Scientists



CARDANO
Gerolamo Cardano (1501 – 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler. He wrote more than 200 works
on medicine, mathematics, physics, philosophy, religion, and music. Cardano's gambling led him to formulate elementary rules in probability,
making him one of the founders of the field.
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 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.
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. 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.
Today, he is best known for his achievements in algebra. 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. The solution to one particular case of the cubic
equation ax^{3} + bx^{2} + c = 0 (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 decadelong 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
(described for the first time by his Italian contemporary Rafael Bombelli, although 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. 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 highspeed 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 assigned to Cardano the credit for the invention of the socalled Cardano's Rings, also called Chinese Rings, but it is very
probable that they are more ancient than Cardano.
Significantly, in the history of education of the deaf, 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 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. It appears that he was still practicing medicine up to his death in 1576.
