RAFAEL Bombelli (also written Raffaele Bombelli) was born in Bologna in 1526 and died there in 1573. He is known exclusively for the treaty “Algebra”. Almost nothing is known of his life, except the little information that he provides in the introduction to his work showing that he was an engineer and worked for Alexander Rufini, bishop of Melfi, to drain the marshes of the Val di Chiana in Tuscany. He wrote the first draft of his book on algebra when there was an interruption to the work in the valley in 1560 and it was printed without the last part only in 1572, a year before his death. The last part, remained unpublished until 1929, when it was discovered and published by the historian of mathematics E. Bortolotti.
His father, Antonio Mazzoli, returned to live in Bologna, after the confiscated family property was returned to the Mazzoli family. There he carried on his trade as a wool merchant and married Diamante Scudieri, a tailor's daughter. Then he changed his name from Mazzoli to Bombelli.
Rafael was the first of six brothers. In his training he witnessed the mathematical issues discussed at that time. He read the works of Girolamo Cardano and followed the dispute between Niccolò Tartaglia and a student of Scipione Dal Ferro - Antonio Maria Fior – about the the solution of cubic and quartic equations. A little later Ludovico Ferrari discovered the formula for the solution of the quartic equations.
He also studied architecture and engineering under the guidance of Pier Francesco Clementi, training in this activity with the patronage of Alexander Rufini, a Roman nobleman who later became bishop of Melfi. Between 1551 and 1556 he worked for his patron to draw the boundaries of the territories that he reclaimed in the Val di Chiana.
He worked on this project until 1555 when there was an interruption to the reclamation work. While Bombelli was waiting for the Val di Chiana project to recommence, he decided to write an algebra book. He had felt that the reason for the many arguments between leading mathematicians was the lack of a careful exposition of the subject.
In 1560, when work at Val di Chiana recommenced, Bombelli had not completed his algebra book, but he gained a high reputation as a hydraulic engineer. In 1561 Bombelli went to Rome but failed in an attempt to repair the Santa Maria bridge over the Tiber. However, he was taken on as a consultant for a project to drain the Pontine Marshes, but his project came to nothing.
In Rome he was shown the manuscript of "Arithmetica" by Diophantus. Bombelli decided to make a translation along with Antonio Maria Pazzi. Although the work was never completed, the material was used in the review of his book on algebra. The work had to be in five volumes: the first three were published in 1572 with the full title of "L'Algebra, opera di Rafael Bombelli da Bologna, diuisa in tre libri con la quale ciascuno da sé potrà venire in perfetta cognitione della teoria dell'Aritmetica", while the fourth and fifth, on geometry, remained in manuscripts, due to Bombelli’s premature death. The manuscripts, discovered in 1923, were printed only in 1929.