### Conclusions

The theory of determinants was a revolutionary discovery for mathematicians, enabling them to obtain even more mathematical results more easily. On the European continent, this theory advanced most rapidly in France and Germany. Between language differences and political upheaval, Italian mathematicians were generally slow to learn of advances such as those in the theory of determinants. The mathematicians of the Kingdom of Two Sicilies would remain largely ignorant of the theory of determinants until Brioschi published these ideas in Italian towards the middle of the nineteenth century. In addition to the geographic isolation of the kingdom, there was a schism between synthetic and analytic mathematical branches that reflected the intellectual and political divides between traditional Bourbon and revolutionary rulers. When the traditional side was in power, traditional, synthetic mathematics dominated the university, colleges, and other advanced schools. This tended to hinder the spread of algebraic theory, like that of determinants, among mathematical scholars of the Kingdom of the Two Sicilies. Even though Raffaele Rubini did not play a crucial role for mathematics in general, he helped kept the analytic branch of mathematics alive in the kingdom. His article on determinants enabled Italian mathematicians to learn of contributions to the theory of determinants by different analytical mathematicians. Although Rubini's article claims to present no original material on the theory of determinants, it is valuable to look at his work, not only due to this intellectual schism, but also because this article can be used by mathematics educators.

It is important to have a full sense of a mathematician's historical background before deciding whether or not an article of his or hers is valuable to read, especially in cases like this where the author very candidly declares that it does not provide any new ideas about the topic at hand. The historical events occurring in a mathematician's life can be very consequential in determining the mathematics he or she publishes, as well as how he or she presents the material to the reader. It would be interesting to examine other works published by Italian mathematicians who lived in the Kingdom of Two Sicilies during this time period to see how they presented the material according to the synthetic and analytic branches of mathematics, and taking into consideration who was ruling the kingdom at the time that the articles were published.

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

### Acknowledgments

We are extremely grateful to Associate Dean Briziarelli for her assistance in the translation of the article, as well as to Professor Rosaria for a primary source providing additional biographical information about Rubini. We would also like to thank Professor R. Bradley, Professor E. De Freitas, and Professor L. Stemkoski for their helpful suggestions on this paper. All five are professors at Adelphi University.

The authors are also extremely grateful to the referees for their many helpful suggestions and corrections. In addition, the authors express deep gratitude to Janet Beery, Editor of *Convergence*, for graciously dedicating so much of her time in making additional suggestions for this paper.

### About the Authors

Salvatore J. Petrilli, Jr., Ed.D., is an Associate Professor of Mathematics and Department Chair at Adelphi University. He has a B.S. in mathematics from Adelphi University and an M.A. in mathematics from Hofstra University. He received an Ed.D. in mathematics education from Teachers College, Columbia University, where his advisor was J. Philip Smith. His general research interests include history of mathematics, mathematics education, and applied statistics. However, the majority of his research has been devoted to the life and mathematical contributions of François-Joseph Servois.

Nicole Smolenski is pursuing a graduate certificate in International Education from Florence University of the Arts. She will next be pursuing her JD and MA in Public Policy to become an Educational Policy lawyer. She taught for the past three years as a middle school mathematics teacher in the New York City public schools and taught an Italian elective for a year. She has a B.S. in Mathematics from Adelphi University and earned her M.A. in Mathematics Education at Teachers College, Columbia University. Her research interests are in Mathematics Education and its history.