Archimedes’ Sand-Reckoner presents a system for naming extraordinarily large numbers, larger than the number of grains of sand that would fill the cosmos. Curiously, Archimedes addresses the treatise not to another specialist but to King Gelon II of Syracuse. While the treatise has thus been seen as evidence for the dynamics of patronage, difficulties in both Archimedes’ treatment of Gelon and his discussion of astronomical models make it fit incongruously within contemporary court and scientific contexts. This article offers a new (...) reading of the Sand-Reckoner based on a reconsideration of the relationship between author and addressee: deferring assumptions about the historicity of that relationship, it analyzes Gelon’s role in the treatise with respect to both the stylistic features of Archimedes’ prose and a broader tradition of narratives about a variety of cultural actors who engage with kings, speaking not so much truth as wit to power. Such a reading resolves the social and scientific difficulties of the treatise, and develops the literary-experimental qualities of Hellenistic science. In turn, the article proposes a revised approach, sensitive to broader patterns of authorship, to understanding ancient scientific authors’ relationship to royal authority. It concludes, finally, that the royal patronage seemingly exemplified by the Sand-Reckoner had greater significance as a cultural trope than as a social institution. (shrink)

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...) to highlight a potential danger of intellectual enculturation. (shrink)

Ancient medical practitioners discussed and debated whether previously unknown kinds of disease had been discovered and whether new diseases could come into existence. The debate over new diseases was of fundamental importance in defining the medical sects which came to dominate elite medicine from the Hellenistic period. This paper offers an overview of the most significant Greek and Roman sources for the debate over new diseases and an account of the origins and significance of this debate.

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...) conceived by ancient Greek mathematicians. (shrink)