Gerolamo Cardano

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Gerolamo Cardano , also Geronimo or Girolamo Cardano (of Milan) and Cardan , Latinized Hieronymus Cardanus (Mediolanensis) ( September 24, 1501 in PaviaSeptember 21, 1576 in Rome ), was an Italian physician, philosopher and mathematician and is one of the Renaissance humanist .


Leone Leoni: Medal by Girolamo Cardano, 1550
Girolamo Cardano: De propria vita , 1643

Gerolamo Cardano began to describe his own life in his last years. In this biography, which he did not finish editing and which was not printed until long after his death, he describes in detail, very openly, but also subjectively colored his physical and mental states, strengths and weaknesses, his life with friendships and enmities, his studies and knowledge as well as the long line of his published and unpublished works.

Cardano was born in Pavia in 1501, the illegitimate son of the Milanese legal scholar Fazio Cardano (1444–1524) (a universally and mathematically literate friend of Leonardo da Vinci , who lectured in Pavia and Milan) and the much younger widow Chiara Micheria. Before they met, she already had three children to look after. When she was expecting Gerolamo, the plague broke out in Milan and she went to Pavia, only to find on her return that her three other children had died of the plague. She later married Fazio Cardano, but they also lived apart for a while. As a child he was often sickly and unhappy. He was an assistant to his father and learned mathematics from him, which awakened in him the desire to become a scholar. Cardano studied from 1520 (following his father's wishes) law, natural sciences and medicine in Pavia and, after the University of Pavia was closed due to the war, in Padua . He was an excellent student, but also made enemies because he didn't mince his words. In 1526 he received his doctorate in medicine in Padua. After the death of his father, he quickly got through his small inheritance and subsequently financed his life mostly through games (cards, chess, dice). However, since this also became an obsession, it led to him getting into financial difficulties again and again. But the game also led him to important discoveries in probability theory .

From 1526 to 1532 he worked as a doctor in Saccolongo (near Padua), where he married Lucia Bandareni in 1531. From this marriage two sons and a daughter were born. From 1534 he was a doctor at the city hospital and hospital in Milan and received lectureships at the Academy for lectures in mathematics, astrology and architecture. In 1539, after long disputes, he was admitted to the College of Doctors of Milan, and in 1541 he became rector of this college. From 1543 he lectured on medicine in Milan. In 1544 he accepted a position as professor of medicine in Pavia. Economic conditions gradually improved.

His works, printed partly in Nuremberg by Johannes Petreius and partly in Basel, made him famous throughout Europe. In 1546 he received offers from Pope Paul III. , 1547 by King Christian III. of Denmark and by the Scottish Archbishop John Hamilton (St. Andrews) for highly paid positions as personal physician . He declined the offers, but traveled to Edinburgh in 1552 via Lyon and Paris. There he healed Hamilton, who had previously been treated in vain by the personal physicians of King Henry II and then by the physicians of Emperor Charles V. The return journey took him via England, the Netherlands, Germany and Switzerland with numerous encounters with scientists, rulers and bishops.

He subsequently received offers as personal physician to the Scottish King, the French King Henry II, the German Emperor Charles V and the Duke of Mantua , and as an engineer for the French Viceroy Brissac , all of which he turned down. From 1560 to 1562, after a period of writing and medical practice, he resumed his professorship in Pavia, but finally stopped it because the small university was insolvent. In 1563 he took over a professorship for medicine at the University of Bologna and was later honored with the honorary citizenship of Bologna .

In 1560, Cardano's eldest son, Gianbattista, was executed for poisoning his wife. The father defended the confessed murderer in court and hoped for a lighter sentence until the end. The dishonorable death of his son, in which he had placed great hopes, was one of the most difficult blows of fate for him.

