Night Story (part 1)
So cubic equations, which were taught a lot at school, were known to be solved by Cardano. However, deep inside it, there was a real big truth that I was going to tell you now: During the Renaissance time, mathematicians always challenged each other to solve problems and the winner would easily find employment, so they had to keep secrets. The cubic equation: “ax^3+bx^2+cx+d” was known to have no general solutions at that time and Scorpio, who went to the University of Polonia”, find one but only to the depressed cubic equation: “ax^3+bx+d=0”.
When Scorpio died, he taught this secret to his student Antonio, who later believed that he would excel at solving depressed cubic equations. Tartaglia, however, did not believe so and they both came to an open math competition. Nicolo gave him depressed cubic equations that Tartaglia could easily solve with his own method, while Nicolo could not solve any problem. He was disgraced, and disappeared.
Cardano has obsered Tartaglia’s ability and asked if he could share his solution with him. After long conversations, letters, Tartaglia wrote a contract, which said Cardano was not allowed to publish or tell anyone. With Tartaglia’s solution, Cardano was able to write another one, but he could not publish it. So he waited, waited, waited for Tartaglia to publish his.
Hearing the rumor that Tartaglia was not the first one to think of it, Cardano started to investigate. He found evidence of Scopio's original one and therefore, the contract was invalid. He published it and that was the end of the story. In part 2, let’s find out more about how the equation was solved.