Girolamo Cardano Girolamo Cardan or Cardano was an Italian doctor and mathematician who is famed for his work Ars Magna which was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learnt from Tartaglia.

Girolamo or Hieronimo Cardano's name was Hieronymus Cardanus in Latin and he is sometimes known by the English version of his name Jerome Cardan. Girolamo Cardano was the illegitimate child of Fazio Cardano and Chiara Micheria. His father was a lawyer in Milan but his expertise in mathematics was such that he was consulted by Leonardo da Vinci on questions of geometry. In addition to his law practice, Fazio lectured on geometry, both at the University of Pavia and, for a longer spell, at the Piatti foundation in Milan.

He was a brilliant student but, outspoken and highly critical, Cardan was not well liked. Cardan squandered the small bequest from his father and turned to gambling to boost his finances. Card games, dice and chess were the methods he used to make a living. Cardan's understanding of probability meant he had an advantage over his opponents and, in general, he won more than he lost. He had to keep dubious company for his gambling. Once, when he thought he was being cheated at cards, Cardan, who always carried a knife, slashed the face of his opponent. Gambling became an addiction that was to last many years and rob Cardan of valuable time, money and reputation.probability Cardan was awarded his doctorate in medicine in 1525 and applied to join the College of Physicians in Milan, where his mother still lived. The College did not wish to admit him for, despite the respect he had gained as an exceptional student, he had a reputation as a difficult man, whose unconventional, uncompromising opinions were aggressively put forward with little tact or thought for the consequences. The discovery of Cardan's illegitimate birth gave the College a reason to reject his application.

Today, he is best known for his achievements in algebra.algebra It is to Cardan's credit that, although one could not expect him to understand complex numbers, he does present the first calculation with complex numbers in Ars Magna. Solving a particular cubic equation, he writes:- Dismissing mental tortures, and multiplying 5 + √ (- 15) by 5 - √(-15), we obtain 25 - (-15). Therefore the product is and thus far does arithmetical subtlety go, of which this, the extreme, is, as I have said, so subtle that it is useless.

Here, in modern notation, is Cardan's solution of x 3 + mx = n.Cardan Notice that (a - b) 3 + 3ab(a - b) = a 3 - b 3 so if a and b satisfy 3ab = m and a 3 - b 3 = n then a - b is a solution of x 3 + mx = n. But now b = m/(3a) so a 3 - m 3 /(27a 3 ) = n, i.e. a 6 - na 3 - m 3 /27 = 0. This is a quadratic equation in a 3, so solve for a 3 using the usual formula for a quadratic. Now a is found by taking cube roots and b can be found in a similar way (or using b=m/(3a)). Then x = a - b is the solution to the cubic.

The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra states Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

The Fundamental Theorem of Algebra Cardan was the first to realise that one could work with quantities more general than the real numbers. This discovery was made in the course of studying a formula which gave the roots of a cubic equation. The formula when applied to the equationCardan x 3 = 15x + 4 gave an answer involving √(-121) yet Cardan knew that the equation had x = 4 as a solution. He was able to manipulate with his 'complex numbers' to obtain the right answer yet he in no way understood his own mathematics.Cardan

In addition to Cardan's major contributions to algebra he also made important contributions to probability, hydrodynamics, mechanics and geology. His book Liber de Ludo Aleae was published in 1663 but the book on games of chance was probably completed by Cardan makes the first ever foray into the, until then untouched, realm of probability theory. It is the first study of things such as dice rolling, based on the premise that there are fundamental scientific principles governing the likelihood of achieving the elusive 'double six', outside of mere luck or chance. Cardan is also credited with the invention of the Cardan joint a type of universal joint in a shaft that enables it to rotate when out of alignment.

Tartaglia gave Cardano his rule in a poem he had written. When the cube and things together Are equal to some discrete number, Find two other numbers differing in this one. Then you will keep this as a habit That their product should always be equal Exactly to the cube of a third of the things. The remainder then as a general rule Of their cube roots subtracted Will be equal to your principal thing In the second of these acts, When the cube remains alone, You will observe these other agreements: You will at once divide the number into two parts So that the one times the other produces clearly The cube of the third of the things exactly. Then of these two parts, as a habitual rule, You will take the cube roots added together, And this sum will be your thought. The third of these calculations of ours Is solved with the second if you take good care, As in their nature they are almost matched. These things I found, and not with sluggish steps, In the year one thousand five hundred, four and thirty. With foundations strong and sturdy In the city girdled by the sea.

Cardan: Autobiography Girolamo Cardano’s little book De propria vita will outlive and eclipse his fame in philosophy and natural science... Cardano is a physician who feels his own pulse, and describes his own physical, moral and intellectual nature, together with all the conditions under which it had developed, and this, to the best of his ability, honestly and sincerely.

De propria vita He desires to spare neither himself nor others, and begins the narrative of his career with the statement that his mother tried, and failed, to procure abortion. It is worth remark that he attributes to the stars which presided over his birth only the events of his life and his intellectual gifts, but not his moral qualities; he confesses that the astrological prediction that he would not live to the age of forty or fifty years did him much harm in his youth. But there is no need to quote from so well-known and accessible a book; whoever opens it will not lay it down till the last page.

De propria vita Cardano admits that he cheated at play, that he was vindictive, incapable of all compunction, purposely cruel in his speech. He confesses it without impudence and without feigned contrition, without even wishing to make himself an object of interest, but with the same simple and sincere love of fact which guided him in his scientific researches. And, what is to us the most repulsive of all, the old man, after the most shocking experiences and with his confidence in his fellow-men gone, finds himself after all tolerably happy and comfortable. He has still left him a grandson, immense learning, the fame of his works, money, rank and credit, powerful friends, the knowledge of many secrets, and, best of all, belief in God. After this he counts the teeth in his head and finds that he has fifteen.

He died on the day he had (supposedly) astrologically predicted earlier; some suspect he may have committed suicide. astrologically

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