See Katscher's article for a complete translation of the poem into both English and symbolic notation. He even points out an error in Tartaglia’s poem. Will be the value of your principal unknown. To the third of the cube of the cose net. Hereafter you will consider this customarily This is the beginning of Katscher’s translation of the poem into English:Įquates itself to some other whole number,įind two others, of which it is the difference.
Perhaps Tartaglia was subliminally urging Cardano to abandon all hope of solving the cubic equation. Incidentally, the rhyme scheme is terza rima (aba bcb cdc etc.), which first appeared in Dante's Inferno. In case you doubted that everything sounds more romantic in Italian, here is Tartaglia’s original Italian poem. I went to a Convergence article, “ How Tartaglia solved the cubic equation” by Friedrich Katscher, to learn more about the poem Tartaglia sent to Cardano. (You can read more about their dispute here.)Ĭonvergence, a magazine published by the Mathematical Association of America, is a great resource for learning about mathematics through its history. Tartaglia shared the formula with Cardano as a poem, and Cardano ended up publishing it. Another mathematician, Girolamo Cardano (1501-1576), wanted to learn the formula and promised not to publish it. 1500-1557) had discovered a way to solve certain kinds of cubic equations.
You can read expanded (sometimes embellished) accounts of it elsewhere, but the part that concerns us is that Niccolò Tartaglia (ca. The eventual solution of the cubic equation is one of the more colorful stories in math history. While versions of the quadratic formula were known to the ancient Babylonians and medieval Islamic mathematicians, the cubic equation stubbornly resisted a general solution for many more years. But did you ever learn the cubic formula? Probably not-it’s quite complicated and not nearly as easy to derive. Many of us memorized the quadratic formula in middle or high school (perhaps to the tune of “ Pop goes the weasel”). The more familiar quadratic equation has the form ax 2+bx+c=0, while a cubic equation generally has the form ax 3+bx 2+cx+d=0. A cubic equation is a polynomial with a 3 as the largest exponent. This month, I stumbled on an early example of mathematical poetry in the solution to the cubic equation. For the past few years, I’ve been taking Stephen Ornes’ suggestion and making it Math Poetry Month. Not only is it the cruelest month (or, in the notation of first-order logic, ∀m (a≤ Cm), but it’s also Mathematics Awareness Month and National Poetry Month.
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