Cardano: Letter to the Basel printer Heinrich Petri, 1562

In 1570 he was imprisoned by the Inquisition without warning and released after three months of imprisonment under certain conditions. The opening of the archives of the Inquisition in the 2000s brought new results on the reasons for Cardano's arrest. An expert opinion on his work De rerum varietate may have been decisive for his imprisonment . An anonymous inquisitor accused him of heretical statements. In the older literature and among contemporaries, the exact reason for his imprisonment was not known - according to the usual practices of the Inquisition, those arrested did not necessarily learn the reason - and gave rise to speculation. Cardano had to remain silent about it as one of the requirements of the Inquisition. Oystein Ore suspected that the arrest was related to the Inquisition's actions against prominent figures in the context of the Counter-Reformation, which a dubious reputation alone could give rise to suspicion. Cardano's writings offered points of attack at various points, although Cardano himself categorically denied any deviation from the teachings of the Catholic Church. He drew up a horoscope for Jesus, wrote a benevolent book about Nero, the persecutor of Christians, and there are passages on astrology that could be interpreted as heretical, since he depicts the destiny of the individual as determined by the stars, which is what the Church teaches ran counter to He was also suspicious that he had many of his books published in Nuremberg , Basel and Lyon , thus circumventing the censorship in his homeland. In addition, the Basel printer had inserted a derogatory reference to the Dominicans in his book De rerum varietate , which according to the Vatican documents had been the main trigger, but Cardano had immediately distanced himself from this and pushed through a correction in a later edition.

Eventually he obtained partial rehabilitation. He was advised to give up his professorship in Bologna, to stop publishing and instead to move to Rome with a papal pension. The Vatican also arranged for his admission to the Roman Medical College. Under the protection and oversight of the Church, Cardano spent his last years in a rather secluded manner, preoccupied with writing his biography. From then on, some of his astrological writings were included in the index of banned books with the addition donec corrigantur (as long as they are not corrected).

Gerolamo Cardano died in Rome six years later. A common but unsupported legend about Cardano is that he claimed to be able to predict his own death down to the hour. When the predicted hour came, he was embarrassed to find that he was in the best of health. Since he did not want to admit his own mistake, he is said to have caused his own death by starvation. This is a typical example of the hostilities and defamation that Cardano was repeatedly exposed to throughout his life and which led to such oddities even after his death.

Cardano, as he describes himself, must have been a strange person. Constantly preoccupied with problems of some sort, he was quick-tempered, cheeky, provocative, often very harsh and sharp-tongued. In old age he became a lonely oddball. He had extensive knowledge and was a good speaker. In his lectures he almost always spoke freely. He also loved scientific disputations and was feared as an extremely knowledgeable, skilful and quick-witted opponent. All this, in addition to obvious admiration, earned him many enemies. He only managed to get his doctorate in Pavia on the third attempt. According to his own statements, he had only a few friends, but his patrons , supporters and patrons were numerous Scholars the lawyer Andrea Alciato and the anatomist Andreas Vesalius . Cardano earned his living primarily as a doctor and lecturer. But he cared little about getting rich. So there were always times in his life when he hardly practiced, but pursued his studies and wrote alongside his passion as a player. Through his countless writings - after he had burned 120 writings in 1573, he listed 55 published and 45 unpublished titles in his biography - he wanted to make his name immortal as a humanist .


Gerolamo Cardano: De rerum varietate , 1557

Gerolamo Cardano is considered one of the last great polymaths of the Renaissance with an astonishing international reputation during his lifetime, which at that time was otherwise more likely to be observed among prominent artists and writers. The large number of areas of knowledge that he has worked on in the form of lectures and writings ranges from medicine, mathematics, philosophy, comparative religion, physics, chemistry, engineering, pharmacy, psychology and dream interpretation, astronomy and astrology to architecture and the history of science. Given this abundance, the enormous scope of his writings is not surprising.

A major merit of Cardano lies in the integration of Renaissance humanism and the new orientation of science in the 16th century with a focus on the natural sciences. This required such a universally educated scholar who was just as qualified in philosophy as in the natural sciences. With De subtilitate libri XXI and de varietate libri XVII , which complement each other and together comprise more than 1200 pages in folio format in the Basel editions of 1554 and 1557, he has an encyclopedic work on the visible world, but also on some supernatural phenomena and magical tricks created. Because Cardano has also dealt intensively with astrology and dream interpretations. He has written numerous horoscopes (for Francesco Petrarch , Erasmus von Rotterdam and Albrecht Dürer , among others ), and omens, premonitions and his own dreams play a significant role in his own biography. This earned him the reputation of a fanatic in the 18th century. This is how Leibniz later judged him: “Knowledge should have charms that cannot be understood by those who have not felt them. I don't understand it as a mere knowledge of facts without their reasons, but a knowledge like that of Cardan, who was really a great man, despite all his faults, and would not have had his peers without them".

