# Girolamo Cardano- Man Behind Complex Numbers.

## Who are re talking about?

**Girolamo Cardano**, Girolamo is also spelt **Gerolamo**, English **Jerome Cardan**, was born on September 24, 1501, at Pavia, in Duchy of Milan [Italy] and he died on September 21, 1576, at Rome. He is an Italian astrologer, physician, and mathematician who gave the first clinical description for typhus fever and his book *Ars Magna* (The great art; or, The Rules of Algebra) is one of the keystones in the history of algebra.

He was educated at the universities of Pavia and Padua, Cardano and received a medical degree in 1526. In the year 1534, he moved to Milan, where he lived in high poverty until he became a lecturer in mathematics. He was admitted to the college of the physicians in 1539, and he soon became rector. His fame as a physician grew exponentially, and many of Europe’s crowned heads solicited his services; however, he valued his independence too much only to become a court physician. In 1543 he accepted a professorship in medicine in Pavia.

## His Remarkable Inventions

Cardano’s popularity rests on the contributions he made in mathematics. As early as the *Practica arithmetic*, which is devoted to numerical calculation, he revealed very uncommon mathematical abilities in the explanation of many original methods of mnemonic calculation and in the confidence with which he altered algebraic equations and expressions. We should keep in mind that he could not use modern explanation because present-day algebra was still verbal. His proficiency in calculation also aided him to solve equations above the second degree, which modern-day algebra was unable to do. For instance, taking the equation that in modern expression is written 6*x*3 – 4*x*2 = 34*x* + 24, he added 6*x*3 + 20*x*2 to each number and obtained, other transformations, like-

4×2(3x + 4) = (2×2 + 4x + 6)(3x + 4),

divided both numbers by 3x + 4, and from the resulting second-degree equation obtained the solution x = 3.

## His Inventions In Mathematics

His vital work, was the *Ars Magna*, in which many new ideas in algebra were well orderly presented. Among them are the rules, today called “Cardano’s rule,” for solving reduced third-degree equations (i.e., they lack the second-degree term); the linear transformations that eliminate the second-degree term in a complete cubic equation (which Tartaglia did not know how to solve); the observation that an equation of a degree higher than the first admits more than a single root; the lowering of the degree of an equation when one of its origins is known; and the solution, applied to many problems, of the quartic equation, attributed by Cardano. Other Notable events were Cardano’s research into approximate solutions of a numerical equation by the method of proportional parts and the observation that, with repeated operations, one could obtain roots always closer to the true ones. Before Cardano, only the solution of an equation was working. Cardano, however, also noted the relations between the roots and the coefficients of the equation and between the sequence of the signs of the terms and the signs of the sources; thus he is indeed considered as the originator of the theory of algebraic equations. In some of the cases he used imaginary numbers, overcoming the reluctance of present-day mathematicians to use them, it was only in the year 1570, in a new edition of the *Ars Magna*, that he added a section named “De aliza regula” (the meaning of *aliza* is unknown; some say it means “difficult”), dedicated to the “irreducible case” of the cubic equation, in which Cardano’s rule is extended to imaginary numbers. According to the fundamental theorem of algebra, all polynomial equations with real or complex coefficients within a single variable have a solution in complex numbers. In contrast, some of the polynomial equations with real coefficients have no solution in real numbers. Girolamo Cardano is credited with introducing complex numbers in his attempts to find solutions to cubic equations.

His inventions are remarkable, and without it, we would not be able to solve complex equations. We need to be thankful for his inventions.

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