Gerolamo Cardano

Italian mathematician, physician, and astrologer (1501–1576)

The work of Cardano constitutes a landmark in the development of algebra and yet in his own time he was chiefly known as a physician. He studied medicine at the University of Pavia, the city of his birth, and at the University of Padua, receiving his degree in 1526. He spent much of his life as a practicing physician, becoming professor of medicine at Pavia in 1543. One of his notable nonmathematical achievements was to give the first clinical description of typhus fever.

It was however in mathematics that Cardano's real talents lay. His chief work was the Ars magna (1545; The Great Skill) in which he gave ways of solving both the general cubic and the general quartic. This was the first important printed treatise on algebra. The solution of the general cubic equation was revealed to him by Niccolò Tartaglia in confidence and Cardano's publication aroused a bitter controversy between the two. Cardano's former servant, Lodovico Ferrari, had discovered the solution of the general quartic equation. In his later Liber de ludo aleae (Book on Games of Chance) Cardano did some pioneering work in the mathematical theory of probability.

Cardano's interests were not, however, limited to mathematics and medicine. He also indulged in philosophical and astrological speculation and this had the unfortunate consequence that in 1570 he was charged with heresy by the Church. He was briefly jailed but was soon released after the necessary recantation. As a result of this episode Cardano lost his post as a professor at the University of Bologna, which he had held since 1562.

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 magnaesive 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.

Additional Sources

Fierz, Markus, Girolamo Cardano, 1501-1576: physician, natural philosopher, mathematician, astrologer, and interpreter of dreams, Boston: Birkhauser, 1983.

In the Italian Renaissance, the professions of scientist and mathematician were just beginning to be defined. One such scholar was Girolamo Cardano, known in English as Jerome Cardan. Cardan's basic source of income was his work as a physician, but he was also at various times a professor of mathematics at the universities of Milan, Pavia, and Bologna. Other sources of income included gambling and astrology; however, he was imprisoned for heresy after he cast Christ's horoscope.

Cardan's reputation as a mathematician is deservedly great, but marred by scandal. His 1545 work Ars magna ("great art") contains the first printed methods for solving all algebraic equations whose highest exponent is three (cubics) and all equations whose highest exponent is four (quartics).

At the end of the 15th century, European mathematicians believed that the cubic would never be solved. But Scipione del Ferro partially solved the cubic early in the 16th century, keeping his solution to himself. Before his death, however, del Ferro passed along his secret method to his pupil, Antonio Maria Fiore. Meanwhile, a self-taught mathematical genius known to posterity as Tartaglia ("the stutterer") discovered how to solve many kinds of cubics. He used his secret methods to best Fiore in a mathematical duel, solving all the problems Fiore posed while Fiore solved none of Tartaglia's.

Cardan somehow persuaded Tartaglia to reveal his secret; in return, Cardan promised to keep the secret so Tartaglia could publish it later. Instead, however, Cardan put Tartaglia's secret method into his own book, Ars magna. He did, however, credit Tartaglia with the original work. Cardan also expanded on Tartaglia's work to cover all forms of the cubic.

Ars magna also contains the method for solving the quartic, the next higher degree equation. But once again Cardan did not work out the solution on his own. Instead he got it from a pupil, Luigi Ferrari, "who invented it at my request."

"Cardanus" redirects here. For the lunar crater, see Cardanus (crater). For the stag beetle genus, see Cardanus (beetle).

Girolamo Cardano
Girolamo Cardano
Born	September 24, 1501 Pavia
Died	September 21, 1576
Nationality	Italian
Fields	mathematics physics
Alma mater	University of Pavia
Known for	algebra

Gerolamo Cardano or Girolamo Cardano (French Jerome Cardan, Latin Hieronymus Cardanus; September 24, 1501 — September 21, 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler.

Biography

He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted lawyer, who was a friend of Leonardo da Vinci. In his autobiography, Cardano claimed that his mother had attempted to abort him. Shortly before his birth, his mother had to move from Milan to Pavia to escape the plague; her three other children died from the disease.

In 1520, he entered the University of Pavia and later in Padua studied medicine. His eccentric and confrontational style did not earn him many friends and he had a difficult time finding work after his studies had ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted due to his reputation and illegitimate birth.

Eventually, he managed to develop a considerable reputation as a physician and his services were highly valued at the courts. He was the first to describe typhoid fever.

Today, he is best known for his achievements in algebra. He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna. The solution to one particular case of the cubic, x³ + ax = b (in modern notation), was communicated to him by Niccolò Fontana Tartaglia (who later claimed that Cardano had sworn not to reveal it, and engaged Cardano in a decade-long fight), and the quartic was solved by Cardano's student Lodovico Ferrari. Both were acknowledged in the foreword of the book, as well as in several places within its body. In his exposition, he acknowledged the existence of what are now called imaginary numbers, although he did not understand their properties (Mathematical field theory was developed centuries later). In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem.

Cardano was notoriously short of money and kept himself solvent by being an accomplished gambler and chess player. His book about games of chance, Liber de ludo aleae ("On Casting the Die") , written in the 1560s, but not published until 1663, contains the first systematic treatment of probability, as well as a section on effective cheating methods.

Portrait of Cardano on display at the School of Mathematics and Statistics, University of St Andrews.

