Complex Numbers: Rafael Bombelli's Life And Work

Complex numbers were first encountered by the ancient Greeks and the ancient Egyptians through their applications of architecture. When dealing with a negative square root in the calculation of the volume of a square pyramid, the famous mathematician Heron changed a negative 63 to a positive 63. Diophantus discarded all negative solutions to his quadratic equations. It was not until Descartes that imaginary numbers were given their name. Imaginary numbers gave mathematicians a way to deal with the square root of negative numbers, but at the time they had no way of operating on the numbers algebraically. It was not until the 16th century that mathematicians began to consider the function of i and the algebra surrounding it. The first mathematicians

His father was a merchant by profession, born to an aristocratic family. Although Bombelli never received a formal university education, he was mentored by a man who was both an architect and an engineer. Bombelli himself would late become an engineer and work with and for his mentor on a variety of projects for the papal government. In between his engineering projects, Bombelli became interested in the algebraic questions of his day and began to work on writing about his own findings and interpretations of the questions and concepts being explored. He would eventually publish three volumes of a work entitled Algebra. The last two volumes would not be completed before his

Although mathematicians centuries before had been getting negative numbers for answers, they had simply disregarded them. To them, negative numbers were non-numbers because they could not practically be used in the physical world. It is not possible to build a pyramid with negative height. Bombellli, however, described the algebra of negative numbers explicitly in Algebra. He was the first person to write the rules of negative numbers down in text. Bombelli's goal was to write a text encompassing everything which was known in his day and everything which he had also found to be true. Unfortunately, Bombelli was not able to finish the work before his death