Mathematical Achievements

Gerolamo Cardano: Ars magna , 1545

Cardano made important discoveries in probability and combinatorics as well as complex numbers. In old age he completed The Book of Games of Chance (Liber de Ludo Aleae) (first published in his Opera Omnia in 1663), which contained the foundations of mathematical probability theory, some hundred years before Pascal and Fermat. He dealt with binomial coefficients and z. B. molecular formulas are given for this. He had found these laws before, but only used them himself at first. With his knowledge, he earned the money from gambling that he earned when he was unemployed, i. i.e. when the university in Pavia could not pay his salary, needed for maintenance.

He was probably one of the first to calculate with complex numbers . He came across them while trying to solve cubic equations . He also proved that negative numbers can be calculated in a similar way to ordinary numbers. Until then, the usual doctrine among mathematicians was that all numbers must be greater than zero. (The Greek mathematician Diophantus is an exception according to the latest research.)

In 1545 his book Ars magna sive de Regulis Algebraicis was published , in which he gave methods for explicitly solving third and fourth degree equations. However, Cardano also created an enemy with it. Because as early as 1535, the Venetian mathematician and politician Tartaglia had used the solutions of a special case of the cubic equations that Scipione del Ferro had discovered before 1530 in public competitions, but kept them to himself because he used this knowledge to solve corresponding problems for a fee solve. However, he had communicated this solution to Cardano in encrypted form. However, Cardano's solution was more general, it included all cubic equations (and the solutions of equations of the 4th degree , which he himself ascribed to his student Lodovico Ferrari ), cf. Cardan's formulas .

Nevertheless, he was accused of theft and perjury by Tartaglia, because Cardano had sworn never to publish this solution. Cardano no longer felt bound by the promise after learning about del Ferro's earlier solution. Tartaglia was then ordered by a Milan court to publicly retract his allegations.

Other mathematical works by Cardano deal with geometry ( cycloid , see also Cardanic circles ) and number theory.

In his work on proportions, published in 1570, he examined fast movements and in the course of this came to insights into the pulse rate , which he published scientifically for the first time with 4000 beats per hour (i.e. 67 per minute) in adults (for children with a high fever he took a heart rate five times faster).


Gerolamo Cardano: De subtilitate . Nuremberg 1550

Gerolamo Cardano's philosophical writings include, on the one hand, his Aristotle reception with his analysis of dialectics and, on the other hand, writings on natural philosophy and works on moral philosophy (ethics). In his philosophy of nature, he tried to grasp the world, heaven and earth, nature and the world of thought as a unified whole. He tried to achieve this by laying a single principle as a basis, the ensouled primordial matter. Leibniz later took up these thoughts with his monadology, where he specifically mentions Cardano's work. Other works deal with e.g. with a comparison of Christian, Jewish and Muslim religion. His major philosophical works are de Uno and de Natura . The rather encyclopedic work De Subtilitate , the first edition of which was printed in Nuremberg in 1550, was a great success with the public and was reprinted more than ten times in Nuremberg, Basel, Lyon and Paris within a few years. It was frequently reprinted long after Cardano's death in the 17th century and can be considered a standard philosophical work of the time.


Cardano was a doctor known throughout Europe. He did research on typhus , tuberculosis , asthma and venereal diseases. From him comes the first clinical description of typhus. He was the first to distinguish between syphilis and gonorrhea (gonorrhea) and described the principles of sanatoriums for the treatment of asthma and tuberculosis some 300 years before this type of treatment became established.