Cardano invented several mechanical devices including the combination lock, the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely, and the Cardan shaft with universal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He studied hypocycloids, published in de proportionibus 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic circles and were used for the construction of the first high-speed printing presses. He made several contributions to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science which contain a wide variety of inventions, facts, and occult superstitions. He also introduced the Cardan grille, a cryptographic tool, in 1550.

Significantly, in the history of Deaf education, he said that deaf people were capable of using their minds, argued for the importance of teaching them, and was one of the first to state that deaf people could learn to read and write without learning how to speak first. He was familiar with a report by Rudolph Agricola about a deaf mute who had learned to write.

Cardano's eldest and favorite son was executed in 1560 after he confessed to having poisoned his cuckolding wife. His other son was a gambler, who stole money from him. He allegedly cropped the ears of one of his sons. Cardano himself was accused of heresy in 1570 because he had computed and published the horoscope of Jesus in 1554. Apparently, his own son contributed to the prosecution, bribed by Tartaglia. He was arrested, had to spend several months in prison and was forced to abjure his professorship. He moved to Rome, received a lifetime annuity from Pope Gregory XIII (after first having been rejected by Pope Pius V) and finished his autobiography.

Miscellaneous

Richard Hinckley Allen tells of an amusing reference made by Boteler in his book Hudibras:

Cardan believ'd great states depend
Upon the tip o'th' Bear's tail's end;
That, as she wisk'd it t'wards the Sun,
Strew'd mighty empires up and down;
Which others say must needs be false,
Because your true bears have no tails.

Alessandro Manzoni's novel I Promessi Sposi portrays a pedantic scholar of the obsolete, Don Ferrante, as a great admirer of Cardano. Significantly, he values him only for his superstitious and astrological writings; his scientific writings are dismissed because they contradict Aristotle, but excused on the ground that the author of the astrological works deserves to be listened to even when he is wrong.

Works

• De malo recentiorum medicorum usu libellus, Venice, 1536 (on medicine).
• Practica arithmetice et mensurandi singularis, Milan, 1539 (on mathematics).
• Artis magnae, sive de regulis algebraicis (also known as Ars magna), Nuremberg, 1545 (on algebra).^[1]
• De immortalitate (on alchemy).
• Opus novum de proportionibus (on mechanics) (Archimedes Project).
• Contradicentium medicorum (on medicine).
• De subtilitate rerum, Nuremberg, Johann Petreius, 1550 (on natural phenomena).
• De libris propriis, Leiden, 1557 (commentaries).
• De varietate rerum, Basle, Heinrich Petri, 1559 (on natural phenomena).
• Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula, Basel, 1570.
• De vita propria, 1576 (autobiography).
• Liber de ludo aleae, ("On Casting the Die") ^[2] posthumous (on probability).
• De Musica, ca 1546 (on music theory), posthumously published in Hieronymi Cardani Mediolensis opera omnia, Sponius, Lyons, 1663
• De Consolatione, Venice, 1542

Notes

1. ^ http://www.filosofia.unimi.it/cardano/testi/operaomnia/vol_4_s_4.pdf An electronic copy of his book Ars Magna (in Latin)
2. ^ p963, Jan Gullberg, Mathematics from the birth of numbers, W. W. Norton & Company; ISBN 039304002X ISBN 978-0393040029

References

• Cardano, Girolamo, Astrological Aphorisms of Cardan, The. Edmonds, WA: Sure Fire Press, 1989.
• ———— The Book of My Life. trans. by Jean Stoner. New York: New York Review of Books, 2002.
• Ore, Øystein: Cardano, the Gambling Scholar. Princeton, 1953.
• Cardano, Girolamo, Opera omnia, Charles Sponi, ed., 10 vols. Lyons, 1663.
• Dunham, William, Journey through Genius, Chapter 6, Penguin, 1991. Discusses Cardano's life and solution of the cubic equation.
• Sirasi, Nancy G. The Clock and the Mirror: Girolamo Cardano and Renaissance Medicine. Princeton University Press,1997.
• Grafton, Anthony, Cardano's Cosmos: The Worlds and Works of a Renaissance Astrologer. Harvard University Press, 2001.
• Morley, Henry The life of Girolamo Cardano, of Milan, Physician 2 vols. Chapman and Hall, London 1854.
• Ekert, Artur "Complex and unpredictable Cardano. International Journal of Theoretical Physics, Vol. 47, Issue 8, pp. 2101–2119. arXiv e-print (arXiv:0806.0485).

External links

• O'Connor, John J.; Robertson, Edmund F., "Gerolamo Cardano", MacTutor History of Mathematics archive .
• http://it.wikisource.org/wiki/Categoria:Testi_in_cui_%C3%A8_citato_Girolamo_Cardano
• Linda Hall Library History of Science Collection
• Jerome Cardan, a Biographical Study, 1898, by William George Waters, from Project Gutenberg
• "Girolamo Cardan". Catholic Encyclopedia. http://www.newadvent.org/cathen/03332a.htm. 
• Girolamo Cardano, Strumenti per la storia del Rinascimento in Italia settentrionale (in Italian) and English

Persondata
NAME	Cardano, Gerolamo
ALTERNATIVE NAMES	Cardano, Girolamo; Cardan, Jerome; Cardanus, Hieronymus
SHORT DESCRIPTION	Italian Renaissance mathematician, physician, astrologer and gambler
DATE OF BIRTH	September 24, 1501
PLACE OF BIRTH	Pavia
DATE OF DEATH	September 21, 1576
PLACE OF DEATH

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