Cardano was the son of a lawyer of great learning who was also a friend of Leonardo da Vinci (1452-1519). The young Cardano was sickly from birth, and was treated poorly by his father, but he was extremely bright and applied himself to the study of the classics, mathematics, and astrology, receiving his doctorate in medicine in 1526. Unfortunately, because of his illegitimate birth, Cardano was refused admittance to the College of Physicians at Milan, Italy, until he had demonstrated excellence in his field. This turn of events greatly embittered Cardano, but he did not allow it to hinder him from becoming one of the best known physicians in Europe, second only to Andreas Vesalius. In 1543 he received the appointment of professor of medicine at the University of Pavia. By this time he had already produced well-known works on astrology (a skill that was quite respectable at the time) and arithmetic.
Cardano's professional career was not without controversy. For example, he obtained the method for solving certain types of third- degree equations (called depressed cubic equations) from Niccolò Tartaglia only after having sworn himself to an oath of secrecy. Nevertheless, six years later, Cardano greatly angered Tartaglia by publishing the method as part of his general solution for cubic equations in his Ars magna after discovering that another mathematician, Scipione dal Ferro, had solved the depressed cubic equation before Tartaglia. Even though Cardano gave full credit to both dal Ferro and Tartaglia, the vindictive Tartaglia began to malign Cardano's character in his widely read writings.
Despite his personal problems, Cardano excelled in the study of mathematics and algebra. Cardano's interest in such games as dice, chess, and cards led him to develop one of the first theories of probability. Cardano's theory presents the idea that, beyond luck, rules of chance govern the outcome of unpredictable events. He developed a mathematical expression of the ratio of favorable results to possible results for an event, and presented a law of large numbers in his work on this subject. Unfortunately, Cardano's theories were never published in his lifetime and had no influence on the development of probability theory that was elucidated by Blaise Pascal and Pierre de Fermat many decades later in the seventeenth century.
Cardano's Ars magna, published in 1545, was his greatest mathematical work and was perhaps the first volume on algebra to be printed. Other topics to which he made significant contributions include mechanics, hydrodynamics, and geology. Cardano correctly observed that the exchange of water on earth is accomplished in a continuous cycle in which ocean water is evaporated into the air. Water in the air falls to the ground in the form of rain and other precipitates, which eventually flow, in the form of streams and rivers, back to the ocean to begin the cycle anew.
Cardano's later life unfolded tragically. In the 1550s he was banished from Milan and took a position at the University of Bologna, Italy. Cardano's children were a source of grief to him; one of Cardano's younger sons was constantly being jailed for various crimes, and in 1560 Cardano's eldest son was executed for poisoning his wife. In 1570 Cardano himself was imprisoned by the Inquisition for having the audacity to cast the horoscope of Jesus Christ, ascribing the events of his life to the action of the stars. Upon his release a few months later, he moved to Rome. By the time of his death in 1576, he had authored over 200 works devoted to topics as diverse as medicine, mathematics, music, and geology.
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