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Gerolamo Cardano-was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world.He was born in Pavia, Lombardy, the illegitimate child of Fazio Cardano, a mathematically gifted jurist, lawyer, a close personal 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 was "taken by violent means from my mother; I was almost dead."He graduated in medicine in 1526 and was famous for treating The PopeCardano was the first mathematician to make systematic use of numbers less than zero.He published with attribution the solution of Scipione del Ferro to the cubic equation and the solution of his student Lodovico Ferrari to the quartic equation in his 1545 book Ars Magna. The solution to one particular case of the cubic equation [math]{\displaystyle ax^{3}+bx+c=0}[/math] (in modern notation), had been communicated to him by Niccolò Fontana Tartaglia (who later claimed that Cardano had sworn not to reveal it, and engaged Cardano in a decade-long dispute) in the form of a poem, but Ferro's solution predated Fontana's. 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. In Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem. He was credited for inventing number locks.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 around 1564, but not published until 1663, contains the first systematic treatment of probability, as well as a section on effective cheating methods. He used the game of throwing dice to understand the basic concepts of probability. He demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes (which implies that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes). He was also aware of the multiplication rule for independent events but was not certain about what values should be multiplied.Cardano had two sons—Giovanni and Aldo Battista—both of whom came to ignoble ends. Giovanni Battista, Cardano's eldest and favorite son, was tried and beheaded in 1560 for poisoning his wife, after he discovered that their three children were not his. Aldo Battista was a gambler, who stole money from his father and was disinherited by him in 1569. His daughter was a prostitute.