Gerolamo Cardano and the Mathematics of Chances

Gerolamo Cardano
(1501 – 1576)


On September 24, 1501, Italian Renaissance mathematician, physician, astrologer and gambler Gerolamo Cardano was born. He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music. But, he is best known for his gambling that led him to formulate elementary rules in probability, making him one of the founders of probability theory.

Gerolamo Cardano started working as a physician in 1526 and began teaching in various fields, like mathematics, architecture and astrology shortly after. Cardano managed to publish several works on his fields of study in the late 1530s, which made him famous across Europe. He received numerous job offers but decided to travel and work throughout Europe and got the chance of meeting more and more scientists along his way.

Serious times came up in 1570. Cardano was arrested by the inquisition for researching on horoscopes and astrology. Luckily, he had great relations to the local cardinals and was released after a few months, but was suggested to quit publishing scientific works and accept a pension while staying in Rome. During his lifetime and beyond, several myths surrounded Cardano. It is said that he attempted to predict his exact date of death but was disappointed when the day came and he was still alive and healthy. Then he is supposed to have committed suicide by starving, but this is just a myth and not completely proven. However, Cardano counts as one of the last great universal academics of the renaissance and to his most impressive achievements belongs his assimilation of the renaissance humanism to sciences of the 16th century.

Cardano was one of the most famous and most respected medical scientists of the 16th century. His research focused on typhus, tuberculosis, and STD. He was the first to publish scientific works on descriptions of the typhus disease and managed to distinguish syphilis from gonorrhea. He was known to being able to heal patients who counted as incurable by others and was famous for innovative therapies including psychological and physiotherapeutic assistance.

Next to medicine, Cardano’s major field of study was mathematics. About a century before Pascal and Fermat, he published a book on gambling with mathematical basics and was one of the first to make basic findings in probability theory. He used these scientific results on gambling himself and earned lots of money on poor times of unemployment. However, his findings let mathematicians and historians assume that he was the first to calculate with complex numbers. Also it was him to notice that calculations with numbers below zero are just as easy as working with positive numbers. To one of his most important publications in the field belongs ‘Ars magna sive de Regulis Algebraicis‘, released in 1545.

In philosophy, Cardano published several works on moral philosophy, dialectics and nature philosophy. He attempted to combine Earth, heaven, nature and thought to a whole. His thoughts and studies depicted important foundations to later works of Leibniz. Cardano’s major works in the field were ‘de Natura‘ and ‘de Uno‘ and were reprinted several times across Europe.

At yovisto, you may enjoy a video lecture on basic probability theory by Professor Faber at Zurich.

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