The math wars of Italy: Part I

The Renaissance was a period of change. All forms of art were undergoing a period of transformation, whether in painting, sculpture, architecture, politics, language, science, technology, and yes, even math. Every mathematician, from England to Turkey, was obsessed with algebra. In fact, let me tell you a story about how math battles in Italy led us to invent a method for solving cubics.

In Europe, there was a concept of a math battle, in which 2 mathematicians would exchange sets of math problems, and the one who solved more problems won. Reputations could be made and destroyed, and some mathematicians even dealt in their fortunes.

These contests were so competitive that mathematicians created specialised problems that could only be solved using hidden methods known only to them. One of these problems was cubics, a type of equation represented as ax^3 + bx^2 + cx + d (e.g., 3x^3 + 4x^2 + 3x + 97), and only one mathematician knew how to solve them.

His name was Scipione del Ferro. Though it is not fully validated, some historical evidence suggests that he knew how to solve certain cubic equations, but he kept the method a closely guarded secret to gain a big edge in math battles.

Nevertheless, to ensure that knowledge of his methods would remain after his death, he entrusted his secret to a few colleagues. One of them was Fior, Scipione's assistant. Fior was mesmerised. In fact, he was ecstatic and started using cubics for his math battles. However, Fior got carried away and used cubics against a clever mathematician, Fontana.

As legend had it, Fior and Fontana had a math battle, and Fior sent problems only about cubics. They had kept a 50-day time limit for the problems. For the first 40 days, Fontana was dumbfounded and didn't know what to do. One week before the deadline, a wave of inspiration struck Fontana. Everything clicked. Within hours, he solved all Fior’s problems and triumphed.

In fact, he created a proper equation by which cubics could be solved easily. He never fully revealed it, though, because of the math battles, and in pure Renaissance style, he hid his solution in a poem. To this day, Fontana’s cubic formula is used in engineering, math, economics, etc.

Follow along for Part II, where I talk about quartic equations.