Some Laws and Problems of Classical Probability and How Cardano Anticipated Them

Gerolamo Cardano (1501–1575)

Cardano’s early years were marked by illness and mistreatment. He was encouraged to study mathematics and astrology by his father and, in 1526, obtained his doctorate in medicine. Eight years later, he became a mathematics teacher, while still practicing medicine. Cardano’s first book in mathematics was the Practica arithmetice. In his greatest math work, Ars Magna (The Great Art), Cardano gave the general solution of a “reduced” cubic equation (i.e., a cubic equation with no second-degree term), and also provided methods to convert the general cubic equation to the reduced one. These results had been communicated to him previously by the mathematician Niccolò Tartaglia of Brescia (1499–1557) after swearing that he would never disclose the results. A bitter dispute thereby ensued between Cardano and Tartaglia, and is nicely documented in Hellman’s Great Feuds in Mathematics. Cardano’s passion for gambling motivated him to write the Liber de ludo aleae, which he completed in his old age and was published posthumously.

In the history of probability, the sixteen–century physician and mathematician Gerolamo Cardano (1501–1575) was among the first to attempt a systematic study of the calculus of probabilities. Like those of his contemporaries, Cardano’s studies were primarily driven by games of chance. Concerning his gambling for twenty–five years, he famously said in his autobiography entitled The Book of My Life:

… and I do not mean to say only from time to time during those years, but I am ashamed to say it, everyday.

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