Girolamo Cardano is sometimes known by his Latin name, Cardan. He was an illegitimate child of a lawyer in Milan, whose expertise in mathematics was such that he was consulted by Leonardo da Vinci on questions of geometry. Cardano at first became his father's assistant, but began to think about an academic career after learning mathematics from his father. He studied medicine, and was a brilliant student. But he was outspoken and highly critical, so he was not well liked.

Cardano squandered the small bequest from his father and turned to gambling to make a living. Cardano'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 Cardano of valuable time, money and reputation.

Cardano was awarded his doctorate in medicine in 1525. He set up a small, and not very successful, medical practice in Sacco, where he married. He repeatedly applied to the College of Physicians in Milan but was not allowed membership due to his reputation and his ignoble birth. Unable to practise medicine, Cardano reverted again to gambling to pay his way. Things went so badly that he was forced to pawn his wife's jewellery and even some of his furniture.

Cardano was fortunate to obtain the post of lecturer in mathematics in Milan which gave him plenty of free time, and he used some of this to treat a few patients, despite not being a member of the College of Physicians. Cardano achieved some near miraculous cures and his growing reputation as a doctor led to his being consulted by members of the College, to which he was eventually admitted in 1539.

In the same year, Cardano's first 2 mathematical books were published. This was the beginning of Cardano's prolific literary career writing on a diversity of topics medicine, philosophy, astronomy and theology, in addition to mathematics.

In 1539, Cardano approached Tartaglia, who had achieved fame in winning a contest on solving cubics, and tried to get him to divulge the method. Tartaglia eventually agreed after getting Cardano to swear an oath that he would not publish the method until Tartaglia had himself published it. For 6 years, Cardano worked on solving cubic and quartic equations by radicals.

One of the first problems that Cardano hit was that the formula sometimes involved square roots of negative numbers, something unheard of at the time. He did the first calculations with complex numbers. From 1540 to 1542, Cardano abandoned his studies and did nothing but gamble, playing chess all day. In 1545 Cardano published his greatest mathematical work Ars Magna. In it he gave the methods of solution of the cubic and quartic equation. In fact, he had discovered in 1543 that Tartaglia was not the first to solve the cubic equation by radicals and therefore felt that he could publish despite his oath.

He became rector of the College of Physicians and gained the reputation of being the greatest physician in the world. Cardano received many offers from the heads of state in Europe, anxious to receive the best medical attention. Cardano was appointed professor of medicine at Pavia University and, with many wealthy patients, he became a rich and successful man.

As Cardano was at the height of his fame, he received what he called his "crowning misfortune". Cardano's eldest son secretly married a girl whom he later poisoned. Following his arrest, he confessed to the crime and he was executed. This was a blow from which Cardano never recovered. As the father of a convicted murderer, Cardano became a hated man. In 1570, Cardano himself was put in jail on the charge of heresy for casting the horriscope of Jesus Christ. On his release a few months later, he was forbidden to hold a university post and barred from further publication of his work.

In addition to Cardano's major contributions to algebra he also made important contributions to probability, hydrodynamics, mechanics and geology. Cardano made the first foray into the untouched realm of probability theory. Cardano also published 2 encyclopaedias of natural science, which contain a little of everything, from cosmology to the construction of machines, from the usefulness of natural sciences to the evil influence of demons, from the laws of mechanics to cryptology.

Cardano 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.