The Italian mathematician, astronomer, and physician Geronimo Cardano (1501-1576) initiated the general theory of cubic and quartic equations. He emphasized the need for both negative and complex numbers.

Geronimo Cardano was born in Pavia on Sept. 24, 1501, the illegitimate son of a local jurist, Fazio Cardano. In spite of a boyhood filled with sickness and extreme poverty, he managed to attend the universities of Pavia and Padua, receiving his medical degree from the later in 1524. In 1532 he was appointed to the chair of mathematics in Milan but continued to practice medicine, albeit without much success. In 1536 he gained some notoriety by attacking the then-existing practices of medicine, but this aided rather than hindered him, for 3 years later he was admitted to the College of Physicians and later was appointed rector of the college. In 1543 he was professor of medicine at the University of Pavia.

Mathematical and Other Writings

In 1539 Cardano published two books on arithmetic, which were based on the lectures he had been giving at Milan, and they proved to be among the best mathematical texts of the time. Of more importance, however, was the Ars magna (Artis magnae sive de regulis algebraicis) of 1545, which was devoted solely to algebra and was the first important printed work on the subject. It was published in Nuremberg and contained the theories of algebraic equations as they were known at that time. Cardano wrote other mathematical works and a book on games of chance which discussed probability theory.

Cardano's most popular work was De subtilitate rerum (1550), an encyclopedia of physical inventions and experiments. It was followed by a companion piece De varietate rerum published in 1557. In both books Cardano shows himself to have been a man of many interests and possessed of a great curiosity. In his writings on magnetism he advanced the idea that magnets can grow old and lose their potency, and that a magnetized needle turns on its pivot spontaneously. He associated magnetism with the pull exerted by a star in the tail of the constellation Ursa Major (the Big Dipper). He distinguished between electrical and magnetic attraction, defining the former as the flow and return of a fatty substance to which dry things adhere.

The medical writings of Cardano covered a wide range of subjects and are again a mark of his intense interest in all aspects of science. He refused to rely on the authorities of the past, such as Galen and Hippocrates, and developed his own ideas in medical practice. He wrote about the instruction of deaf-mutes and blind persons, treatment of syphilis and typhus fever, causes of disease, and character determination from facial appearances. In his concern with life itself, he hinted at an evolutionary process and believed that there was infinite variability in animal species.

Later Years

Cardano may perhaps be regarded as typical, yet very special, among the men of the Renaissance. In spite of his accomplishments and devotion to science, he remained a strong believer in astrology and even cast the horoscope of Jesus Christ. He was also interested in philosophy and wrote two books on the subject. His character was anything but admirable, and he can be described as a liar, gambler, lecher, and possibly a heretic.

Following his professorship at Pavia, which he had to resign after his son's conviction for murder, Cardano was appointed professor of medicine at the University of Bologna (1562). However, here he again found difficulties and was jailed in 1570 on a charge of heresy. Upon his release he was deprived of his university chair and left for Rome. His fame had undoubtedly mitigated his punishment, and at Rome he was allowed to stay in the College of Physicians and was given a pension by Pope Gregory XIII. Cardano died in Rome on Sept. 21, 1576.

Further Reading

• Recommended for information on Cardano are his autobiography, The Book of My Life (1643; trans. 1931), and Oystein Ore, Cardano, the Gambling Scholar (1953). For a general survey of the history of mathematics, E. T. Bell, The Development of Mathematics (1940; 2d ed. 1945), and Morris Kline, Mathematics and the Physical World (1959), are quite satisfactory.
• Fierz, Markus, Girolamo Cardano, 1501-1576: physician, natural philosopher, mathematician, astrologer, and interpreter of dreams, Boston: Birkhauser, 1983.