ax3 + bx = c
Gerolamo Cardano would later show how the solution to the depressed cubic equation leads to the solutions of the general cubic equation.
Del Ferro was born on February 6, 1465 in Bologna, Italy. His father was a papermaker which was a profession that was growing in importance due the invention of the printing with moveable types (this was invented by Johannes Gutenberg in 1447). Not much is known about del Ferro's early life but it is believed that he attended University of Bologna which had been founded in the eleventh century.
In 1496, del Ferro became a lecturer in mathematics at the University of Bologna. If del Ferro wrote any books, none of them survive. It is believed that he was very secretive about his discoveries and communicated them only with close friends and selected students. He kept his discoveries in a notebook. This notebook would later become an important record in establishing that del Ferro had indeed discovered the solution to the depressed cubic equation.
There is a story often told that del Ferro kept his solution to the depressed cubic equation secret until on his deathbed, he revealed it. According to the MacTutor biography, this story is false. There are numerous people who had knowledge of del Ferro's solution.
Del Ferro is believed to have died on November 5, 1526. On his death, his notebook was given to his son-in-law Hannibal Nave. It was discovery of this notebook that motivated Cardano to release his famous math book Ars Magna. Cardano had promised Tartaglia that he would not reveal the method but he felt that del Ferro's earlier discovery of the method excused him from this promise.
Today, with the notebook lost, it is very difficult to assess the mathematical contributions of del Ferro. There is no doubt that he was the first to solve a very difficult problem which would later give birth to imaginary numbers and group theory.
Cardano would later write (quoted from MacTutor biography on del Ferro):
Scipione Ferro of Bologna, almost thirty years ago, discovered the solution of the cube and things equal to a number [which in today's notation is the case x3+ mx = n], a really beautiful and admirable accomplishment. In distinction this discovery surpasses all mortal ingenuity, and all human subtlety. It is truly a gift from heaven, although at the same time a proof of the power of reason, and so illustrious that whoever attains it may believe himself capable of solving any problem.
- "Scipione del Ferro", MacTutor