Thursday, November 16, 2006

Girolamo Cardano

Girolamo Cardano's father Fazio Cardano, a lawyer by profession, had a deep interest in mathematics. He had developed a reputation as an expert and lectured on geometry at the University of Pavia. It was said that Leonardo da Vinci once consulted with him on mathematics.

Chiara Cardano, Girolamo's mother, was a widow with three children when Fazio met her. This was a time of the plague and when Chiara was close to giving birth, she traveled to Pavia to avoid the plague which had hit Milan where she lived. She would later learn that her three children had caught the plague and died. When Cardano was born, his parents were not married.

Cardano was born on September 24, 1501. He was a sickly child. As he grew older, he worked as an assistant to his father where he learned mathematics. Despite his interest in mathematics, when he entered the University of Pavia, he decided to study medicine.

This was a time of instability and war in Italy and when the University of Pavia was temporarily shut down, Cardano transferred to the University of Padua.

It was at this same time that his father died. Cardano received a small inheritance which he quickly spent. He began to rely on gambling as a source of income.

In 1525, Cardano graduated from the university and sought to become a member of Milan's College of Physicians. His application was rejected because of his illegitimate birth.

Cardano tried to set up a medical practice in a small town. There, he met his wife, Lucia but was unable to succeed as a physician. He applied again to the College of Physicians in Milan and again was rejected. By 1533, gambling was taking up his time and money. He pawned his wife's jewelry at this time and found himself in the poorhouse.

Cardano's fortune changed when he managed to get his father's old position as lecturer in mathematics. At the same time, his medical practice began to take off even though he had not been accepted by the College of Physicians. In 1536, he wrote a book critical of the College of Physicians. Despite this, his reputation and influence grew. Using his growing social connections, he was able to become a member of College of Physicians in 1538.

In 1539, he heard about the mathematician Tartaglia who had discovered a method to solve certain forms of cubic equations. He convinced Tartaglia to reveal the details of his method which Tartaglia did on the condition that Cardano wouldn't publish the method unless Tartaglia published it first.

Over the next six years, Cardano began to study cubic and quartic equations. It was at this time that he was able to come up with a general solution for the cubic equations using radicals. This was a significant advance over the method of Tartaglia.

Later, Cardano's assistant, Lodovico Ferrari came up with a general solution of quartic equations using radicals. In 1545, Cardano published his very important book Ars Magna in which he discussed the general solution for the cubic equation and the quartic equation. The book was a best seller and established Cardano's reputation as a great mathematician. There is much that has been written about the dispute between Cardano and Tartaglia so I will not write about it here. (See the references for more details.)

In 1546, his wife Lucia died. By this time, he had become rector of the College of Physicians in Milan. He once traveled to Scotland in order to provide a cure for Archbishop of St. Andrews. The archbishop made a complete recovery. Cardano was now helping a very rich set of clients. He was a wealthy man and he became professor of medicine at Pavia University.

Cardano's eldest son was in an unhappy marriage. After years of unhappiness, he poisoned his wife and confessed to the murder. The judge ruled that his son's life could be spared if Cardano could settle with the wife's parents. Such a settlement did not occur and Cardano's son was executed on April 13, 1560.

Cardano now moved to Bologna where he became a professor of medicine. His other son had a terrible gambling problem and once, when in need of money, took large amounts of money from his father. The son was later banished from Bologna for the crime.

In 1570, Cardano was accused of being a heretic for providing a horoscope and for writing a book that praised the emperor Nero. It is believed that his son helped to raise the charges. Cardano was now imprisoned for several months. On his release, he traveled to Rome where he met with the Pope. Somehow, despite everything that had occurred, the pope granted him a pension.

Cardano predicted the date of his death and sure enough, he died on that day. It is said that he committed suicide. Although, he later made peace with his son, in his will, he left all of his belongings to his grandson.


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