Selected Mathematical Paradoxes In The Scientific Works Of Joseph Solomon Delmedigo.

The purpose of this study is to explore and examine a portion of the mathematical writings of Joseph Solomon Delmedigo, an early seventeenth century physician, philosopher, astronomer and mathematician. He is of historical and mathematical interest, since he was one of the first in the Jewish world to attempt to integrate the new scientific knowledge into the religious aspects of Jewish life and culture, and to advocate the dissemination of these new ideas among his people.

The mathematical portions of his seminal work, Elim, which was written entirely in Hebrew, are translated and analyzed, focusing on the fifth book of this work, Ma'ayan Hatum, wherein Delmedigo responds to seventy mathematical paradoxes posed to him by his pupil, Zerah ben Natan.

The body of this dissertation consists of a detailed inquiry into Delmedigo's work, along with a discourse upon the historical significance of each of the mathematical paradoxes which he undertook to treat. Also included herein are analyses of the relationships of his work to the works of his contemporaries and predecessors, including Galileo, Regiomontanus, Vieta, Cardan, Van Ceulen, Isaac Israeli, Abraham Ibn Ezra, Maimonides and others. Errors extant in the text and diagrams, and all Biblical and Talmudic references are duly noted and commented upon. Also contained herein, is a glossary of scientific and mathematical terminology which was encountered in the reading of Elim, and a small section on Delmedigo's philosophy of education.

It may be concluded from this work that Delmedigo was a significant mathematical scholar of his time, but did not make important original contributions. It appears that he considered his role as that of an educator and disseminator, rather than that of an innovator. Although his mathematics was generally lacking in originality and novelty, the paradoxes he presented and his approach to their solution, merit scholarly attention.