Gerolamo Cardano

Gerolamo Cardano

Infobox Scientist
name = Gerolamo Cardano
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caption = Gerolamo Cardano
birth_date = September 24, 1501
birth_place = Pavia
death_date = September 21 1576
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citizenship =
nationality = Italian
ethnicity =
field = mathematics physics
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alma_mater = University of Pavia
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doctoral_students =
known_for = algebra
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Gerolamo Cardano or Girolamo Cardano (French Jerome Cardan, Latin Hieronymus Cardanus; September 24, 1501September 21 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler.__NOTOC__


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 allowed 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, "x"3 + "ax" = "b" (in modern notation), was communicated to him by Niccolo 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", 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.

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 was one of the first to state that deaf people could learn without learning how to speak first.

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. 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. He died there on the day he had (supposedly) astrologically predicted earlier; some suspect he may have committed suicide.


* "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). [ An electronic copy of his book "Ars Magna" (in Latin)]
* "De immortalitate" (on alchemy).
* " [;step=thumb 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", 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



* 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

* [ Linda Hall Library History of Science Collection]
* " [ Jerome Cardan, a Biographical Study] ", 1898, by William George Waters, from Project Gutenberg
* " [ Girolamo Cardano, Strumenti per la storia del Rinascimento in Italia settentrionale (in Italian)] and [ English] "

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