born: 1501 in Pavia, Italy

died: Sept 20, 1576 in San Marco, Italy

**Cardano was an ambitious, dishonest, hot-tempered, quarrelsome, conceited and humorless man, but capable of generosity, kindliness and merciless self-revelation. His parents were an abominable pair; his favorite son was executed for murder; his other son was a scoundrel who managed to escape the gallows but brought Cardano nothing but unhappiness and disgrace.**

(J. R. Newman)

Prominent physician. Prolific writer on all topics. First published solutions for roots of third and fourth-degree polynomials. First booklet on probability.

Cardano’s father was a physician, lawyer and geometer, and the whole family beat Cardano as a child, only stopping later because it might hinder his job of carrying his father’s baggage. At 19 Cardano entered the University of Pavia to study medicine. Because of his background and personality, good positions were not available to him and he became a country doctor in a small village. Cardano considered his life idyllic: “I gambled, played musical instruments, took walks, was of good cheer and studied only rarely. I had no pains, no fears. It was the springtime of my life.”

Cardano got married at age 30 and moved to Milan. At first things went so badly that he and his family had to stay in a poorhouse, but finally his fortunes began to improve and he was appointed to teach mathematics. He published several books on mathematics (arithmetic) and medicine and was elected to the College of Physicians. Before he was 50, he was one of the most respected physicians in Europe and was even called to Edinburgh to treat the Archbishop of Scotland who suffered from severe asthma. Cardano’s treatment was very reasonable in light of modern practice (he got rid of the Archbishop’s featherbed among other things), and the Archbishop got well enough to pay Cardano the exorbitant sum of 1800 gold crowns. Cardano wrote books at an incredible rate (131 altogether plus manuscripts for another 111) on a wide variety of subjects: “mathematics, astronomy, astrology, physics, horoscopy, chess, gambling, consolation, marvelous cures, poisons, air, water, dreams, urine, teeth, the plague, wisdom, morals, music, … .” Cardano’s book on consolation was the source of Hamlet’s famous remarks on sleep and death.

Of all of his writings, Cardano is primarily remembered for Ars Magna, the first great Latin book entirely about algebra. It discussed the theory of equations and included for the first time in print techniques for solving cubic and quartic equations. The techniques, however, were not discovered by Cardano. His student, Ferrari, discovered the method for solving quartics, and Tartaglia discovered the method for cubics. Tartaglia was understandably upset to see his secret method for solving cubics included in Cardano’s Ars Magna, and he accused Cardano, who had promised to keep the method a secret, of theft and a number of other low crimes. Ferrari, sharp-tongued and hot-headed, was put in charge of defending his teacher Cardano in public, and a public feud raged.

Cardano’s 15-page booklet on probability, Liber de Ludo, was not printed until 1663 when a 10-volume collection of his complete works was published. The Liber de Ludo is primarily a practical guide to gambling, including cards and dice and cheating, but in the mathematical sections Cardano talks about probability, some properties of probabilities for compound events, mathematical expectation, frequency tables for dice, a part of the formula for the binomial distribution, and even a form of the ‘law of large numbers.’ Cardano anticipated many of the fundamental results of Pascal and Fermat by more than a century, but is seldom given credit for them.

Cardano’s eldest son, Giambatista, had problems with his marriage, and, since divorce was not an option, Giambatista put arsenic on a cake and fed it to his wife and several of his in-laws. His wife died, and Giambatista was tortured, convicted of murder and executed in 1560. This broke Cardano’s heart, and he resigned his professorship at Milan.

Two years later Cardano accepted a post in medicine in Bologna, accompanied by his other son, Aldo, who managed to get thrown into jail eight times in the next two years. Finally, Cardano banished Aldo from Bologna, but continued to send him money. In 1670, Cardano was himself imprisoned, for heresy. His luck got better and he was not tortured or forced to recant anything publicly. Instead, he “just” lost his job and was forbidden to publish in the future. Cardano appealed to the Pope who finally granted him a small pension and allowed him a limited practice in medicine, a situation which continued until Cardano’s death in 1676.

Condensed from a review (Scientific American, June 1953) by J.R. Newman of Cardano, The Gambling Scholar by O. Ore, and from An Introduction to the History of Mathematics, 4th ed., by H. Eves (1976, Holt, Rinehart and Winston). DTH

Last Updated September 21, 2022