Analysis and Translation of Raffaele Rubini's 1857 'Application of the Theory of Determinants: Note'

Overview

Scholars in the Kingdom of Two Sicilies, which united the island Kingdom of Sicily and the mainland Kingdom of Naples (the southernmost regions in modern-day Italy) from 1815 to 1860, were exposed to some of the works of French mathematicians after translations of these works were completed. However, until Francesco Brioschi (1824-1897) published his works of algebraic theory, beginning in 1854 with his Teoria dei determinanti (Theory of Determinants) [O'Connor and Robertson, 2006], these scholars had limited knowledge of algebra, specifically determinants. Their ignorance was due not only to the kingdom's geographic isolation, but also to an academic schism between two branches of mathematical thought, synthetic and analytic. This schism had consequences for several Italian mathematicians, including Raffaele Rubini (1817-1890), and led Rubini to publish his 1857 article, “Application of the Theory of Determinants: Note." The present article provides the first English translation of Rubini's article on determinants, along with some biographical information on this obscure mathematician. The analysis of Rubini's work will examine his purpose in publishing it and the ways in which he achieved his aims. Finally, we suggest how this article might be incorporated into a high school mathematics curriculum that follows the Common Core through the process of “Stealing Time."

Download the authors' English translation of Raffaele Rubini's article, "Application of the Theory of Determinants: Note."