contribution to the “Artis Magnae”: the solution of the equations x4+axtwo+b=cx (Rafael Bombelli later showed that the method works for all equations of degree 4).
Ferrari wanted a live duel, but Tartaglia, who had been a stutterer since childhood, insisted that it be in writing. Also, poor man, he asked that the bet could be deposited in the form of books, instead of gold. You can’t help but sympathize with the poor guy…
But Tartaglia ended up agreeing to face Ferrari in person and, even more, at his own base in Milan. Perhaps he was forced by necessity, hoping to gain money and fame if he won the duel. The meeting took place in the church of Santa Maria, at 10 pm on August 10, 1548, and we do not know exactly what happened.
Tartaglia stated that he was prevented from speaking by Ferrari’s friends. Discussions went on into the night, over obscure mathematical points, until everyone had to leave. Tartaglia returned to Brescia the next day, fearing for his life.
It looks like Ferrari has been declared the winner of the duel. His star shone from there, having received several job offers, including from Emperor Charles 5th of the Holy Roman Empire. He eventually accepted to work for the Cardinal of Mantua, Ercole Gonzaga. Poor health forced him into early retirement, and he died in 1565, aged 43. Tartaglia had died eight years earlier. Cardano lived until 1576.
