On August 10, 1548, two men met in the church of Santa Maria del Giordano in Milan for a fierce duel. Instead of swords, weapons were mathematical ideas. But that did not make the fight any less implacable, for the victor would have glory and fortune; to the loser shame and ostracism. For both, who had never left the poverty into which they were born, much was at stake.
Niccolò Fortuna (Tartaglia, meaning “stutterer”, was a cruel nickname) was born in Brescia around 1500. His father died when he was 6 years old, leaving the family in destitution. Self-taught out of necessity, he early discovered his talent for mathematics, which earned him teaching jobs in Verona and Venice. We know that he had a family and lived with difficulties.
In 1535, he gained fame when he faced Antonio Maria del Fiore in a mathematical duel, who had learned from his master Scipione del Ferro a method for solving equations of the form x.3+px=q. Tartaglia had rediscovered the solution, and managed to extend it to other types of cubic equations. This allowed him to defeat Fiore forcefully.
But in 1539 he agreed to reveal his method to another mathematician, Girolamo Cardano. The latter promised that his colleague would have priority in the publication, but ended up including the solution in his great work “Artis Magnae”, published in 1545. This infuriated Tartaglia, who proceeded to attack and insult Cardano in his writings.
Ludovico Ferrari was born in Bologna in 1522. Having lost his father in childhood, he went to live with an uncle in Milan, where he became Cardano’s employee. Noticing the young man’s exceptional brilliance, his employer taught him Greek, Latin, and mathematics, and soon began to use his services as a secretary. Ferrari has repaid him with total loyalty throughout his life. He never published mathematical works in his name, and his best discoveries — including the spectacular solution of the 4th degree equation — he yielded for publication in “Artis Magnae”.
Faced with Tartaglia’s attacks, which Cardano ignored, Ferrari took the pains for his master. Between 10 February 1547 and 24 July 1548 he wrote six pamphlets (cartelli), to which Tartaglia gave an equal number of replies (riposte). Alongside insults and personal attacks, cartelli and riposte have remarkable mathematical content. The correspondence culminated in the fateful duel of 10 August. Don’t miss the sequel.
