Girolamo Cardano was born the illegitimate child of Fazio Cardano and Chiara Micheria on September 24, 1501. His father was a lawyer in Milan, who also had a great deal of expertise in mathematics. It is said that his father was consulted by Leonardo da Vinci with questions concerning geometry. When he was in his fifties, Fazio met Chiara Micheria, who was a young widow in her thirties, struggling to raise three children. Chiara became pregnant and fled Milan to escape the plague. Cardan was, therefore, born in Pavia, a small town outside of Milan.

Cardan’s first job was as his father's legal assistant. Fazio also taught his son mathematics, and Cardano eventually began to think of an academic career. He entered Pavia University, where his father had studied, to read medicine. Cardan was awarded his doctorate in medicine in 1525 and applied to join the College of Physicians in Milan. The College did not wish to admit him, despite the respect he had gained as a exceptional student, he had a reputation as a difficult man. He was rejected from the College on grounds of his illegitimate birth.

Cardan soon turned to gambling to boost his finances. Card games, dice and chess were the methods he used to make a living. Cardan's understanding of probability meant he had an advantage over his opponents and, in general, he won more than he lost. Gambling became an addiction that was to last many years and rob Cardan of valuable time, money and reputation.

In April 1532, he moved to Gallarate, near Milan. He married his wife Lucia, and applied again to the College of Physicians in Milan, but again was not allowed membership. Unable to practice medicine, Cardan again turned to gambling, and in 1533 things went so badly that he was forced to pawn his wife's jewelry and even some of his furniture.

Cardan moved himself and his wife into Milan. Cardan was fortunate to obtain his father’s former post of lecturer in mathematics at the Piatti Foundation in Milan. This gave him plenty of time to work out ideas in his head, and to practice his medicine, although he still had not been admitted into the College of Physicians. During this time he was credited with performing several medical miracles, and was eventually admitted into the College.

In 1539 Cardan approached Tartaglia, a mathematician who had achieved fame in winning a contest on solving cubics, and tried to get him to divulge the method. Tartaglia eventually agreed. There followed a period of intense mathematical study by Cardan who worked on solving cubic and quartic equations by radical over the next six years. One of the first problems that Cardan hit was that the formula sometimes involved square roots of negative numbers even though the answer was a 'proper' number.

In 1545 Cardan published his greatest mathematical work Ars Magna. In it he gave the methods of solution of the cubic and quartic equation. He also, although he did not understand exactly what he had done, presented the first calculation with complex numbers. Solving a particular cubic equation, he writes:-

Lucia died in 1546, but Cardan seemed not greatly saddened, being more interested in the fame he had achieved from his book, which became very popular. He became rector of the College of Physicians and gained the reputation of being the greatest physician in the world. He is most noted for being called to cure Archbishop John Hamilton, of Scotland, who was suffering from severe and chronic asthma. Whether by luck or by genius, Cardano diagnosed an allergy to feathers. This bolstered his fame, and made him a rich man.

Following a string of misfortunes, including, the execution of his eldest son, his own imprisonment by the church, during the Holy Inquisition, and the theft of much of his money, by his younger son, Cardon lost most his money and fame.

Cardon finished his days in Rome, where he received immediate membership of the College of Physicians and was granted a pension by the Pope. Cardan is reported to have correctly predicted the exact date of his own death but it has been claimed that he achieved this by committing suicide.

In addition to Cardan's major contributions to algebra he also made important contributions to probability, hydrodynamics, mechanics and geology. His book Liber de Ludo Aleae was published in 1663, although this book on games of chance was most likely completed in 1563. In it, Cardan explores the untouched realm of probability theory. "It is the first study of things such as dice rolling, based on the premise that there are fundamental scientific principles governing the likelihood of achieving the elusive 'double six', outside of mere luck or chance." Cardan also published two encyclopedias of natural science.

Today Cardon is probably most known for a minor invention that he is credited with. In a rear-wheel-drive car, the gear box is connected to the rear axle by a type of universal joint known as a cardan-shaft. It has the effect of absorbing the vertical movement of the vehicle. Not only does this joint lead to a smoother drive, but it is more efficient and less prone to breakdown because the drive shaft is always at a ninety-degree angle to the axle. The first such universal joint was fitted to a carriage belonging to the Holy Roman Emperor Charles V in 1548.

Written By:

Alexandra Church and Alexander Weisman

Sources:

The MacTutor History of Mathematics archive

http://www-gap.dcs.st-and.ac.uk/~history/index.html

http://www.findarticles.com/cf_0/m1373/1_49/53588900/p1/article.jhtml

Picture from:

The MacTutor History of Mathematics archive

http://www-gap.dcs.st-and.ac.uk/~history/index.html

Map From:

Mapquest

http://www.mapquest.com