**Rafael Bombelli** was an Italian algebraist who was born in January 1526 in Bologna (Italy) and died in 1572, probably in Rome, Italy. Perhaps he was the most important mathematician in Italy, pioneering the study of imaginary numbers. His main five-volume publication on algebra (Algebra) was not published until the year following his death (1573).

He was the eldest of Antonio Mazzoli's six children, whose family had come to Bologna in the previous century (1443). With control of the city taken from Giovanni II Bentivoglio by Pope Julius II (1506), his father became involved in an attempt to regain power by the former rulers. But they were defeated, their family was exiled, and all their possessions were confiscated. After several years of exile the Mazzoli were pardoned and Antonio Mazzoli could return to Bologna, reclaim his family property and become a successful wool merchant.

Although uneducated, he changed his name to Bombelli in an attempt to disguise his offspring and, after several minor activities, went to work for a Roman nobleman, Alessandro Rufini, future bishop of Melfi. During this period he became interested in mathematics and became involved in the pertussis of the time, which was the solution of cubics and quartics, involving del Ferro, Fior, Tartaglia, Cardano and Ferrari, ending with the meeting between Ferrari and Tartaglia in Milan (1548). ). He studied mathematics with Professor Pier Francesco Clementi (1548), and when his boss acquired the rights to the Val di Chiana region (1549), which now belonged to the Papal States, he was commissioned to demarcate the borders (1551-1555). , when he had to interrupt his services because of a complaint from the border neighbors.

It was during this period, while awaiting the resumption of demarcations, that he decided to write his famous algebra book, starting from Cardano's studies. He began writing it when work at Val di Chiana was still suspended (1557). When work resumed (1560) the book was still being written. After a visit to the University of Rome professor Antonio Maria Pazzi, he showed him a manuscript of Diophantus, Arithmetic, which delighted him and they decided to make a translation.

But in his book III, although 143 of the 272 existing problems were based on Diophantus' writings, he did not give due credit to the great Greek mathematician. Unfortunately, he probably died in Rome before completing books IV and V. Researcher Bortolotti found his manuscripts in a library in Bologna (1923) and republished his five books (1929), a fundamental contribution to the study of complex numbers. In his algebra he wrote, for example:

MORE times MORE equals MORE;

LESS times LESS equals MORE;

More often LESS equals LESS;

LESS times MORE equals LESS;

+ SQUARE ROOT OF -n. + SQUARE ROOT of -n = - n;

+ SQUARE ROOT OF -n. - SQUARE ROOT of -n = + n;

- SQUARE ROOT OF -n. + SQUARE ROOT of -n = + n;

- SQUARE ROOT OF -n. - SQUARE ROOT OF -n = - n.

Examples of notations employed by Bombelli:

In his work, he described the addition, subtraction and multiplication of complex numbers and provided the correct solution of the cubics using the Cardano-Tartaglia formula whenever situations with square roots of negative numbers occurred. Another admirable contribution was the notation employing symbols in their mathematical expressions.

Source: Photo and information taken from* MacTutor History of Mathematics archive**(//www-history.mcs.st-andrews.ac.uk)*.