Gerolamo Cardano

Lore & Background

Cardano was born on 24 September 1501 in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted jurist, lawyer, and close friend of Leonardo da Vinci. In his autobiography, Cardano wrote that his mother, Chiara Micheri, had taken 'various abortive medicines' to terminate the pregnancy; he said: 'I was taken by violent means from my mother; I was almost dead.' She was in labour for three days. 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. After a depressing childhood, with frequent illnesses, and the rough upbringing by his overbearing father, in 1520, Cardano entered the University of Pavia. During the Italian War of 1521–1526, however, the authorities in Pavia were forced to close the university in 1524. Cardano resumed his studies at the University of Padua, where he graduated with a doctorate in medicine in 1525. His eccentric and confrontational style did not earn him many friends, and he had a difficult time finding work after he completed his studies. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth. However, he was consulted by many members of the College of Physicians, because of his irrefutable intelligence.

Reader's Guide

Cardano's significance lies in his foundational work in algebra and probability. In his 1545 book Ars Magna he made the first systematic use of negative numbers in Europe, published (with attribution) the solutions of other mathematicians for cubic and quartic equations, and acknowledged the existence of imaginary numbers. He introduced the binomial coefficients and the binomial theorem in Opus novum de proportionibus. His book Liber de ludo aleae, written around 1564 but not published until 1663, contains the first systematic treatment of probability, as well as a section on effective cheating methods. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes. He was also aware of the multiplication rule for independent events. Cardano partially invented and described 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 made significant contributions to hypocycloids, published in De proportionibus in 1570. The generating circles of these hypocycloids, later named 'Cardano circles' or 'cardanic circles', were used for the construction of the first high-speed printing presses. In his mid-16th-century work De Subtilitate, Cardano drew attention to the physical properties of steam, specifically the process of condensation as a means of creating a vacuum. In historiography, these observations are interpreted as a milestone in the renewed interest in steam power.

Did You Know?

• Cardano wrote that his mother took 'various abortive medicines' to terminate the pregnancy, and he said: 'I was taken by violent means from my mother; I was almost dead.'
• He was the first European mathematician to make systematic use of negative numbers.
• His book Liber de ludo aleae, written around 1564, contains the first systematic treatment of probability and a section on effective cheating methods.
• Cardano's observations on steam condensation in De Subtilitate are considered a milestone in the renewed interest in steam power.
• He stated that deaf people were capable of using their minds and 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.