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Wednesday, July 21, 2010

Niccolo Fontana Tartaglia: Forgotten Mathematics Genius

I remember reading years ago about Niccolo Fontana Tartaglia and his work on the trajectory of cannonballs. As it turned out, he ended up being an important firgure in the development of mathematics and engineering.

Read more about this remarkable, albeit forgotten, person here.

Oh before I forget. He was born and died poor.

"In the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics competitions. It was in just such a competition, in 1535, that the unlikely figure of the young Tartaglia first revealed a mathematical finding hitherto considered impossible, and which had stumped the best mathematicians of China, India and the Islamic world.

Niccolò Fontana Tartaglia was a poor, self-taught mathematician, often referred to as “The Stammerer” for a speech defect he suffered due to an injury he received in a battle against the invading French army. He was an engineer known for designing fortifications, a surveyor of topography (seeking the best means of defense or offense in battles), and a bookkeeper from the Republic of Venice.

But he was first and foremost a mathematician. He distinguised himself by producing, among other things, the first Italian translations of works by Archimedes and Euclid from uncorrupted Greek texts (for two centuries, Euclid's "Elements" had been taught from two Latin translations taken from an Arabic source, parts of which contained errors making them all but unusable), as well as an acclaimed compilation of mathematics of his own.

Tartaglia's greates legacy to mathematical history, though, occurred when he won the 1535 Bologna University mathematics competition by demonstrating a general algebraic formula for solving cubic equations (equations with terms including x3), something which had come to be seen by this time as an impossibility, requiring as it does an understanding of the square roots of negative numbers. In the competition, he beat Scipione del Ferro, whose had coincidentally produced his own solution to the cubic equation problem. Although del Ferro's solution perhaps predated Tartaglia’s, it was much more limited, and Tartaglia is usually credited with the first general solution."

Lodovico Ferrari, along with Geralamo Cardano, were also an important individual in the development of modern mathematics. Both, incidentally, were engaged in a feud with Tartaglia. From Story of Mathematics:

"Tartaglia’s definitive method was leaked to Gerolamo Cardano, a rather eccentric and confrontational elder mathematician. Cardano published it himself in his 1545 book "Ars Magna" (despite having promised Tartaglia that he would not), along with the work of his own brilliant student Lodovico Ferrari. Ferrari, on seeing Tartaglia's cubic solution, had realized that he could use a similar method to solve quartic equations (equations with terms including x4).

In this work, Tartaglia, Cardano and Ferrari between them demonstrated the first uses of what are now known as complex numbers, combinations of real and imaginary numbers of the type a + bi, where i is the imaginary unit √-1. It fell to another Bologna resident, Rafael Bombelli, to explain, at the end of the 1560's, exactly what imaginary numbers really were and how they could be used.

Although both of the younger men were acknowledged in the foreword of Cardano's book, as well as in several places within its body, Tartgalia engaged Cardano in a decade-long fight over the publication. Cardano argued that, when he happened to see (some years after the 1535 competition) Scipione del Ferro's unpublished independent cubic equation solution, which was dated before Tartaglia's, he decided that his promise to Tartaglia could legitimately be broken, and he included Tartaglia's solution in his next publication, along with Ferrari's quartic solution.

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