Numerous successful healings of patients who were considered incurable by contemporary physicians have been reported. His patients included many high ecclesiastical and civil dignitaries in Scotland, England, France and Italy, including the Archbishop of St Andrews (Scotland) and the Benedictine Prior in Milan. He was of the opinion that the administration of pharmaceuticals only makes sense after a thorough investigation of the patient and his illness. He used diets, physiotherapy and psychological care for treatment. He had to endure a lot of hostility because of his writing on "bad medical practice", in which he strongly criticized the usual practice of his colleagues.

technology and inventions

Cardano was the first to describe gimbals , invented before him . Later, the term cardan joint or cardan shaft was also used for the universal joint and the cardan shafts fitted with it , since Cardano designed a cardan shaft for a carriage for Emperor Charles V around 1548. Cardano was also the first to distinguish between static electricity and magnetism - in 1550. Another invention involves the encryption of messages using the Cardan grid , which is named after him . In the construction of high-speed letterpress presses at the beginning of the 19th century, the principle of Cardan circles was used.


  • The lunar crater Cardanus and the asteroid (11421) Cardano are named after him.
  • Gotthold Ephraim Lessing defended Cardano against accusations of atheism in one of his “Rescues” published in 1754.
  • The blockchain-based project Cardano with its own cryptocurrency ADA is named after him.

Fonts (selection)

Gerolamo Cardano has written over 230 books in various fields of knowledge, 138 of which have been printed.

Text editions and translations

  • Jean-Yves Boriaud (ed.): Girolamo Cardano: Somniorum Synesiorum libri quatuor. Les quatre livres des Songes de Synesios. 2 volumes. Olschki, Florenz 2008, ISBN 978-88-222-5736-9 (critical edition with French translation).
  • Marco Bracali (ed.): Girolamo Cardano: De sapientia libri quinque. Olschki, Florence 2008, ISBN 978-88-222-5753-6 (critical edition).
  • August Buck (ed.): Hieronymus Cardanus: Opera Omnia. Facsimile reprint of the Lyon 1663 edition . 10 volumes. Frommann-Holzboog, Stuttgart-Bad Cannstatt 1966, ISBN 978-3-7728-0094-8 .
  • Hermann Hefele (translator): Girolamo Cardano of Milan's own biography. Eugen Diederichs, Jena 1914, digitized (with detailed introduction).
    • New editions: Kösel, Munich 1969 and Chiron, Tübingen 2014.
  • The great art or the rules of algebra. English translation of the 1545 edition with additions to the 1570 and 1663 editions, Cambridge (Mass.) 1968.
  • Nikolaus Eberl (ed.): Cardano's Encomium Neronis. Peter Lang, Frankfurt am Main 1994, ISBN 3-631-46116-X (critical edition with translation and commentary).
  • The book on games of chance (Liber de ludo aleae) , Holt, Rinehart and Winston 1961 (Foreword Samuel S. Wilks).
  • John M. Forrester (ed.): The 'De Subtilitateʼ of Girolamo Cardano. 2 vols. ACMRS, Tempe 2013 (bilingual Latin-English edition with commentary).


  • Moritz Cantor : Hieronymus Cardanus. A scientific portrait of life from the 16th century. In: New Heidelberg yearbooks. Volume 13, 1905, pp. 131–143, digitized .
  • Øystein Ore : Cardano, the gambling scholar. With a Translation from the Latin of Cardano's Book on Games of Chance by Sydney Henry Gould. Princeton University Press, Princeton, NJ 1953.
  • Mario Gliozzi: In: Charles Coulston Gillispie (ed.): Volume 3: Pierre Cabanis - Heinrich von Dechen. Charles Scribner's Sons, New York 1971, pp. 64–67.
  • Giuliano Gliozzi: Cardano, Gerolamo. In: Alberto M. Ghisalberti (ed.): Dizionario Biografico degli Italiani (DBI). Volume 19: Cappi-Cardona. Istituto della Enciclopedia Italiana, Rome 1976.
  • Markus Fierz : Girolamo Cardano. (1501-1576). Physician, natural philosopher, mathematician, astronomer and interpreter of dreams (= Poly. Volume 4). Birkhäuser, Basel et al. 1977, ISBN 3-7643-0892-3 .
  • Eckhard Kessler (ed.): Girolamo Cardano. Philosopher, natural scientist, doctor (= Wolfenbüttel treatises on Renaissance research. Volume 15). Harrassowitz, Wiesbaden 1994, ISBN 3-447-03599-4 .
  • Hans Peter Balmer : Philosophy of human things. European moralism. Francke, Bern/Munich 1981, pp. 53–57.
  • Anthony Grafton : Cardano's Cosmos. The Worlds and Works of a Renaissance Astrologer. Berlin-Verlag, Berlin 1999, ISBN 3-8270-0168-4 .
  • Ingo Schütze: The natural philosophy in Girolamo Cardano's De subtilitate. Fink, Munich 2000, ISBN 3-7705-3474-3 .
  • Thomas Soren Hoffmann : Philosophy in Italy. An Introduction to 20 Portraits. marixverlag, Wiesbaden 2007, ISBN 978-3-86539-127-8 .
  • Rudolf Bock: Vacuum - Electricity - Gases. 2300 years of philosophy and research. Principal Verlag, Munster 2011, ISBN 978-3-89969-093-4 .
  • Andreas Lerch: Scientia astrologiae. The discourse on the scientific nature of astrology and the Latin textbooks 1470–1610. AVA, Leipzig 2015, ISBN 978-3-944913-48-3 .
  • Sara Confalonieri: The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations: Gerolamo Cardano's De Regula Aliza. Springer, Wiesbaden 2015, ISBN 9783658092740 .

