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Cardano, Gerolamo

Category: Genius

Gerolamo (or Girolamo, or Geronimo) Cardano (24 September 1501 – 21 September 1576) was an Italian Renaissance mathematician, astrologer and philosopher. He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music.  Cardano was always 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 around 1564, contains the first systematic treatment of probability, as well as a section on cheating methods.

Cardano also 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 and in 1553 he cured the Scottish Archbishop of St Andrews of a disease that had left him speechless and was thought incurable. The diplomat Thomas Randolph recorded the "merry tales" rumoured about his methods still current in Edinburgh nine years later. Cardano himself wrote that the Archbishop had been short of breath for ten years, and after the cure was effected by his assistant, he was paid 1,400 gold crowns.  Much of Cardano’s skill appears to have been as a natural healer.  He appears to have used a form of hypnotherapy.

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 ended. In 1525, Cardano repeatedly applied to the College of Physicians in Milan, but was not admitted owing to his combative reputation and illegitimate birth.

He tends to be known today within the science community as a mathematician.  Cardano was the first mathematician to make systematic use of numbers less than zero.  He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna.  Some of the discoveries he made appear to have been achieved by visionary experience. 

For example, the solution to one particular cubic equation, was ‘communicated to him’ in the form of a poem.  Niccolò Fontana Tartaglia later claimed that Cardano had somehow obtained it from him and engaged Cardano in a decade-long fight.  Cardano also described the existence of what are now called imaginary numbers, but admitted he did not understand their properties.  The necessary mathematical theory of fields was not to be developed for hundreds of years. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem.

Cardano also invented several mechanical devices including the combination lock, and the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely.

He invented 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 published two encyclopaedias of natural science which contain a wide variety of inventions, facts, and occult facts. He also introduced the Cardan grille, a cryptographic tool, in 1550.

Significantly, 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.

In his book De Subtilitate 1552 Cardano proposed that petrified shells, “clearly indicated the former sojourn of the sea upon the mountains.”  Remember that this is the 1500s.

Cardano had a very rough private life.  His eldest and favourite 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.  And Cardano himself was accused of heresy in 1570 because he had computed and published the horoscope of Jesus in 1554. 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. It appears that he was still practicing medicine up to his death. The date of his death is disputed, but a death year is given as 1576.

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