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During the latter half of the fifteenth century was a time when the Europeans
had great intellectual discoveries. However, this time might not have
been so amazing had Johannes Gutenberg not invented the printing press in
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1450. With the printing press now available, many books were published
and Universities like Bologna, Paris, and Oxford became places for great
education. These were not only times for mathematical improvement but
also artistic careers blossomed.
Summa de Arithmetica was produced by Luca Pacioli. He stressed the
solving of linear and quadratic equations. This book was great because it
was one of the first steps toward the type of arithmetic that we use
today. Pacioli was great with arithmetic but when he came across trying
to solve the cubic he could not do it and said it was impossible. Later,
in the late 1400's, a man by the name of Scipione del Ferro took the
challenge of proving Pacioli wrong.
Ferros first did something quite interesting when he turned the standard
cubic equation (x^+mx=n) into a "depressed cubic" (ax^+cx+d=0). This
step was very important and so Ferro chose to keep his findings an
absolute secret. He chose to do this because he could use the depressed
cubics in scholarly battle and assure himself victory. It wasn't until
Ferro almost met his death that he passed on his solution. The lucky boy
was Antonio Fior.
With his new knowledge Fior challenged Fontana, a.k.a Tartaglia, in 155. Right before the deadline Tartaglia figured out how to solve depressed cubics and made Fior look like a fool. Shortly after this a fruity man named Gerolamo Cardano entered the game of Xtreme math. He desired to learn much more about cubics from Tartaglia.
Cardano made such great contributions to the world that he felt he needed a biography written about himself and who better to do the job than Cardano! Once he was done with this thrilling story Cardano began to pratice medicine in Sacco. Here he indulged in gambling and even wrote a book on games of chance. Even with all these other activities going on, Cardano managed to become the greatest doctor in Europe. Geralomo Cardano had become a fabulous man. However, his son didn't exactly follow his father's footsteps. In the 1550's, Giambattista killed his wife and was beheaded in 1560. In fact, Geralomo somewhat took after his son. In 1570 he was sent to jail on charges of heresy. Just years after he got out of jail, Cardano died in 1576.
Now, back to the proof. Cardano wrote many letters to Tartaglia asking him for the solution to the cubic; all of these were rejected. It wasn't until 15 that Tartaglia revealed his knowledge to Cardano.
Ludovico Ferrari became Cardano's slave and friend in the 150's. Together they worked to solve advanced depressed cubics and made great progress. They discovered the solution for the quartic polynomial equation. Later they traveled to Bologna and read some of del Ferros' solutions to the cubic and got exactly what they needed to create the great theorem. Oh yeah, they took Tartaglia's goods and played him like a fool to create this theorem.
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