web links

Commons : Gerolamo Cardano  - Collection of images, videos and audio files


  1. De propria vita liber . Jacques Villery, Paris 1643; Hermann Hefele (translator): Girolamo Cardano of Milan's own biography. Jena 1914 (new editions Kösel, Munich 1969 and Chiron, Tübingen 2014).
  2. Cf. also Barbara I. Tshisuaka: Cardano, Geronimo. In: Werner E. Gerabek , Bernhard D. Haage, Gundolf Keil , Wolfgang Wegner (eds.): Encyclopedia of Medical History. De Gruyter, Berlin/ New York 2005, ISBN 3-11-015714-4 , p. 230.
  3. Peter Bietenholz: The Italian humanism and the heyday of book printing in Basel (= Basel contributions to historical science. Volume 73). Helbing & Lichtenhahn, Basel 1959, pp. 140–142, 152, 154 and 157; Frank Hieronymus: 1488 Petri - Schwabe 1988. Second half volume. Schwabe, Basel 1997, ISBN 3-7965-1000-0 , pp. 1014-1057, no. 348-368.
  4. Gerolamo Cardano: De rerum varietate . Heinrich Petri, Basel 1557, p. 995 .
  5. Hermann Hefele (translator): Des Girolamo Cardano of Milan's own biography. Jena 1914, especially pp. 37-42.
  6. Hermann Hefele (translator): Des Girolamo Cardano of Milan's own biography. Jena 1914, p. 164.
  7. Giuliano Gliozzi: Cardano, Gerolamo. In: Alberto M. Ghisalberti (ed.): Dizionario Biografico degli Italiani (DBI). Volume 19: Cappi-Cardona. Istituto della Enciclopedia Italiana, Rome 1976, p. 761.
  8. ^ Cf. Wolf-Dieter Müller-Jahncke : On the concept of magic in Renaissance medicine and pharmacy. In: Rudolf Schmitz , Gundolf Keil (eds.): Humanism and Medicine. Acta humaniora, Weinheim 1984 (= German Research Foundation: Communications from the Commission for Humanism Research. Volume 11), ISBN 3-527-17011-1 , pp. 99-116, here: p. 106.
  9. Gottfried Wilhelm Leibnitz: The Theodicy . Translated and explained by Julius H. von Kirchmann. Koschny, Leipzig 1879, § 254, digital .
  10. Opus novum the proportionibus numerorum [...]. 1570, pp. 50 and 249.
  11. Werner Friedrich Kümmel : The pulse and the problem of measuring time in the history of medicine. In: Medical History Journal. Volume 9, 1974, pp. 1–22, here: p. 5.
  12. In De subtilitate (1550), Cardano discusses the differences in the attractive effects of lodestone and (frictionally charged) amber , cf. Wayne M. Saslow, Electricity, magnetism, and light (Academic Press, 2002), p.