Renaissance mathematicians dueled in public to solve a 'forbidden' equation
In 1535, Antonio Fior challenged Niccolò Tartaglia to a contest: each gave the other thirty problems to solve. All of Fior's problems required cubic equations of the form x³ + px = q, a method Fior's own teacher had claimed to have found. Tartaglia had independently discovered a general solution just days before the deadline. Who won -- and what happened when he later shared the secret formula with Gerolamo Cardano?
Reveal the answer
Tartaglia solved all thirty of Fior's problems within two hours using his own method; Fior solved none of Tartaglia's. Tartaglia later revealed the formula to Cardano after extracting an oath of secrecy, but Cardano published it anyway in his 1545 Ars Magna once he found an earlier, unpublished solution by Scipione del Ferro -- igniting a bitter priority dispute still remembered as the Cardano-Tartaglia controversy.