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Gerolamo Cardano

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


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 ("Book on Games of Chance") , written in 1526, 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.

Someone also assumed to Cardano the credit for the invention of the so called Cardano's Rings, also called Chinese Rings, but it is very probable that they are more ancient than Cardano.

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.


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.


* 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


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


* 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, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Cardan.html .
* 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

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